Critical Thinking Basic Theory And Instructional Structures Of The Skin


Historically, the idea that language could shape thinking was considered erroneous and untestable (Bloom and Keil, 2001). However, with the input of a few decades of research in modern fields such as linguistic, sociology, psychology or anthropology, we have learned that people who speak different languages do indeed think differently and that even flukes of grammar can profoundly affect how we see the world (Levinson and Wilkins, 2006; Weiler, 2015). Thus language shapes our experiences of the world much like Piaget who considered children as entities able to build elaborated models of their environment by evolving from low to high-level conceptual prototypes (Inhelder, 1978). Vygotsky’s views add to the discussion, by pin pointing to when the integration of speech and thought culminates, around 2 years of age, where infants become able to transfer language to their internal thinking, making their cognitive process more rational (Vygotsky, 1978). Thus, we contend with many that thinking and learning are inseparable systems; and thinking is facilitated through language, which is fundamentally the most important concept for human learning (Halliday, 1993; Weiler, 2015). Chomsky (1956, 1975) suggests that thought and speech are largely separated and argues that, in humans, thought is depending on specific cognitive domains. Chomsky believed in the innateness of the language ability. He proposes that our ability to use language, operationalized in some brain specialized regions (akin to module or domain specific perspectives) (Inhelder, 1978; Cowie, 1997; Devitt, 2006), is based on our understanding of its mechanisms, which guides our speech and understanding of others’ speech (Inhelder, 1978). Thus the implication is that language should have measurable effects on learning.

We can infer, from a number of critical thinking models, that they all suspect language to have a role in thinking, however, it is rarely clearly outlined. Indeed, despite a tremendous amount of research conducted on language or critical thinking, the interplay between the two has received less empirical attention (Romano, 2007). For example, Bloom et al. (1956) developed a model to classify the various levels of thinking complexity, but absent from this model is the role of language at each or either of these stages. Yet, language has been found to have particular effect on memory, perception, problem-solving, and judgment which in essence confirms the language-thought relationship (Hardin and Banaji, 1993). Zlatev and Blomberg (2015) may have successfully revived the language-thought relation hypothesis (postulating that thought and thinking take place in a mental language) by arguing: (1) for the disentanglement of language and thought; (2) that language from culture and social interaction can be unraveled; and (3) that all forms of linguistic influences are possible.

Finally, among the major theories explaining development through the lenses of experience and the human biological blueprints, Vygotsky (1978) and Rogoff and Lave (1984) posit yet in addition, that no development could happen without the sociocultural fabric we are born into (rearing, society’s norms, language, traditions, etc.). Such views have been validated by the important cultural gaps observed between different ethnic groups within or across different continents. Thus, in the quest for best practices when it comes to conceptualize learning, the argument of this article also contends that the cultural fabric permeating through language must be taken into account and fundamentally understood, in any thinking/learning model, to be truly representative of the diversity of learners. Interestingly, culture does shape how we learned and it is also where implicit biases are formulated. Piaget (1976) note, “…everything suggests that, on discovering the values accepted in his immediate circle, the child felt bound to accept the circle’s opinions of all other national groups.” It is through the critical thinking processes that we must identify and overcome the impacts of stereotypes and biases. However, do culture-language dynamics take our critical thinking process hostage, especially in light of research that has shown its clear impacts on our judgment, analysis, and decision-making?

It is the goal of this essay to argue that language, a unique human communication system, is central to our experience, and appreciating its role in constructing our mental lives, brings us one step closer to understanding the very nature of human learning. We argue that we must fundamentally consider the fact that all theory of learning must have language as a tenet to be considered truly encompassing of the issue of learning. We will further in this essay explore connections between language and human curiosity, language as used in instruction, and the impact of culture within the dynamics of learning, language, and instruction. We seek to understand in what ways and to what degree language affects cognition, and how lacking or struggling with language development creates more or less impeding deficits for learning and thinking.

The Interplay of Language and Thinking in the Literature

Some scholars argue that specific word items in a given language influence how the mind splits reality into different categories, while others have proposed that the thoughts amalgamate into larger complexes through syntax (Bloom and Keil, 2001). The well-known Sapir-Whorf hypothesis (Whorf, 1956; Kay and Kempton, 1984) states that the structure of language determines and greatly influences the modes of thought and behavior characteristics of the cultures in which it is spoken. This hypothesis also suggests that certain thoughts in one language cannot be understood by speakers of another language.

For example, Russian speakers are better than English speakers at distinguishing colors, while Japanese speakers tend to group objects by material rather than shape unlike any other groups (Weiler, 2015). This shapes how people from different cultures orient themselves in space or influences how they process color. The Aboriginal community defines space relative to the observer, which means that a speaker would not be able to express themselves properly, or even get past a greeting if they are not constantly being oriented in space.

In this sense we ask, does language become a vehicle for the growth of new concepts, which were not in the mind, and perhaps could not have been there without the intercession of linguistic experience? The possibility that language is a central medium for concept formation has captured the interest of many linguists, and educators alike. Concepts are core foundations of thinking. They are grouping strategies to allow human beings navigate and understand their world as concepts are held in memory and help us in every day decision-making. Language then helps use create concepts for our communication.

A great body of evidence is suggesting that language influences conceptual development in humans (Markman and Hutchinson, 1984; Waxman and Kosowski, 1990; Boroditsky, 2001). This is illustrated in situations where individuals lack language, the progress of learning is impeded (Spelke and Hermer, 1996). It does seem that language affects our on-line perception of the world, shaping the categories we form, enabling us to perform logical inferences, and causal reasoning. For example, as Bloom and Keil (2001) argue, language brings about social reasoning, and structures the basic ontology about time, space, and matter. The character described in Schaller (1991), “Man Without words,” did not have language for 27 years, and subsequently could not say anything about what it was like during this “wordless” time. A similar experience is reported in stroke victims’ experiences after losing language to trauma (Sinanović et al., 2011).

In this article, we examine the interplay between language and thinking as discussed in Crogman and Trebeau Crogman (2016) learning model. This model establishes how to reach critical thinking, which involves thinking reflectively and productively, and evaluate evidence. Such thinkers have a tendency to be creative, open to new information, and aware of more than one perspective. Language is very functional in expanding children’s curiosity, reasoning ability, creativity, and independence (Conley, 2007b). Students who engage in critical thinking uses questions as tools to gain quality information that will help in making good judgments and decisions. Thus the question becomes how does language aids this process to make us better critical thinkers, or to say differently, efficient concept jugglers.

The Role of Language in Learning and Critical Thinking Engagement

How well we ask questions is based on how well the language in which we think is developed. If language does refine human thinking then we cannot escape the fact that it must play a pivotal role in learning theory. How does language make us better thinkers? Crogman et al. (2015) started by initially connecting thinking, question asking and learning by showing that: “Description invites students to ask ‘what,’ ‘when,’ ‘who,’ whereas analysis focuses on ‘why’ and ‘how,’ and evaluation encourages students to think beyond the phenomenon by going deeper and asking ‘what if’.” The ability to question at increasingly complex levels refines the learning experience.

Crogman and Trebeau Crogman (2016) illustrate the interplay between students, the environment, and the educational practitioner (Figure 1). The practitioner uses pedagogies to influence the environment and awaken the student’s curiosity, which in turn causes questions to arise in the mind of the learner. Questions naturally lead to inquiry, and inquiry leads to critical thinking, causing the learner to apply old knowledge or create new ones. In this context Crogman and Trebeau Crogman (2016) suggest that learners that may have less access to expressive language, may internalize their questions creating challenges in the feedback loop that should be happening between thinking, questioning, and learning.

Figure 2 makes two important additions to the learning model of Figure 1, these modifications are essential to critical thinking, and often overlooked: the addition of language and comprehension. For the most part, the importance of language on learning is known but the truth is that it is essential in the comprehension of knowledge as well. Language allows thinking (Tversky and Kahneman, 1985; Pelham et al., 2002; Boroditsky, 2003; Pica et al., 2004), and thinking allows question asking (Crogman and Trebeau Crogman, 2016), but the relationship between language and comprehension has largely not been discussed in learning models. How do they influence the learner’s curiosity? In what way do they help in the critical thinking process?

Figure 2. Language-comprehension modification.

To address these two questions we must see language as not a domain of human knowledge (except in the special context of linguistics, where it becomes an object of scientific study), but as the essential condition of knowing, the process by which experience becomes knowledge (Halliday, 1993). Further, as we are seeking to understand and to model how we learn, we should not isolate learning language from all other aspects of learning. Language in essence serves as the “signifier” for higher-level systems of meaning such as scientific theories (Lemke, 1990; Martin, 1991) and is a prototypical resource for making meaning (Halliday, 1993).

When there are difficulties in the process of language development, there may emerge neurobiological problems such as dyslexia or reading and comprehension deficiencies. Comprehension involves building meaning from language (Sparks, 2012). The ability to make meaningful connections across contexts helps textual and discourse comprehension. However, prior to that skill comes the need for having developed basic knowledge about those contexts and other more general facts. That base allows developing memories, which in turn informs on the contexts illustrated. Comprehension also requires a fairly automatized phonological process of binding and separating components of language, into units that can constitute knowledge to be stored (Sparks, 2012). Language, serves as a set of processing cues or instructions that guide construction of memory for discourse (Gernsbacher, 1990; Givón, 1992).

The nature of language is also combinatory (Spelke, 2010), thus the learner’s language ability consists of a basic level (e.g., decoding and fluency) and higher order processes (e.g., the ability to make inferences). This requires the learner to possess a rich vocabulary, oral language skills, and reading skill (Sparks, 2012). The better the learner’s language development, the more successful is their comprehension. This means that success in comprehending larger units of knowledge requires that learners make inferences to connect ideas both within and across local and global discourse contexts. Sparks (2012) explains that, “prior knowledge is crucial for disambiguating concepts, making predictions, and inferring unstated connections among ideas.” Thus, comprehension is directly related to thinking (Aloqaili, 2012) because it pushes the reader to reflect on prior knowledge to apply it or create new ones. Therefore, successful comprehension will result in the learner retrieving, updating, manipulating, and applying knowledge in order to ask questions and solve problems. Young infants, whom language is not yet well developed, rely more heavily on thoughts and action with impulsivity rather than rationalization. Gradual sophistication of our language ability helps us to think: that is, to logically reason about the world, while we also develop inhibitory control: “the ability to ignore distractions and stay focused, and to resist making one response and instead make another” (Diamond, 2006). Increase in inhibitory control aids children in regulating their emotions, and, behavior and helps them become more effective problem solvers. Therefore, good thinking is related to how well the learners comprehend, and allows them to construct meaning. Getting a sense of language is not based solely on syntax or word meaning understanding, but on understanding what is intended when those words are put together. Children with comprehension deficit experience show weakness in processing written and oral language, higher order thinking skills, and visual and auditory memory. Crogman and Trebeau Crogman (2016) argued that such deficit can be corrected through question asking, since it is so basic to understanding and learning. A pedagogy that involves learners in the skill of asking questions will improve their comprehension, which is directly associated with language development. Through that feedback process (Figure 1) question asking directly impacts comprehension and language.

Sparks (2012) points to the fact that prior knowledge, which includes information recently activated in short term memory (e.g., previously mentioned text concepts), as well as the personal experiences, facts, ideas, and understandings stored in long-term memory, is the most critical variable. As such, in Figure 1, a change in the learner’s environment is sensed through their sensory receptors, which brings about a response. Crogman et al. (2015) deconstructed the connection between environment and thinking processes showing how changes in the environment evoke perception and provoke responses, which are the result of thinking. They point out to two possible outcomes: (1) thinking creates a question that is answered by memory content. This is illustrated in Figure 1 by the arrow that goes to knowledge. Thus, from prior knowledge, curiosity is awakened by the question generated (question mark), otherwise, the path ends caused by lack of interest (Stop). It is comprehension of this prior knowledge that determines the direction of learning. Kandeou et al. (2003) highlighted the importance of considering the influence of anterior knowledge in the construction of relations between concepts and ability to comprehend and predict language. These are examples of skills to acquire, at different levels of language development complexity (e.g., from simple decoding to inferring) to be able to communicate effectively both orally and in writing or reading. In Figure 2, comprehension of prior knowledge requires language development of the learner. This analysis is normally on low order questions asking. (2) when thinking does not meet prior knowledge, curiosity is aroused, and pushes the generation of new questions (see also Loewenstein, 1994). Curiosity drives both low and higher order question (hoq)-asking mechanisms. Language clearly impacts cognitive curiosity as shown in Figure 3.

Figure 3. Illustrate the connection between language curiosity.

The learning model illustrated in Figure 1 requires the educational practitioner to use pedagogies to entice the learner’s engagement. That is, drawing the learners’ curiosity in. Curiosity then becomes the first stage to inquiry and/or critical thinking. Both Berlyne (1954, 1966) and Malone (1981) divide curiosity in two stages: perceptual or sensory which is present in all animals and humans, and cognitive which is a human-only domain. We address here the implications of this difference in the interaction of language and learning. In Berlyne’s (Berlyne, 1965) model, perceptual curiosity arises from conceptual conflict, which then morphs into epistemic (related to knowledge) curiosity, through question asking. Malone’s model starts with the sensory curiosity, which is aroused through environment as in Figure 1, to bring about cognitive state processes. Loewenstein (1994) suggests that curiosity is the intersection between cognition and motivation, which manifests cognitive induced deprivation as result of a perception gap in knowledge and understanding. Loewenstein did posit the idea of the “information-gap” perspective, which states that, in order for curiosity to be present, the learner must already have some level of knowledge. Chomsky’s (Chomsky, 1956) model suggests this as well in his exploration of the existence of some form of language in infants. As we explained, since language helps to formulate concepts, an, as Loewenstein (1994) suggests, infants’ curiosity is aroused by cognitive conflict, then such conceptual conflicts are factor that could facilitate student learning. This stems from the incompatibilities between symbolic responses and the conflict engendered by them (Berlyne, 1960). Berlyne thought that it must underlie the notions of truth and falsity, which can only be achieved if there is prior knowledge as Chomsky infers.

We push back a bit here to suggest that curiosity, at its basic stage, is found in all animals and is purely sensory. Meaning that it is not based on any prior knowledge. For example, a newborn may be curious about a colorful stimulus without having prior knowledge or concept about color to begin with. However, cognitive curiosity is based on prior knowledge or concept, and arises from conflict in information or unresolved stimuli interaction. Cheney and Seyfarth (1998) speculate that animals lack language for the following reasons: no rudimentary theory of mind, and no ability to generate new words, and syntax, which are all present in young children. Animals have a number of in-born qualities they use to signal what they feel, but these are not like the formed words we see in the human language. Thus it is reasonable to conclude that animals could only have a notion of concepts if their communicative gestures were primitive forms of language; this being said, we must realize that Berlyne’s perceptual curiosity is developed after sensory interaction with the environment which births the communicative gestures seen in both animal and children. Therefore, Malone’s conception of curiosity must be the first stage before knowledge is acquired. This difference in cognition between humans and animals is experimentally verified. Kalia et al. (2008) point out that, in both animals and humans, there is categorization of non-geometrical modules (concrete concept or object such as a rock; allowing one to compute orientation in relation to a wall), and geometrical ones (abstract concept or object such as color concrete concept or object such as a rock; allowing one to compute orientation in relation to a wall). In animals as well as in newborn to toddlers these modules do not speak to each other. Fernyhough (2008) argues that humans are able to integrate geometric information (the short wall on the right) with the non-geometric information (the blue short wall, not the white). It is believed that this is the result of language development in humans. Therefore, learning is driven by question asking, which leads to further inquiry behaviors. How does question asking play such an important role?

Because language does impact and streamline thought, it must affect a child’s curiosity, leading to good question asking behavior. There is a clear development in the learner’s ability to formulate questions in response to their curiosity development (Crogman and Trebeau Crogman, 2016). To formulate questions language is important. We speculate that there is not a direct correlation between sensory curiosity (i.e., “curiosity base”—Figure 4) and language. Animals exhibit curiosity even though they do not have language. Spelke and Hermer (1996) speculate that one of the main differences between humans and animals is the human formulation of language. They compared children (newborn to toddlers) and rats, on diverse tasks and their findings indicate that children deviate significantly from rats at about age six (Hermer-Vazquez et al., 2001), a point at which they are able to express complex language within their now fully integrated cultural norms. In human adults reorientation exercises are solve easily that is they quickly find an object left of a blue wall (Hermer and Spelke, 1996). Spelke (2010) propose that this ability emerges in synchrony with the development of spatial language such as expression of left or right terms, and is well known in developmental studies.

Figure 4. Interplay of language between Base and Cognitive curiosity, and their subcategories.

Another case study described by Schaller (1991), when the subject did not have language, he still exhibited curiosity, even though his ability to think was somewhat impeded. The transition to language in toddlers is what correlates to Berlyne’s (Berlyne, 1954, 1965, 1966) and Malone’s (Malone, 1980) second aspect of curiosity. From toddler to preschool where the learner’s access to language is facilitated, more basic questions can be asked to aid their exploration (Borowske, 2005). Language develops the cognitive process in humans, how exactly this is done is up for debate. The link between cognition and language was proposed by Chomsky (1956), who believed that children are born with specific language acquisition devices and linguistic knowledge. The more accepted view today is centered on learning and not on innate structures (Harris, 2006). Piaget emphasized the commonalities between language and cognition proposing that language emerged out of the same broad cognitive changes that transform the sensorimotor processing of infants into formal and logical mind of adults (see Figure 3). Cognitive research has led to the idea that both language and cognition have complex similarities and differences influenced by genetic (Chomsky, 1956), environmental input (Elman et al., 1996), and cultural learning factors (Harris, 2006). It is through these basic questions that the critical thought process is engaged. Once comprehension has occurred (Figure 2), the learner generates hoq asking.

Figure 4 proposed to divide curiosity into Cognitive and Base Curiosity where Base is further, divided into two parts: sensory and perceptual. We propose that perceptual curiosity results from the effect of the cognitive on the sensory. Thus, because of language, there is a constant interaction between the sensory and the cognition as shown in Figure 3. The back arrow (Figures 3 and 4) is fainter to represent that cognition’s influences base curiosity through language. We can reason that because language is interconnective between the geometric and the non-geometric modules, it gives rise to specific cognitive processes in humans (represented in forward arrows in Figures 3 and 4). Cognition then is a reflective interplay in thought process to thinking in a coherent and sequential manner.

Further, seeing the result when humans seem not to have language or have a deficit in it, this suggests that language influences thinking in very profound ways. Language may not completely determine thoughts but it is clear that it streamlines thoughts and strongly influences thinking. Recent work from Zlatev and Blomberg (2015) supports that idea in their disentanglement of language from thought and culture to show that it is fundamental to human learning. For the most part the human thought process seems very random; for example a young child may experience an electrical shock by sticking an object into a plug or get burned by the stove. The child learns from this terrible experience, which prevents future repeats as this is stored in memory. This response may be completely behavioral to begin with, but here the pathway commences where the child uses language to formulate conceptual understanding in the mind and this development continues such that the child’s curiosity transitions beyond mere behavioral. The child’s experience of learning lends to the blank check theory of learning by Locke (1975) and Piaget (1976) that children learn gradually from their environment, in which every experience builds a set of a priori knowledge for the next (Crogman and Trebeau Crogman, 2016). Communication at this stage is limited, making it more difficult to communicate what has happened with clarity or express how they felt; it is here that language helps the human thought process in order to convey feelings and perceptions of the world around.

How to make sense of the following experiment performed by Hermer-Vasquez et al. (1999)? Adults participated in a reorientation task where they listened to a tape recorded prose passage and repeated it continuously, word for word (verbal shadowing); they were observed to lose the ability to combine geometric and non-geometric information and performed like rats and children tested on the same task. Their thought process was “foiled,” and word sense disconnected by the temporary lost of language. When the experiment was repeated with a second group using a different task by listening to a tape-recorded percussion sequence and repeating the sequence by clapping (rhythm shadowing), the adults were able to combine geometric and non-geometric information. The researchers concluded that natural language helps in the construction of new spatial concepts and their active use. We see this as evidence that language is strongly correlated with thought and determines structured thinking (the ability to organize thought logically).

Furthermore, one finding of cognitive research is that curiosity tends to decrease with age because children become cautious (Hutt and Bhavnani, 1972), however, language development continue over the life of the learner. Since the result of good language development makes the learner a better questioner, then question asking stands as a method to counter the effect of declining curiosity (Crogman and Trebeau Crogman, 2016). Questioning can also be used to deepen and enrich knowledge as well as expand the understanding of content. Question asking helps learners link all prior knowledge, think about the exact content, draw out meaning in order to make coherent explanations, develop inference skills, and construct key points to build mental representations (Martin and Duke, 2011; Crogman et al., 2015). Therefore, language is directly linked to question asking. Further, we use language to think aloud, which is an effective comprehension strategy that requires the learner to extract, construct and think about the content, which facilitates knowledge. It taps into a metacognitive process where learners monitor their reading before, during, and after reading (Baker 2009). The end goal for the learner is to become better at critical thinking to effectively solve problems, this skill is inevitably based on how developed language is.

Thus, we outlined a prior learning model, which has taken into account important aspects of learning, which are the environment and how educators manipulate it, their ability to arouse curiosity, and to drive learning by teaching how to ask questions. In that first model however, language and comprehension have been overlooked. In Figures 2–4, are illustrated the role of language in the skill of learning. We see the importance of developing language skills to operate such critical skills as thinking and asking questions, without which learning is not possible. These skills separate us from all animals, and must be taken into account in any Learning Model, using language. The issue is, how can educators operate such strategies to expand learners’ horizon when there are language barriers in their students (outside of ethnic foreign language barriers)? Indeed what does happen when language is misunderstood, and what is the impact of such a problem in the learning processes of developing learners?

Language and Culture’s Influences on Critical Thinking

Human cultures provide the framework in which languages develop, and influences how they are used and interpreted. In some groups more than others, gestures, glances, changes in tones, along with other devices are widely used to emphasize what is communicated. Language is closely related to culture, but in reality its influence is often overlooked (Hadley, 2000). Nida (1998) suggests that language and culture cannot exist without each other, and languages not only represent elements of culture, but also serve to model culture. If the influence of culture on language is ignored however, serious misunderstandings will emerge in communication. Nida (1998) proposes that words are determined by both syntagmatic and cultural contexts, but language still may change in word meaning faster than it changes culture itself.

Ricci and Huang (2013) argue that cultural influences do affect thinking styles, shape personal thinking preferences, and have their grip on critical thinking strategies since it has been shown to affect individuals’ thought processes, judgment, and decision-making and inhibit the ability to be unbiased. There are no empirical data found in the literature that addresses the issue of the interplay between culture and critical thinking directly. Yet, in the context of learning and thinking contexts, such as education for example, the place of culture and language is important as culture comes with bias in thinking. In that pursuit, a number of researchers (Paul and Adamson, 1990; Ennis, 1998; Ricci and Huang, 2013) argue that the ability to address bias is an important dimension of critical thinking. How can this be true if thinking in itself has fallen prey to cultural conditioning? If language and culture impact an individual’s thinking, does it mean that critical thinking, which is a tool for overcoming biases is inherent with them?

Language is the vehicle through which we often experience cultural biases. This is a preference or an inclination that inhibits impartiality; prejudice (American Heritage Dictionary, 1983), or “a predisposition or a preconceived opinion that prevents a person from impartially evaluating facts that have been presented for determination. A bias held limits the critical thinking processes” (West’s Encyclopedia of American Law, 2005). The issue with most biases is that they can becomes unconsciously activated. To illustrate, a new White teacher, working in the predominantly Blacks and Hispanics South Bronx said one day in class, “…And for homework, I’m going to give you people….” The reaction of the students immediately turned to anger. The incident became a teaching moment when a student asked, “What do you mean by You People? We don’t like to be called You People!” to which the teacher apologized. Such is a perfect example of cultural misunderstanding attached to language. As we will detail further, good critical thinking skills helps us to examine our biases. It is here that the language-culture dynamic exerts its influence on thinking, which could be very harmful to the learning process, meaning that critical thinking in itself is subjected to cultural influences, which causes thinking in itself to be shaped into such biases.

Levinson and Majid (2011) by looking at the differences in the thinking processes associated with the type of language spoken found that language and culture influence cognition. Such data are evidence that language is used to form concepts and categories, which are born by culture, and influenced by their specific rules and choices in language usage. For example, Davidson’s (Davidson, 1994) argues that in Japanese culture, critical thinking is inhibited due to a number of cultural demands, which do not encourage diversity of opinions as most of their education processes are based on rote memorization.

In the United States, culture strongly influences the education system through which policy and instruction are formulated. An impressive body of research spanning decades addresses such issues and leads to some uncomfortable conclusions, yet, it is difficult to isolate effects of race and culture from other factors. The things we experience and observe in our culture or about other cultures compel us to create biased (meaning often unilateral or containing only partial information) concepts, categories, and stereotypes. Hamilton and Trolier (1986) define stereotypes as positive and/or negative belief, expectations, and knowledge established about designated or singled out groups. Bigler and Liben (2007) along with a large number of researchers from diverse disciplines, posit that such categorizing is an innate cognitive behavior. They explain that humans gravitate toward this type of cognitive strategies by mere need to conserve mental energy, understand and predict the world, and reinforce the feeling of belonging that “ingrouping” and “outgrouping” affords. Some researchers explain that such biased “grouping” become so ubiquitous that the stereotypes attached to them are integrated into unconscious layers of our cognition. If it is unconscious, then those biases and stereotypes will be applied broadly without the use of more analytical thinking. The goal of the argument further is to examine the impact that negative stereotypes can have on the critical thinking process. Their influence on critical thinking is best reflected in the performance of Blacks and other minority groups. The focus will be the effect of stereotypes on learning and thinking in the African American learners.

Stereotypes, are cognitive constructions which encompass a set of convictions and assumptions that are presumed, in the case of “racial stereotypes” here, to be shared among members of a same racial group, often in a negative context (Jewell, 1993; Peffley et al., 1997). These stereotypes are played out in society at large in their influence on public policies and opinions against particular groups. The culture of the dominant Caucasian group in the US (we will call it here “the ruling class”) has the largest representation in political and legislative decisions where these negative biases often appear in the formation of policy. Jewell (1993) argues that there is an obvious trend in American culture to discriminate against, and deny access to social institutions to Blacks. These stereotypes formulated in the language of the ruling class will continue their effects on such groups for generations. It is well documented that the ruling class tends to think negatively of Blacks: males are deemed violent and brutish, while females are seen as dominant, and lazy (Peffley et al., 1997). Blacks are considered to be inferior to all other groups, for example, they were believed to be mentally inferior physically, culturally unevolved, and apelike in appearance for centuries. Such absurd perspectives were well engrained in our historical highest institutions, infrastructures, and resources like the Encyclopedia Britannica published in 1884, stating authoritatively that “the African race occupied the lowest position of the evolutionary scale, thus affording the best material for the comparative study of the highest anthropoids and the human species” (Plous and Williams, 1995, p. 795). Contrary to common opinions, such views still exist today and are propagated in the educational system of the American classrooms in more or less subtle ways.

Recent research has shown that members of the ruling class are likely to hold these stereotypes especially with respect to issues of crime and welfare (Green, 1999). Welch (2007) points out that the ubiquitous stereotype of Black men as “criminal predators” is so engrained in society’s perception that it permeates the global unconscious to the point of affecting systems such as Justice or Law Enforcement, and influencing their practices and justifications for bias. Another example is the overrepresentation of Blacks as sports figures (Peffley et al., 1997). Edwards (1973) observed that the arguments from social Darwinism that helped solidify the stereotypes in American communities such as natural ability of Blacks and intelligence of Whites are still used as mutually exclusive attributes to account for racial differences in sports performance. An experiment by Stone et al. (1999) showed the impact of stereotypes on athletes’ performances. Black participants performed significantly worse than did control participants when performance on a golf task was framed as diagnostic of “sports intelligence”; on the other hand, White participants performed worse than did controls when the golf task was framed as diagnostic of “natural athletic ability.” What does this tell us about the influence of language on concept formation such as cultural stereotypes? What is the impact on classroom learning or development of critical thinking skills in some groups if the perception of the teacher and students are shaped by these stereotypes? The Clark Doll experiment (Clark, and Clark, 1939) illustrates the pervasiveness of racial bias and how early it seems to be engrained in the mind of children, who then grow up unknowingly categorizing according to these implicit biases. Children aged 6–9 were asked to choose a doll to play with, and also to indicate which one looked like them. It was found that black children often chose to play with the white dolls more than the Black ones. In another experiment (Davis, 2009), children were asked to tell which doll was the mean one and which doll was the nice one. Children overwhelmingly chose the Black doll as the mean one. The devaluing of the Black doll is evidence of racial biases as induced by many factors in society, and will impact individuals at every level of the social fabric. Since it is stereotypical belief that Whites are smarter than Blacks, this will affect how teachers perceive Black students, how Black learners perceive themselves, and how their peers perceive them. Correcting these stereotypes implies reformulation and acceptance of cultural language diversity, to restructure the belief system attached to racist stereotypes that creates a false narrative in our youths.

The problem is twofold: instructors having a grasp of what cultural diversity really is and avoiding the pitfalls of stereotyping, and also understanding that that diversity comes with language hallmarks that may not sound or look like what they are accustomed to. The degree with which one tends to stereotype has been connected to the degree to which one holds the belief that people’s characteristics cannot change or tend to be the same and constant among certain groups (Levy and Dweck, 1999). McKown and Weinstein (2003), for example, show that these beliefs, crystallized into stereotypes can translate into behaviors that may impact children school performance. However, they argue that, with proper guidance and intervention, such tendencies can be reversed, and the deleterious effects of biases transformed. As argued by great thinkers of the beginning of the century such as DuBois (1903), in the case of African Americans, such stereotypes as born by the ruling class, have caused them to choose to close the door to higher education to these groups, thereby also stifling their opportunity to take part into the academic exercise of critical thinking. Countless research has established to date that such stereotypes about race have permeated education in harmful waves, and pushed individuals, who vowed to educate the masses, to close off opportunities of education to underrepresented groups even by their grading attitudes, expectations, and behaviors in class. Researchers analyzed educational, demographic, and survey data of 10,000 high school sophomores and their teachers using the Education Longitudinal Study of 2002, to show that teachers typically underestimating their students’ abilities, actually created a negative impact on their academic expectations of themselves, and this was especially harmful among Black students (Cherng and Halpin, 2016; Cherng, 2017). Further, Fleming (1984), and Smedley et al. (1993) along with a large body of recent research (Locks et al., 2008; Hurtado et al., 2009) demonstrated that racial biases encountered in school severely negatively impacted Black students’ academics, critical thinking, sense of belonging, and emotional development through heightened stress levels. However, they stress that the distress experienced by racism in school has a different impact on these students and creates unique sets of cognitive states unlike other regular sources of strains, pressures, and difficulties. Indeed, such concepts as “stereotype threat” (the belief about racial inferiority), have been coined to show how much of an insidious impact cultural stereotypes have created on the minds of those who are the aware victims of these issues, and how much of an effect these views have had on their ability, or even their beliefs about their ability to think and reason. The resulting impact is a negative effect on the development of students’ critical thinking due to teachers’ biased perception of students, and the students of themselves.

Diversity in the classroom is notoriously misunderstood, and a known source of miscommunication between educators and students. Thus, when it comes to the language differences brought by cultural diversity, a representative from an Asian cultural background may not experience society and educational system pressures through the same negative stereotypes as do Blacks, even through their English speaking may be strongly influenced by their culture. In another experiment, researchers attempted to distinguish if distinction between stimuli such as colors was based on language or some other visual mechanism (Kay and Kempton, 1984). In their first experiment, they asked English speaking and Tarahumara speaking participants to explain which of three colored chips was the odd one in the context of their color distance, knowing that English speakers and Tarahumara speakers do not see color distance the same way. Expectedly both groups did not give the same distinctions between the three chips. To assess whether language was the reason for that difference, in another experiment the researchers eliminated part of the choice and also constrained the choice to how much blueness and greenness difference there was, thereby eliminating the color categorization afforded by language specificity. Surprisingly, English speakers aligned with the Tarahumara. Language was somehow a barrier to the two groups seeing eye to eye on color categorization. This experiment could potentially be expanded to other domains to highlight how language constrains perception, concepts, categorization and other vital skills necessary to communicate. Researchers showed that linguistic differences influence how speakers of two different languages view events. In one experiment German and English speakers were compared on ambiguous and goal-oriented scenes matching. German speakers matched twice as much as English speakers situations showing that they, more than English speakers, were focused more on people’s actions outcomes than on the actions per se.

Thus the specificities of language are fundamental to many aspects of communication, and multilinguality adds another layer of complexity to the problem. Multilingual individuals are more advantaged in the classroom because speaking in other languages aids cognition and thinking processes at different levels (Kubota, 2013). Indeed, multilingual individuals have been found to present clear cognitive advantages and to be more easily flexible in their thinking. A large meta-analysis looking at over 6,000 bilingual individuals showed superior abilities for example in attention, memory, metalinguistic awareness, and understanding of symbolism (Adesope et al., 2010).

Multilingualism by nature also often affords multiculturalism, which can allow individuals to have more accepting attitudes toward others (Kubota, 2013). This begs the question why do Blacks tend not to be seen more positively and perform better in the classroom given their inherent multiculturality? Could it be that multilingualism also constitutes a setback? For example, it may emphasize commonality and natural equality across racial, cultural, and gender differences for everyone, which then may perpetuate certain stereotypes such as Asian students being passive and silent learners, who fail to become autonomous learners (Zhao, 2008). In the case of Blacks, the uniqueness of the African American English language, strongly influenced by the African slave ancestry, and creole cultures for example (Green, 2002), bares the marks of a history that still holds prejudice on its shoulders without the respect due to its legacy. Thus in the classroom, as pointed out by Kubota (2004), ethnic customs and traditions are merely displayed and consumed without learning about their sociopolitical origin. Differences are ignored in this multicultural environment, which obscures the ruling class’ power and privilege. Kubota (2004) argues that failing to appreciate this diversity of culture can only promote the continuation of “racial and linguistic hierarchies.” The impact of school and language should have given Blacks a much better foothold in the American society, but instead the whole culture still seems to be condemned and deemed as negative.

How do we mitigate this negative aspect of culture and language perceptions on individuals’ success in learning? Kubota (2004) argues for “critical multiculturalism.” By this she means that one must understand and appreciate the invention and performance of identity in intercultural communication, through examination of how groups construct their identity in social and historical ways (Kubota, 2004). This types of multiculturalism demands that both students and teachers, “critically examine how curricula, materials, daily instructions and social differences are constructed, legitimated and contested within unequal relations of power” (Zhao, 2008), a critical reflection about the discourses’ power/knowledge and social impact.

The point here is that language and culture are so intertwined that when culture bares the burden of prejudice, so does language, and all learning attached to this context is highly impacted. Thus a better understanding of culture also implies a better understanding of language, and thereby improves learning and teaching directly and indirectly. Further, it requires a certain degree of ones’ own awareness of one’s biases in order to even start applying the critical thinking process to those biases, to remove them from our cognitive procedures when we apply our judgment to understand or know others. Thus, the data examined here show that under the pressure of certain stereotypical stressors, students’ performances is negatively impacted, which is a reflection that their critical thinking processes are also affected.

The Case for Language and Dyslexia: How Black Children can be Impacted

Chapter Six: Analyzing Arguments


I.    Introduction

As I have characterized it in this handbook, critical thinking is primarily about the evaluation of arguments. Evaluation of arguments requires that we have arguments to evaluate, and it has been the purpose of the preceding chapters to describe how we locate and represent such things. Once we have them, though, we can get down to business. Evaluation is, after all, the central activity of critical thinking, and it is in this chapter that we will focus on this activity. The goal is to provide the tools to use in detecting good arguments. This contrasts with the goal in the next chapter, which is to provide tools to use in detecting bad arguments. We begin this chapter by discussing the nature of argument evaluation, and the relationship between this stage of critical thinking and the stages we have discussed in earlier chapters.

As we observed in Chapter Three, arguments understood as products have both form and content. In light of this, it should come as no surprise that they can be evaluated in terms of their form and their content. Both types of evaluation will be discussed in this chapter. Evaluation of form, or formal analysis, falls within the province of logic. Logic, as a discipline, concerns the identification and development of formal patterns of reasoning (and related concepts) that meet certain standards, such as validity or non-deductive strength. After discussing the nature of argument analysis in general, we will turn to a development of the logical tools necessary to engage explicitly in the evaluation of argument form. Evaluation of content, or subject matter analysis, will vary from field to field. This sort of evaluation requires familiarity with specific disciplines, their facts, theories, and standards. As such, there is little we can say here about the specific character of this form of analysis, but there are some general considerations that I address in the penultimate section. The final section is devoted to the third stage of evaluation, context analysis. After assessing an argument for merit on its own, we must examine if it serves the purposes of the arguer. Does it advance her persuasive goals, and if so, how does it advance them?

II.    The Nature of Argument Analysis

II.1 A Worked Example

Consider the following argument:

I plan to vote for someone other than Al Gore, and I think you should follow my lead. He's a Democrat, and Democratic presidents in the last 30 years have not done the job--Carter left hostages in Iran and Clinton brought dishonor to the office. We have to vote for someone else if we hope to have effective federal government.

Is this a good argument? Before answering this, we must determine exactly what the argument is. The conclusion is that we must vote for someone other than Al Gore in the upcoming Presidential election. The reasons offered turn on the effectiveness of Democratic Presidents in the recent past. In particular, the argument contends that Gore will be ineffective because he is a Democrat and the last two Democratic Presidents, Carter and Clinton, were ineffective. The argument can be represented in standard form as follows, bringing in a few implicit premises to fill it out:

    1. Carter, a Democrat, was an ineffective President because he left hostages in Iran.

    2. Clinton, a Democrat, is an ineffective President because he brought dishonor to the office.

    3. These are all the Democratic Presidents in the past 30 years. (Implicit)

    4. All Democratic Presidents in the past 30 years have been ineffective, and so Gore, a Democrat, would be ineffective too.

    5. If we want effective government, we should vote for an effective leader. (Implicit)

    6. We want effective government. (Implicit)


    1. We should vote for someone other than Gore.

Let's consider this first from the perspective of its form. As reconstructed, the argument is a combination of a couple of lines of reasoning. First, steps (1) through (3) supply what we will call inductive support for step (4), and then steps (4) through (6) supply what we will call deductive support for the final conclusion. To assess these, we assume that the supporting reasons are true and then ask whether they provide any support for their conclusions. The first line of reasoning is, from a formal perspective, rather weak for a couple of reasons. Any generalization that is based on two data points should be regarded with some suspicion--two instances rarely prove any rule. Second, while Gore is in the same party as Carter and Clinton, the nature of the party has changed considerably since Carter was President. Given this, it would appear as though only one data point, Clinton, is relevant to an assessment of a possible Gore Presidency, cutting the strength of an already weak inference in half. Turning to the second line of reasoning, we find an argument in good formal shape--if (4), (5), and (6) are true, then (7) is also true.

Formal analysis involves assessing whether the conclusions are supported by their reasons, assuming that the reasons are true, and this suggests that the first line of reasoning is weak, a fact that threatens to vitiate the argument as a whole. Content analysis involves asking whether the reasons are in fact true. It is here that the argument would really appear to founder on the rocks. Whatever you may think of Carter and Clinton, it isn't at all clear that if they are or were ineffective, this was due to the factors cited in the argument. While (3) is true, the formal concerns raised above should lead us to suspect the truth of (4)--we are supposed to believe this on the strength of (1) through (3), but even if those claims were true, which is in doubt, they would not supply much support for (4). In addition, it is not obvious that you must have an effective leader to have an effective government, contrary to what (5) asserts. And if (4) and (5) are not true, then the argument fails to supply a compelling reason to believe (7). On the whole, the claims that constitute this argument do not exactly inspire one to embrace the final conclusion.

Lastly, we evaluate the argument relative to the persuasive context in which it appears. This is difficult here, given that I've supplied no contextual information, but there are a couple of things that we can say. First, the argument would appear to be in the service of a practical agenda, viz., to convince the audience to vote for someone other than Gore. Previous analysis reveals that the argument is weak, a fact that makes it ill suited to advance the arguer's agenda.. Note, though, that even if it weren't so weak, it still might not serve the arguer well. In particular, this argument focuses on one generalization, and as such it ignores many factors that bear on an advance assessment of a Presidency. Thus, the consideration adduced by this argument may be outweighed by competing considerations, thereby undermining the arguer's goal.

II.2 Formal Analysis

When you analyze an argument, you determine whether the conclusion is supported by the premises. One part of this effort is formal analysis, or evaluation of the form of an argument. When engaged in this type of analysis, you hold the content of the argument constant and experiment with the form to see if it is well-suited to convey you from premises to the conclusion. As we saw with the example, this is done by assuming for the sake of argument that the premises are true and then assessing whether their truth gives one good reason to believe that the conclusion is true as well. Thought experimentation of this sort reveals if the argument would support the flow of truth from premises to conclusion, on the assumption that the premises are in fact true. (Compare: you would test whether a canal worked in the first instance by assessing the dry channel and asking whether it could convey water from one end to the other, if the water were released into it.)

Formal analysis is largely a structural matter. There should be connections of content between reasons in an argument, but these reasons must be structurally related in an appropriate way for them to provide support for the conclusion. The trick in teaching formal analysis is to train students to distinguish between appropriate and inappropriate structural relations. One way to do this would be to present them with a system of logic, deriving truth preserving structural relations from axioms and primitive inference rules. This is, however, not the tack I take in this handbook. Instead, I will introduce standards of appropriateness and then describe a number of common patterns of reasoning that meet these standards. Such patterns of reasoning come in all shapes and sizes. Here are three paradigmatic examples, organized according to types we will discuss in the next few sections:

  1. Propositional Inference: Deductive

1. If I left my wallet at home, I'll have to go without lunch.

2. My wallet is at home.


C. Therefore, I will have to go without lunch.

  1. Categorical Inference: Deductive

1. All men are mortal.

2. Socrates is a man.


C. Therefore, Socrates is mortal.

  1. Inductive Inference: Non-Deductive

1. 1000 people have taken drug X without developing negative side-effects.


C. Therefore, drug X has no negative side-effects.

Patterns such as these form the subject matter of logic, which studies the structure of such patterns with a view to distinguishing those that are argumentatively strong from those that are not. For our purposes, the leading idea is that there exists identifiable principles which can be used to distinguish good arguments from bad ones. When one "does logic," one investigates these principles by developing and exploring systems of inference that they constrain. Critical thinking is not logic. While there is overlap, they have different subject matters and have different goals. Critical thinking is a discipline with a practical goal, viz., to produce people who are in control of their own beliefs. Logic, by contrast, is a branch of mathematics and is concerned with deriving results about axiomatic structures. Nevertheless, it is important to spend time with logic, for several reasons:

  1. Logic reveals principles that are satisfied by good arguments.

  2. Logic makes plain the skeletal structure of arguments, and this can help one distinguish the relevant from the irrelevant when one is reconstructing an argument.

  3. Attention to logic enables one to develop a facility with inferences.

You cannot be an effective critical thinker unless you are attuned to the form of arguments, and the best way to become attuned is to spend some time studying logic.

II.3 Subject Matter Analysis

The second stage of analysis is subject matter analysis. There are a number of differences between these stages of analysis. First, formal analysis requires us to consider whether we have good reason to believe a conclusion of an argument on the assumption that the premises are true. Subject matter analysis is devoted to determining whether those premises are in fact true. Second, formal analysis reveals patterns of reasoning that are found in many different domains, from religion to politics to medicine to sports. Subject matter analysis, by contrast, requires attending to facts and claims that are typically part of a single domain. To analyze the content of the argument at the beginning of this section, we must know something about the recent political history of the United States, for instance. Related to this is the third difference: logic is useful as a tool for formal analysis, but it is not for subject matter analysis unless logic is itself the subject matter of the argument in question.

It may seem that logic has more of a role to play in subject matter analysis than this. In particular, there will be occasions when you take a premise to be true because of an associated, supporting argument. While it is true that in such a case, you will likely avail yourself of logic to help in assessing the supporting argument, in the end you will need to ask of its premises whether they are true. Perhaps you will decide that they are, and perhaps this decision will be based on further arguments. But the premises of these must be evaluated for truth or falsity, and so on and so on. This process can take a good deal of time and energy, but eventually it must stop if you are going to pass judgment on the argument. Logic will be of assistance as you search for the truth values of the premises, but at some point you will need to ground your assessment in facts or intuitions whose truth is non-argumentatively established.

Subject matter analysis requires knowledge of the subject matter of the argument, and this is generally is non-logical. Thus, when teaching critical thinking, you must make sure to emphasize the importance of factual knowledge to the process. If you can establish that premises are true, based on independent knowledge of the content of those claims, and if you further know that the argument has a form that conveys truth from premises to conclusion, then you have good reason to believe in the conclusion. In either of these fail, i.e., if you conclude that a premise is false or that the form of the argument is weak, then while the conclusion may nevertheless be true, the argument does not give you reason to believe it.

II.4 Context Analysis

Only in the cold, antiseptic climate of the critical thinking classroom will you find arguments stripped from all context, served up without any introduction or background. Outside the doors of this classroom, arguments are almost always asked to serve some larger purpose, e.g., to convince others, to protect oneself, to establish credentials, etc. Evaluation of the relationship between an argument and these larger purposes forms the focus of our third stage of analysis, viz., context analysis. An argument might be strong when considered independently of context, but it may not fit well with the broader purposes of the arguer. For instance, it may be a strong argument for a conclusion that is unrelated to their broader goal or perhaps even, unbeknownst to the arguer, aconclusion that undermines their broader goal. On the other hand, an argument might turn out to be weak but nevertheless effective if the way in which it is delivered enables it to serve the goals of the arguer; in such a case, it might prove as effective as a stronger argument. In both cases, proper evaluation of the argument as a move in a persuasive discourse requires understanding it in its context.

This sort of analysis requires that one identify the broader practical goals of the arguer. What work is the arguer asking the particular argument to do? How does it relate to other things the arguer has said? Is it consistent with them? Inconsistent with them? If consistent, does it strengthen them or is it unrelated? An effective critical response to the argument requires knowing the big picture, and this typically requires that one engage in context analysis after having assessed the quality of the argument considered on its own.

III. Formal Analysis

Formal analysis reveals whether the form of a given argument is capable of supporting a justified conclusion. Here the analogy, mentioned above, of the canal is instructive. To convey water from one place to another, a canal must have the appropriate structure, e.g., it must lead from one point to the other, it must have a certain depth at all times, etc.; it might fail even if it does have the correct structure, but it will certainly fail if it lacks this structure. Consider also a building: if you wish to construct a building for a certain purpose, it must be structurally sound; it may fail to meet the specs for other reasons even if it has structural integrity, but it will certainly fail to meet them if it lacks it. Analogously, an argument must be of the appropriate form to support a justified conclusion if it is going to compel people to believe that conclusion. In particular, it must be of a form that conveys truth from premises offered to the conclusion. As with the other structures, a structurally solid argument may fail to yield a justified true conclusion--for instance, it may be the case that one or more of the premises are false--but it will certainly fail to yield a justified true conclusion if it lacks structural integrity.

In this section, I introduce the elements of formal analysis, elements that are rooted in logic. I separate these elements into two broad categories, viz., deductive analysis and non-deductive analysis, which I introduce in the next section. I then devote an extensive section to each category, each of which begins with a discussion of the standards that are applied when engaging in the relevant type analysis followed by a description of the different argument structures that measure up to these standards. I close each of these two sections by remarking on techniques for applying these standards to argument structures that are not discussed.

III.1 Deductive Validity and Non-deductive Strength

In what follows, it will be helpful to identify two broad types of arguments: those that are deductively valid and those that are non-deductively strong. Deductively valid arguments are those in which the conclusions must be true given that their premises are true. That is, if the premises of these arguments are true, then it is impossible for the conclusion to be false. Arguments are non-deductively strong when it is improbable that their conclusions are false given that their premises are true, where the degree of strength varies directly with the degree of improbability. Note that, as defined, arguments that are deductively valid are non-deductively strong; in fact, they are the most non-deductively strong arguments. For the sake of clarity and precision, we will require that non-deductively strong arguments are not deductively valid. Thus, we have the following definitions:

D1. An argument is deductively valid just in that case where its conclusion must be true given that its premises are true.

D2. An argument is non-deductively strong just in that case where it is improbable that its conclusions is false given that its premises are true and it is not deductively valid.

There are a number of things to be said about these properties. First, they are both conditional properties. That is, an argument can be deductively valid or non-deductively strong even if its premises are one and all false. What each definition supplies is a conditional property, i.e., an "if then" property. Consider deductive validity: IF the premises are all true, THEN the conclusion must be true; however, in the case that the premises are not all true, then we don’t know anything about the truth of the conclusion. And then there is non-deductive strength: IF the premises are all true, THEN it is improbable that the conclusion is false; however, in the case that the premises are not all true, we do not know anything about the truth or falsity of the conclusion. Thus, you could have an argument that is deductively valid but that is nevertheless bad because it has a false premise. This fact brings out the fact that these are structural properties of arguments: the fact that an argument has one does not tell us if its premises represent the world correctly (i.e., if the premises get the facts correct), but it does tell us that if they represent the world correctly, then we are justified in believing its conclusion because the form of the argument conveys the argumentative virtue from premises to conclusion.

Second, they are related to one another on a scale of justification: a deductively valid argument can supply all the support a conclusion can get, whereas an non-deductively strong argument can supply only some large percentage of that support. The trick will be, of course, to determine what counts as a "large percentage" in the case of non-deductively strong arguments. As with most decisions of this nature, I believe that there is no pat answer that will work in all cases. It must be greater than chance, of course, but beyond that what counts as a "large percentage" will vary from case to case, depending on the role the argument plays in the discourse, the needs and purposes of the discourse participants, and the nature of the subject matter, to name a few considerations. There is no similar problem with deductively valid arguments—when they are good, they supply 100% support, since the conclusion cannot but be true when the premises are.

Third, an argument is deductively valid just in case the conclusion does not say anything that is not already implicit in the premises. Consider an argument where the conclusion makes a claim that goes beyond what is claimed by the premises. For instance, consider a conclusion that makes a claim about all UI students that comes on the heels of premises that only talk about UI students in philosophy classes. In such an argument, the premises could all be true but nevertheless fail to guarantee that the conclusion is true—what is true of all UI philosophy students might not be true of, say, a UI ag econ student, and if it isn’t, then any conclusion which generalizes over all UI students will be false. Indeed, the only way to guarantee that the conclusion is true, given the truth of the premises, is to require that the claim made by the conclusion go no further than those claims made by the premises. In other words, the information contained in the premises must include the information that receives mention in the conclusion. This restriction, however, does not apply to non-deductively strong arguments. In fact, they are of interest precisely because their conclusions do go beyond their premises and do so in a way that is nevertheless justifiable.

III.2 Deductively Valid Arguments

In this sub-section, I begin by introducing the two principal standards associated with analysis of deductively valid arguments. Then, I consider two categories of deductively valid arguments, propositional arguments and categorical arguments, describing along the way common forms of propositional and categorical arguments. I close by describing techniques for determining the validity of arguments in general.

III.2.A Standards for Deductively Valid Arguments

Two standards are apropos to the analysis of deductively valid arguments. The first, validity, has been defined above with D1. An argument is valid just in case it is deductively valid. Note that the term ‘valid’ is one that, in common parlance, serves a great many purposes. It is used so variously as to be almost colorless, similar in this way to other terms of positive appraisal, such as ‘good’ and ‘right’. However, in formal analysis, ‘valid’ is a technical term with a precise meaning, and should be introduced as such. (Consider that arguments can be good, in the sense of being non-deductively strong, even though they aren’t valid, thereby establishing that the two terms cannot be used interchangeably when doing formal analysis.)

The second standard relevant to assessment of deductively valid arguments is soundness. An argument is sound just in that case where it is valid and its premises are true. Thus, it includes the formal standard of validity as a part. This is the more important of the two standards, as it is not merely formal but concerns also the relationships between the constituent claims and the world they purport to represent. When we analyze these arguments in our daily lives, we really care about their soundness. However, since soundness involves a component that concerns the subject matter of the argument, it is not a standard that will receive attention here. We will attend to part of it in this section, viz., validity, and we will return to it when we take up subject matter analysis in the next section.

In sum, two standards are relevant to the analysis of deductive arguments:

S1-D: An argument is valid just in that case where its conclusion must be true given the truth of all its premises.

S2-D: An argument is sound just in that case where it is valid and its premises are true.

III.2.B Types of Deductively Valid Arguments

We will study two forms of deductively valid arguments in this handbook: propositional arguments and categorical arguments. Propositional arguments are built up out of propositions, which are claims that can be evaluated for truth or falsity. Propositions can be either simple or complex. Simple propositions are claims like "Maggie is tall" or "The Bush/Cheney ticket is exciting." They consist of a single subject term and a predicate. Complex propositions are built up out of simple propositions with the help of sentential connectives, such as ‘and’, ‘or’, ‘if ... then’, and ‘just in case’. Propositional arguments turn on relationships among complex propositions that are grounded in the connectives out of which the complex propositions are constructed. For example, if one premise in the argument is a complex claim of the form ‘P and Q’, then you can validly assert either P or Q because if ‘P and Q’ is true, then P is true and so is Q. Thus, an argument that contained ‘P and Q’ as a premise and P as a conclusion would be valid, and it would be valid because of the relationship between the claims, a relationship grounded in the connective ‘and’ and that appears in the premise.

Categorical arguments are also built up out of propositions, but some of these propositions are marked by the presence of terms like ‘some’, ‘each’, ‘all’, and ‘every’. These terms indicate a concern with some subset of a group of objects, such as people in "All people are mortal" or Republicans in "Some Republicans wanted Elizabeth Dole for Bush’s running mate". As these examples illustrate, the groups are determined by properties associated with terms in the sentences, such as being a person, or being a Republican. Call these general propositions. Categorical arguments include at least one proposition that makes a claim about a category or group of objects. They turn on relationships of inclusion or exclusion among the categories, or among the categories and individuals, that are mentioned in the constituent claims., and these relationships are grounded in the categories introduced by the constituent general propositions. For example, consider the famous syllogism: All men are mortal; Socrates is a man; therefore, Socrates is mortal. This is a valid categorical argument because the individual named in the second premise, Socrates, is a part of a group, men, that is itself part of another group, mortals, and the conclusion asserts essentially this, leaving out the middle term. Thus, Socrates is included in the group of mortal things, and this relationship of inclusion is guaranteed by the fact that he is a man and that all men are mortal things.

In a course on symbolic logic, one would begin with basic elements, such as predicate symbols (i.e., symbols for those linguistic items that mention the properties that define the relevant categories in general propositions), propositional symbols, connectives, and quantifier terms (i.e., terms like ‘some’ and ‘all’), and build a system that could be used to identify valid arguments in general. This, however, is not our goal here. Instead, what I want to do is introduce a number of valid propositional and categorical argument forms, and then identify what it is about the constituent propositions that identify them and that secure their validity. In addition, I discuss techniques for determining valid forms of propositional and categorical arguments in general. I do this in the next two sub-sections.

III.2.C Propositional Arguments

Propositional arguments are a type of deductively valid argument that depend for their structural characteristics on connectives and the complex propositions they support. Connectives are terms, such as ‘and’ and ‘or’, that connect propositions together to form more complex propositions. For example, we can take the proposition Maggie likes pomegranates and the proposition Maggie likes persimmons and combine them with the sentential connective ‘and’ to yield the complex proposition Maggie likes pomegranates and Maggie likes persimmons, or what amounts to the same complex proposition in a more compact form, Maggie likes pomegranates and persimmons. In addition to ‘and’ and ‘or’, we will concern ourselves with the connectives ‘not’, ‘if ... then’, and ‘just in case’ (i.e., ‘if and only if’).

Because propositional arguments depend for their validity on the complex propositions they comprise, it is worthwhile to devote a bit of time to the nature of these propositions. We will do this by considering the impact that each of our five connectives has on the propositions into which they figure.

  1. ‘and’: a complex proposition formed with ‘and’ is written ‘P and Q’, and it is true just in case both P and Q are true. Other terms in English that have the logical force of ‘and’ include ‘but’, ‘whereas’, and ‘although’. Examples: Maggie likes peas and Jon likes carrots; Maggie likes peas and carrots; Maggie likes peas and so does Jon; Maggie likes peas but Jon likes carrots.

  2. ‘or’: a complex proposition formed with ‘or’ is written ‘P or Q’, and it is true just in case either P is true or Q is true or both are true. (This is known as the inclusive interpretation, and is contrasted with the exclusive, or "soup or salad", interpretation.) Examples: Maggie likes peas or carrots; Maggie likes peas or Jon likes peas; Maggie or Jon likes peas.

  3. ‘not’: this applies to a single proposition, ‘not P’, and so is only a connective by courtesy. Other English terms and phrases that can express the same logical force are ‘no’ and ‘it is not the case that’. Examples: Maggie does not like peas; It is not the case that Maggie likes carrots; No people came to see the gallery opening.

  4. ‘if ... then’: a complex proposition formed with ‘if ... then’ is written ‘if P, then Q’, and it is false just in case P is true and Q is false, but true otherwise. The ‘if’ proposition is called the antecedent and the ‘then’ proposition is called the consequent. Other terms in English used to express this type of claim are ‘provided’, ‘when’ (the non-temporal sense), and ‘only if’. Examples: If Maggie likes peas, then she likes something nutritious; Maggie likes something nutritious, provided she likes peas; Maggie likes peas only if she likes something nutritious.

  5. ‘just in case’: a complex proposition formed with ‘just in case’ is written ‘P just in case Q’ and is true just in case P and Q always have the same truth value. Another term that is used to express this type of claim is ‘if and only if’. These connectives are those found in definitions. Examples: Max is a bachelor just in case he is an unmarried male person; ‘P just in case Q’ is true just in case P and Q always have the same truth value.

With these in hand, we can proceed to a specification of argument forms involving complex propositions formed from these connectives. I will list common and important forms in association with the connectives that underpin them. In so doing, I will first introduce them in schematic form, using the proposition symbols ‘P’ and ‘Q’, and then I will supply an illustration.  

  1. ‘and’: If P and Q is true, then P is true. If I own a cat and I own a dog, then I’m a dog-owner.

  2. ‘or’: Either P or Q is true; if P, then R; if Q, then R; either way, R must be true. (Proof by Cases) Either I had beef wellington on Friday or I had prime rib. If I had beef wellington, I violated my low cholesterol diet, and the same is true if I had prime rib, so either way, I violated my diet.

  3. ‘not’: Let’s assume that P is true. If it is, then we can show that it leads to a contradiction or other sort of absurdity or unwanted consequence; therefore, P must not be true. (That is, not P must be true.) (Proof by Contradiction)   Let’s just say I really do work on your car; then, the next thing you know, you’ll be blowing a head gaskets, throwing rods, and dropping transmissions all over the place; believe me, you don’t want me working on your car.

  4. 'or' and 'not': Either P or Q is true; P is not true; therefore, Q is true. (Disjunctive Syllogism) Either my keys are in my jeans pocket or in the car; they are not in my jeans; therefore, they are in my car.

  5. ‘if ... then’ (1): If P, then Q; P is true; therefore Q is true. (Modus ponens) If I’m in my office, then my lights are on; I am in my office; therefore, my lights are on.

  6. ‘if ... then’ (2): If P, then Q; not Q; therefore, not P. (Modus tollens) If I’m on my way to the pool, I’m in my swimming trunks; I’m not in my swimming trunks; therefore, I’m not on my way to the pool.

  7. ‘just in case’: P just in case Q; one of them is true; therefore, the other is. (Or: P just in case Q; one is false; therefore, the other is.) John is a bachelor just in case he is unmarried; John is (isn’t) unmarried; therefore John is (isn’t) a bachelor. (Note: this will work with the propositions mentioned in the second and third claims reversed.)

There are several points to make about these. First, it is not uncommon that you have to dig to uncover the argument form in a particular case. People will use different terms and phrases in structuring their arguments, so it is important that you become familiar with the different terms associated with the sentential connectives. Further, it isn’t always the case that arguers mention the connectives—they may use gestures, or rely on a look or a tone. Finally, there is some flexibility to argument form, as we saw in our discussion of argument reconstruction. Second, the symbolic expression of the forms reveals their formal nature. The fact that you can represent the argument forms in this way demonstrates that the actual content of the propositions involved, i.e., what they say, is irrelevant to their structure. ‘P’ and ‘Q’ can be replaced by any proposition and, so long as they are related in the indicated ways, the argument produced will have a valid form. Third, most propositional arguments introduced in conversation or in written texts are complicated mixtures of the various forms introduced above. In effect, these forms serve as inference rules, transmitting you from claims with a certain structure to a new claim; as such, they can be linked in sequence to form longer and more complex arguments.

Finally, a word or two about procedures for verifying that an argument form is valid. As I have indicated, the forms above are valid because of relationships grounded in the connectives. The connectives serve as the foundation for the relationships between propositions because they guarantee that the complex proposition of which they are a part will have a certain truth value given the truth values of the constituent propositions. Given this, if a complex proposition containing a connective is taken to be true, we can expect certain claims to follow in certain conditions. For example, if we take ‘if P then Q’ to be true, then we can expect Q to be true when P is; in addition, we can expect P to be false when Q is false. These expectations are grounded in our understanding of the way that the truth value of the complex proposition depends on the truth values of its parts, a dependency that is secured by the sentential connective that connects these parts. In effect, sentential connectives are functions of truth values—they take as inputs the truth values of the constituent propositions and yield the truth value of the complex proposition as output. It is for this reason that sentential connectives are called truth-functional connectives. Thus, sentential connectives are the backbone of propositional argument forms, and when they are valid, these forms depend for their validity on their truth functional character.

This conclusion points to general method for assessing the validity of propositional argument forms. The truth-functional character of connectives can be represented with truth tables, which are tabular representations of input and output truth values. Truth tables are robust enough to represent entire arguments, and so can be used to reveal the truth functional relationships between the propositions in these arguments. Thus, they can be used to identify whether a given argument form is valid or invalid. Call this the Method of Truth Tables. For more on this method, see Lectures 9 and 10  and the handouts for Chapters 3 through 6 on the Philosophy 202 homepage.

III.2.D Categorical Arguments

Categorical arguments are a type of deductively valid argument that depend for their validity on the relationships between categories and individuals mentioned in their constituent propositions. In particular, these are relationships of category inclusion or exclusion. These categories are introduced by terms that express properties, terms like ‘zebra’ and ‘likes grass’. These property terms can either appear in subject position in a sentence, joined to what are called quantifier terms, such as ‘all’, ‘some’, and ‘none’, or they can appear in predicate position. Quantifier terms indicate how much of the category is involved in the claim. The sentence, "All zebras like grass," includes a property term, ‘zebras’, in subject position, and a property term, ‘likes grass’, in predicate position. The subject phrase in this sentence expresses the property being a zebra, while the predicate expresses the property, being a grass liker. The quantifier term, ‘all’, indicates that every item that falls under the category term—in this case every zebra—is involved in the claim. This sentence, then, expresses the proposition that every thing that is a zebra is also a grass liker. That is, the proposition claims that the category zebra is included in the category grass liker. These sentences express what we will call general propositions, as they do not concern individual items but rather categories of objects.

Category terms that form part of subject phrases in conjunction with quantifiers are typically common nouns, such as ‘plant’ and ‘coffee cup’. The categories that these terms contribute to the claim can be delimited by modifying the terms with adjectives, such as ‘wilted plant’ and ‘chipped coffee cup’, or with prepositional phrases. Two quantifiers contribute to these phrases, viz., universal quantification and existential quantification. Universal quantifier terms include ‘all’, ‘every’, ‘each’, and ‘any’, while existential quantifier terms include ‘some’, ‘a few’, ‘many’, ‘a’, ‘an’, and ‘the’ (as in "The tiger is a dangerous predator"). Terms like ‘no’ and ‘none’ are also used as quantifiers, functioning very much like a universal quantifier since they are used to assert something negative about an entire category. Predicates can also introduce categories into a claim. Predicates are verb phrases that typically combine a verb with a modifier, such as an adverb or adjective, such as ‘runs quickly’ or ‘tastes sour’. They can also explicitly express category containment with the copula followed by another common noun or noun phrase, ‘are animals’ or ‘is a disease’. (Note that ‘a’ as it appears in the second example is considered a quantifier, akin to ‘some’.)

Categorical arguments typically include sentences containing these terms and phrases that express general propositions, or propositions that relate one category to another. There are many such propositions, but the categorical relationships they express are variations on four forms, known variously as the categorical forms or the Aristotelian forms, as these were the focus of Aristotle’s syllogistic logic. These forms, listed in association with their traditional letters, are as follows, with ‘S’ and ‘P’ appearing in the position of category terms:

  1. A form: All S is P. Examples: All tigers are animals; each student in the class is bright; any fan of the Vikings is long-suffering; every forest fire should be respected; tigers eat meat. (Note the lack of a quantifier in the last example.)

  2. E form: No S is P. Examples: No bighorn sheep were seen by the group; none of the candidates impressed us; no chores were completed this morning.

  3. I form: Some S is P. Examples: Some of those apricots were mine; a few of the articles were worth reading; many people like gangsta rap; a person left his or her book here. (Note that an I form proposition is true even if only one S is a P.)

  4. O form: Some S is not P. Examples: Some students do not like logic; many people do not like gangsta rap; a few of the participants went away unhappy.

There are several things worth noting about these forms. First, the A and E forms are universal, in the sense that they apply to every member of the indicated category, whereas the I and O forms are existential, applying to some but (perhaps) not all of the members of the relevant category. The A and I forms are obvious, but the presence of negation in the E and O forms renders their status somewhat more uncertain. Nevertheless, an E proposition makes a claim about all members of class S, viz., that they do not have the property expressed by P, while an O proposition makes the same claim but only about some members of the class S. Recognition of this connection between E and O propositions reveals another pattern in the forms: A and I are what we can call affirmative forms, whereas E and O are negative forms. Thus, there are two generalizations that cut across our four forms, a fact that can be represented with the following table:






A form

I form


E form

O form


This exhaustively represents all of the relationships that can obtain between the categories S and P. Third, these forms can be realized by sentences that do not come close to matching the examples given above. As with most of the elements of critical thinking so far discussed, life in the real world of argumentative give-and-take is not so clean and neat—sentences are put to uses for which they are not well-suited, and eloquence can create complexity that conceals the basic message. There will come many a time when you must decide whether a lengthy and overwrought sentence expresses a short and simple categorical form, and you will do this by first looking for the relevant categories and then asking whether the sentence expresses a proposition that relates these categories by inclusion or exclusion. If the answer to this question is affirmative, you have yourself a categorical form. Fourth and finally, it is worth calling attention to the fact that the logical nature of these forms remains a topic of heated debate amongst linguists and philosophers. For instance, the logical nature of the definite article, ‘the’, has been a flash point for a century, with some arguing that noun phrases formed with the article (e.g., ‘the sentence you’re reading’, ‘the shortest spy’) are referring expressions, like names, that pick out particular individuals, while others argue that ‘the’ is a quantifier and these phrases are existential. While these debates rage on, most of the live rounds are discharged in academic journals and do not threaten those who teach or learn critical thinking skills.

We are now positioned to consider several common categorical argument forms. As before, I offer only a sampling of these forms, but the ones I offer are common and important. Nevertheless, there are other common and important forms that will remain unmentioned because of limits of space—a text on critical thinking or classical logic will supply many more for further consideration. As with the propositional argument forms, I introduce these first symbolically and then by example.

  1. All Ps are Qs; All Qs are Rs; therefore, all Ps are Rs.Example: All isosceles triangles are triangles; all triangles are planar figures; therefore, all isosceles triangles are planar figures.

  2. All Ps are Qs; Some Ps are Rs; therefore, some Qs are Rs. Example: All crab fishers love danger; some crab fishers fear death; therefore, some people who love danger fear death.

  3. All Ps are Qs; No Qs are Rs; therefore, no Ps are Rs.Example: All notetakers can write; no writers are illiterate; therefore, no notetakers are illiterate.

  4. All Ps are Qs; X is a P; therefore, X is a Q.Example: All Dead fans miss Jerry; Flower is a Dead fan; therefore, Flower misses Jerry.

  5. No Ps are Qs; X is a P; therefore, X is not a Q.Example: No Republican delegate will vote for Al Gore; Henry is a Republican delegate; therefore, Henry will not vote for Al Gore.

  6. No Ps are Qs; X is a Q; therefore, X is not a P.Example: No one who will vote for Al Gore for President is dead now; Millard Fillmore is dead now; therefore, Millard Fillmore will not vote for Al Gore for President.

  7. X is a P; X is a Q; therefore, some Ps are Qs.Example: Al Gore is a Vice President; Al Gore is from Tennessee; therefore, some Vice Presidents are from Tennessee.

  8. X is a P; X is not a Q; therefore, some Ps are not Qs. Example: George W. Bush is a Yale grad; George W. Bush is not from Connecticut; therefore, some Yale grads are not from Connecticut.

Once again, a few notes before moving on. First, as can be seen from these examples, categorical arguments do not contain only general propositions, and the general propositions they do contain need not be premises in the arguments. A categorical argument can maintain the inclusion or exclusion of individuals in categories, as well as categories in categories. The critical feature is that whereas propositional arguments are valid or not independently of any concern over category inclusion, categorical arguments essentially depend on this concern. Second, as with propositional arguments, it is often difficult to spot these straightaway, and they are often combined in complicated ways. In general, pulling an argument from a text is a risky business, and categorical arguments are no different. Third, the symbolic representations once again establish that form contributes substantially to good argumentation. The examples given above share their valid forms with countless other instances of impeccable argumentation. Of course, it is also true that countless bad arguments have valid forms (e.g., replace ‘P’ with ‘students’, ‘Q’ with ‘aliens’, and ‘R’ with ‘cats’ in (1) above), which just goes to show that form isn’t everything.

I conclude this survey of categorical arguments with a few words about procedures for determining validity. As should be clear by now, categorical arguments do not rely on truth-functional connectives for their validity, so the truth table method introduced above will be of no use to us here. Instead, we must introduce a method that captures the categorical relations of inclusion and exclusion that obtain among categories and individuals. The method to us involves Venn diagrams. These interlocking circles can be used to express relations between categories, and we can also introduce other mechanisms to extend the reach of the method, such as an ‘X’ for an individual and shading for the absence of individuals. Call this the Method of Venn Diagrams. For more on this method, see Lecture 6 on the homepage for Philosophy 404, or Chapter zxcv in Fogelin and Sinnott-Armstrong's book Understanding Arguments, which is mentioned at the end of the Applications section for this chapter.

III.3 Non-deductively Strong Arguments

I begin this subsection with a brief discussion of the general standards associated with non-deductively strong arguments and then turn to four important argument types: induction, abduction (i.e., inference to the best explanation), argument by analogy, and confirmation. I illustrate each of these types of argument and then speak to the standards of evaluation appropriate to each.

III.3.A Standards for Non-deductively Strong Arguments

Recall that non-deductively strong arguments are arguments that meet the following conditions: (a) the truth of their premises make it highly improbable that their conclusion is false, and (b) they are not deductively valid. Without the second condition, we would be forced to classify deductively valid arguments as non-deductively strong, since their conclusions must be true when their premises are, making it not only improbable but impossible that their conclusion is false when their premises are true. However, the second condition is not included as a way of deflecting attention to some weaker forms of argument; rather, it marks a difference in kind and not degree between arguments that deserve our attention. As I noted above, the conclusions of deductively valid arguments do not outstrip their premises—these conclusions present information that is contained implicitly within the information expressed by their premises. It is for this reason that they cannot fail but be true when the premises are true; after all, they don’t really say anything new. Conclusions of non-deductively strong arguments, by contrast, do outstrip their premises. They include generalizations or explanations that are only suggested by the premises, or they offer predictions that extend the information expressed by the premises into new and different quarters. Thus, they promise to tell us something that we don’t already know, at least implicitly, and thereby extend our knowledge. Painting with a broad brush for a moment, we can say that deductively valid arguments are the medium of conceptual analysis, exposing to the sunlight what lies hidden in the folds of a theory, whereas non-deductively strong arguments are the medium of empirical investigation, extending knowledge and understanding into new and uncharted territories. Given this role, it is crucial that we make sense out of what it is that renders an argument non-deductively strong, and this amounts to identifying the standards we apply when assessing it.

The place to start this search is the first part of the definition of non-deductive strength. Two notions stand out as central to this: the improbability of the conclusion, and the fact that we are given that the premises are true. Let’s begin with the second of these. An argument should be non-deductively strong because the premises support the conclusion; that is, the truth of the premises are what account for the fact that the conclusion is likely true. Thus, there must be some connection between the truth of the premises and the likelihood of the conclusion, and so "given that" cannot be read "when" or "while". Consider this argument: I passed a coffee shop on my way to work today, just as I did yesterday, and the day before that, and so on and so on; therefore, Bill Clinton is from Arkansas. If we were to read "given that" as "when"—and so take non-deductive strength to consist in the likelihood of the conclusion when the premises are true—then this would count as an non-deductively strong argument; after all, the conclusion is true as a matter of fact, and so is quite likely to be true when the premises are. The problem with this argument is that there is no connection between premises and conclusion—the premises do no work in transforming the conclusion into a highly probably truth. Therefore, we must take the truth of the premises to stand in some content relation with the conclusion, such that their truth explains our assessment of the conclusion. When we are given that the premises are true, we must evaluate the conclusion in light of that fact and not independently of it.

Second, there is the matter of probability to consider. It is this notion that separates the good from the bad. There are a lot of arguments out there that share their form with non-deductively strong arguments but are nevertheless putrid examples of reasoning. In the good arguments, it is highly improbable that the conclusions are false when the premises are true, but it may not even be better than chance that they are false in bad arguments of the same form. Thus, probability is at the core of our standards of non-deductive strength. But how are we to interpret probability here? And what counts as highly improbable? With respect to the first question, would that we were in a better position to say. While deductively valid arguments have an associated logic that describes their structure and underwrites their standards, there is no consensus choice for a logic of non-deductively strong arguments. In fact, there are serious problems with inductive probability and with the notion of strength that undermine general agreement about such logics. Nevertheless, for the purposes of critical assessment, we can rely on a standard model of probability to guide us in identifying principles that distinguish non-deductively strong arguments from those that are non-deductively weak. As for the second question, what counts as strength will depend on the interests and purposes of those engaged in the discourse. In scientific circles, there are statistical conventions in place to determine what counts as adequate strength—failure to meet these conventions will make it difficult to win grants and publish papers. Outside of these circles, things are much fuzzier, and this fuzziness vitiates any systematic attempt at interpretation. In lieu of such an attempt, I will introduce and justify context sensitive principles associated with the four forms of non-deductively strong arguments discussed below. In general, these principles require that the evidence cited in support of a generalization, an explanation, or a prediction be broad, diverse, extensive, and relevantly representative—in other words, that it reduce the probability of the risk taken in reaching beyond the premises by ensuring that the conclusion is as much like the premises as possible.

III.3.B Types of Non-deductively Strong Arguments

In this section, we consider four types of arguments that can be non-deductively strong. The first type, inductive arguments, is marked by a conclusion that generalizes more specific evidence cited in the premises. For instance, concluding that all John Waters’ films are quirky and bizarre on the basis of having seen a few of them is an inductive argument. Secondly, we have abductive arguments, or arguments that involve an inference in the conclusion to what one takes to be the best explanation of facts cited in the premises. Sherlock Holmes did a fair bit of abduction, and so have you if you’ve ever played the game Clue. So did I the other day when I inferred that I had left my paycheck stub in my jeans when I washed them from all the water-soaked paycheck confetti that was stuck to the entire load after the last spin cycle. Third, there are arguments by analogy. These arguments press conclusions about one matter that are motivated by the similarity between that matter and something else. When my friend argues that he will be a good father because he is good to his dog, he argues by analogy. Finally, there are confirmation arguments, or the testing of hypotheses. These arguments typically assert the truth of a theoretical claim on the basis of observational evidence that purportedly confirms the claim. These tend to start with conditional claims that include the theoretical claim as the antecedent and an observation as the consequent. Consider this instance: if exposure to the sun causes skin cancer, then we should find a higher incidence of skin cancer among those who spend a great deal of time in the sun; we do find such an incidence; therefore, exposure to the sun must cause skin cancer. Notice that in all of these cases, the conclusion reaches out beyond the premises, and therefore, it is possible that the conclusion is wrong in each case even given the truth of the premises. Such is life when you run with the non-deductively strong.

III.3.C Inductive Arguments

Inductive arguments begin with observations about specific instances of a particular type and then infer from these a more general claim about instances of that type. For example, on a hike at Robinson Park, I see only robins for the first 15 minutes, and this leads me to conclude that I will only see robins on my hike. There are several elements of this characterization that require elaboration. First, there is the nature of the type. In our illustration, the type is quite simple, viz., bird species spotted on my hike. However, the type in question can be complex, as when the observations concern a correlational relationship between events. For example, I have experienced countless events involving the opening of kitchen faucets, followed by the flow of water. This leads me to expect water when I turn a kitchen faucet on, and this expectation is grounded in the inductive generalization from my past experiences to my future experiences. The correlation in this case is causal, but it needn’t be, as when we correlate being good at the piano with being good at mathematics. Second, there is the nature of the generalization that is based on the particular observations. In the first example, I generalize to a conclusion about all the birds in my type, i.e., all the bird species I’ll spot on my hike. However, I might choose to weaken the generalization by commenting only on most of the bird species that I’ll see. Similarly, the faucet inference could be to a conclusion about all faucet opening events, but instead concerns only those that will figure into my future experience. (I might be suspicious about the overall generality of this claim.)

Arguments of this type are not valid, since the conclusion will cover instances of the type that you have not observed and so will extend beyond the premises, leaving open the possibility that they are true while the conclusion is false. I might see only robins for all but the last few seconds of my hike, when a flock of cedar waxwings catches my eye, or I might go to a friend’s house and find beer flowing from the tap. However, arguments of this sort can be strong nevertheless. Several standards bear on evaluations of this type of argument. They are:

  1. Representativeness: The more the observed events represent that type of event, the stronger the argument will be. If the observations are representative of the type, covering a sample that corresponds to a cross-section of the type as a whole, then the inference is much stronger than if it is not representative.

  2. Number: The greater the number of observations, the stronger the argument will be. The strength of the inference will vary directly with the number of observations.

  3. Strength of the Conclusion: The stronger the conclusion, the weaker the argument. If the conclusion represents a big reach, say to a universal claim of some sort, then it extends farther beyond the observations listed in the premises, and so is more susceptible to falsification. (This will be a standard for all non-deductive arguments.)

III.3.DAbductive Arguments

An abductive argument is an inference from a set of considerations, such as facts or clues about the matter at hand, to a conclusion that is deemed "best" of the available alternatives. This evaluation of the conclusion is made relative to a goal that motivates the arguer to serve up the argument. Two aspects of this argument type merit close scrutiny: the goal and the conclusion. First, the goal. For an example of one goal, we can turn to inference to the best explanation, where one is presented with a data set and infers from that a claim which does the best job of accounting for the data in the set. The goal in this case is explanation, and the conclusion is presented as the best available explanation of the data. If you’ve ever played Clue, or read a good mystery novel, then you have engaged in inference to the best explanation—in each of these cases, you collect together a set of clues and seek to determine whodunit, where identification of the criminal will best explain the available clues. (Here’s another example: "There is dirt on the floor by the plants and one of the stuffed animals is ripped up on the floor—the dog must have gotten loose again.") Abductive arguments needn’t be inferences to the best explanation; they might instead be inferences to the best judgment, or the best policy, or the best plan. (In fact, it would not be inappropriate, given our definitions, to consider inductive arguments to be a type of abductive argument, viz., inference to the best generalization.) In each of these cases, the goal motivating the arguer differs. As an example, consider how a university might determine a policy for dealing with hate speech: they could collect judicial opinions about First Amendment protections, advice from staff attorneys, views of students, faculty, and alumni, and precedents from other universities; once all of this information is collected, they would examine it to determine if an overriding policy direction emerges, and this might then become the policy they adopt. In such a situation, we have an inference to the best policy, where the considerations include the evaluative opinions of other experts and institutions.

And then there is the conclusion. To begin, it is important to note that these arguments typically do not purport to identify the best possible way to achieve the goal; rather, they claim only to identify the best available way. The alternative conclusions available will vary dramatically, often as a function of awareness and imagination, to name two important factors. Second, there will be nothing about the considerations you adduce that force you to adopt one of the available conclusions over the other alternatives—it could always turn out to be the case that one of the other conclusions is in fact superior. This points to the invalid nature of the inference; since there is nothing about the considerations that are mentioned in the premises that force the conclusion to be true, the argument is not deductively valid. (In fact, if you run an argument like this and you find one conclusion forced on you, it may well be better to represent it as a deductively valid argument.)

But once again, even though this form of argument is not deductively valid, it can nevertheless be strong. The strength of the argument turns on two issues: (a) whether the conclusion is really the best (or is at least debatably the best) of the available alternatives, and (b) whether the set of alternatives includes legitimate and plausible members. The standards one must impose in analyzing these arguments are keyed to these two issues, and so we will organize the standards accordingly.

  1. Best Conclusion: The more relevant considerations accommodated by a conclusion, the stronger that conclusion will be. Furthermore, the more apparent relationships between the considerations accommodated by a conclusion, the stronger that conclusion will be. If the list of considerations is long, it may be that no one conclusion accommodates them all. In such a case, you will likely be guided in your assessment of the alternatives by a hierarchical ordering of those considerations, from most important to least important, trading off breadth of coverage for importance of considerations covered. It may also turn out, in the course of things, that some of the considerations adduced are noise, i.e., considerations that appeared to be relevant but were not.

  2. Plausible Alternatives: This assessment is made of the set of alternatives as a whole, and it is highly context-sensitive. What might seem a plausible set to you, given the issue, may well appear narrow and implausible to someone with more imagination or more experience. On the other hand, it may turn out that what all regard as plausible up front turns out to be implausible because every available alternative fails to satisfy a crucial desideratum and so they must all be rejected. (For example, consider a criminal investigation in which all the suspects have solid alibis.) Or perhaps in the course of assessing the alternatives, new information comes to light, pointing the way to new and different alternative conclusions. The important thing here is to remember this dimension of analysis—the best car from a bad lot is still a lemon.

III.3.E Argument by Analogy

An argument by analogy consists of two salient parts, viz., an analogy and an argument. First, there is the analogy. This involves the telling of a story that is intended to parallel some take on the topic in question in certain salient respects. For instance, if in a conversation about cats a friend draws an analogy between caring for a cat and caring for a teenager, the analogy will be suggestive only if there are significant similarities that shine through the many differences. In this case, there are, since both involve taking care of another organism that doesn’t seem to want much to do with you. Here the care of cats is the topic and the care of a teenager is the story. Note that the similarities are primarily structural, while the differences are material, i.e., the topic and story are similar at the more abstract level of the relationship between care giver and cared for, with the differences entering in as these roles are occupied in each case. Good analogies have that character: they involve a story that is structurally similar to the topic, even though the specific content of each may differ dramatically.

Second, there is the argument. One may introduce analogies for all manner of reasons, among them amusement, intellectual exercise, and literary flourish. One significant role analogies are asked to play is that of motivating a conclusion. As such, they serve as reasons for the conclusion, and so are at the heart of the argument. When an analogy is put to argumentative work, it is typically done in the following way: once the story is introduced, the arguer derives an inference from it, perhaps to a moral; then, because of the structural similarity between story and topic, the arguer suggests that the topic motivates a similar conclusion, differing only in the content-related ways that story and topic differ. In the story, a certain conclusion follows, so because the story and the topic have the same structure, the same conclusion (mutatis mutandis) should follow from the topic. (Consider: "My son said something like that to my daughter when he was trying to trick her into giving him her allowance. Are you trying to swindle me?") This is a very suggestive and powerful way to argue. Among other virtues, it can keep a highly controversial topic on the table by retaining its structure through changes in detail that are meant to defuse the passion and controversy that frustrate straightforward attempts to address the topic. A classic argument found in discussions of abortion exemplifies this: consider that a fetus is to a person as an acorn is to an oak tree; note that when you kill an acorn, you are not killing an oak tree; therefore, when you kill a fetus, you are not killing a person. Without passing judgment on the merits of this argument, it does demonstrate how an analogy motivates transferring a conclusion from one an uncontroversial context to a more controversial context. However, this form of argument is obviously invalid, since an analogous story must be different from the topic in several, if not many, respects, and so there is quite a bit of room for falsehood to creep in. Thus, the analogy may be a good one, but the differences that exist between story and topic might be enough to undermine the inference from the topic to the desired conclusion.

Even so, some arguments by analogy are better than others, and we can identify standards that help distinguish the good from the bad. Some important standards that apply are as follows:

  1. Plausibility: The more plausible the story, the stronger the argument.

  2. Structural Similarity: The more structurally similar the story in an analogy is to the topic, the stronger the argument formed around this analogy will be. Structural similarity may increase either in spread or in detail, where one but not the other of these might be more important in particular argumentative contexts.

  3. Inferential Strength: The more closely connected the conclusion about the story is to the shared structural elements, the more closely connected the desired conclusion (mutatis mutandis) will be to the topic.

III.3.F Confirmation Arguments

The last non-deductive argument we’ll consider is the confirmation argument. This type of argument, one begins with a theory, or perhaps just a hunch, and reasons that if this were true, then so would some additional claim; upon further investigation, one establishes that this additional claim is indeed true, and this supplies a certain degree of confirmation for the theory. The argument is a report of this process, beginning with an assertion of the starting point and the claim it implies, followed by the announcement that this claim is in fact true, establishing that at least on this point, the starting point is confirmed. This type of argument is at the heart of the experimental method in the sciences—an experiment is a controlled test of an implied claim (i.e., a hypothesis) designed to determine if the theory that implies this hypothesis is deserving of credence. Thus, science is home to many instances of this type of argument, but it is also instantiated in much less controlled and elaborate settings. Consider: "Look, if you are who you say you are, then you should remember the time we went out to the dam, back after high school graduation, and ... —you do remember! It must be you!."

This argument type has a number of elements that deserve further elaboration. First, there is the starting point. As noted, this could be a full-blown theory, or it could be something as sketchy and provisional as a hunch. In any case, it will be some sort of representation the truth of which is in question. The confirmation argument is designed to buttress the claim this representation has on truth, and it does this by focusing on a claim this representation implies. Thus, the representation must be robust enough to imply substantive claims that can themselves be tested for truth. The relation between representation and the implied claim is the second element. This could be deductive implication, but it needn’t be—it could, for instance, be some sort of non-deductive implication, such as an abduction. The key to this sort of argument is that the truth of the representation increase the likelihood of the implication, so that if the implication is found to be true it casts a positive light back on the representation. The more the implication depends on the representation, the greater the degree of confirmation it can supply. Third, there is the nature of the implied claim. The crucial thing about the implied claim is that it must be testable—if it isn’t, then it will not contribute to a confirmation argument. In scientific cases, it will typically be an observable claim about the physical world. (There are cases of implied claims that cannot be tested as yet, or perhaps can never be tested; these are claims that, while implied, are not part of any confirmation arguments.) In the more mundane cases, the claim will still be testable in some fashion, and in most cases the test will involve observation in some central way. Finally, there is the nature of the test. In arguments intended to establish conclusions with scientific precision, the test could be some sort of controlled experiment. Alternatively, the test might involve the type of discovery that field work or just dumb luck could supply. In less constrained cases, the test might involve simple observation. In all cases, however, the test involves assessing the implied claim for truth, and how this is done will vary with from claim to claim, depending on whether it is more observational or theoretical in character.

An example of a very well-developed account of this type of argument is found in Hempel 1966. In this book, Hempel details what has come to be called the hypothetico-deductive method for determining assessing hypotheses and, ultimately, the theories from which they derive. According to this account, scientific labor involves (a) the identification of hypotheses, or candidate explanations of phenomena, that flow deductively from background theories, and (b) the empirical and often experimental evaluation of these hypotheses to determine their truth. If they are revealed as true by their evaluation, then they offer a certain measure of confirmation for the theory that implied them; however, if they are shown to be false, then deductive logic takes over and conveys the falsity back to the theory, in conformity with modus tollens. Of course, the actual situation is much more complicated than this simple sketch suggests—falsity is often difficult to determine, for sure, and the falsity conveyed back to the theory may only reveal the inadequacy of some auxiliary assumption that can be rejected without damage to the background theory. But even so, the method supports either confirmation or falsification, depending on the evaluation of the hypothesis.

Like the other forms of non-deductive inference, confirmation arguments are invalid when they supply confirmation for theories. In fact, when the hypothesis is deductively inferred from the background claims, the argument shares its structure with a famous fallacy that we will study in the next chapter, viz., affirming the consequent. Even so, this sort of argument captures the importance we typically assign to consequences—if the consequences of some set of claims are themselves valuable according to some measure, then this value redounds to the credit of the set of claims. (This sort of reasoning is especially prevalent in moral theory.) However, a given hypothesis designed to lend such support may wind up serving as a part of a deductively valid modus tollens argument for the falsehood of a theory. The centrality in this discussion of confirmation and falsification of theories by the hypotheses they imply exposes the important connection between this type of argument and prediction. One desideratum of a theory in any domain is that its predictions be realized, and confirmation arguments derive their force from value ascribed to predictive success. This can be contrasted with, for example, abductive arguments, which are keyed to a different desideratum, viz., explanation. Together, these argument types underwrite the rational attempts we make to understand the world of our experience.

Given the importance of confirmation arguments to the construction of a rationally defensible worldview, it is incumbent on us to identify the standards that divide the good from the bad. These are grounded in the structure of the inference type, the elements of which were identified above. Thus, we have the following standards:

  1. Strength of Implication: The stronger the connection between background claims and implied hypothesis, the greater the degree of confirmation afforded the background claim given the truth of the hypothesis. Strength of connection is determined in accordance with the standards listed in this chapter, where deductive implication is stronger than any sort of non-deductive implication.

  2. Experimental Certainty: The argument will only be as strong as the degree of certainty associated with the truth value of the hypothesis. If it is directly established through unmediated or repeatable observation, it will be stronger than if it is established indirectly through mediated observation or theoretical implication.

  3. Strength of Conclusion: The more a confirmation argument is asked to confirm, the weaker the confirmation supplied.


IV. Subject Matter Analysis

Formal analysis is devoted to evaluating the structure of arguments. An argument that is poorly structured will be ill equipped to compel one to embrace the conclusion, given the truth of the premises. But while form can break an argument, it cannot make it. An argument with unimpeachable form must still pass muster at two additional levels of analysis, viz., subject matter and context, if it is to be rationally compelling in most episodes. In this section, I focus on subject matter analysis.

Subject matter analysis concerns what the argument is about, where this is determined by its constituent claims. Each premise, along with the conclusion, will make a claim that is either true or false of the world, broadly construed, and the claim made by each of these counts as its content; the content of the claims taken together counts as the content of the argument. An analysis of the subject matter of an argument, then, is an analysis of its content, and this resolves into an analysis of the content of its constituent claims.

We analyze the content of the constituent claims in two ways. First, we need to be sure that the set of claims is thematically coherent. Second, we need to be sure that the claims themselves are true. We begin with a few remarks about coherence. A necessary condition on compelling arguments is that their conclusions concern the same subject matter as their premises. One can have arguments that are formally impeccable even though they fail to satisfy the thematic coherence standard. For instance, consider this argument:

P1. If the Democrats succeed in countering the negative effects of Clinton’s misdeeds, they will win in 2000.

P2. The Democrats will succeed in countering the negative effects of Clinton’s misdeeds.
C. Either this handbook is here or it isn’t here.

Since there is no way the conclusion of this argument can be false when the premises are true, this is a deductively valid argument by our lights; however, the argument is nevertheless in bad shape, due to its failure to satisfy the standard of thematic coherence. In a case such as this one it is easy to detect a failure to satisfy the standard, but it is not easy to make precise exactly what it takes to meet it. Fortunately, our purposes in this handbook do not require a precise definition of the standard. The crucial thing to determine for any argument is whether the conclusion and premises either share predicates and/or names of items, or contain predicates and/or names that stand in semantical relationships that are relevantly similar, given the nature of the argument. This is altogether too vague, of course, and it isn’t clear that the context couldn’t justify violation of this. (Consider: the above argument failed to meet the standard, but it did the job of illustrating the point I wanted to make and so was perfectly legitimate.) In most episodes, however, sensitivity to this rough and ready rule of thumb will ensure that a violation of thematic coherence is duly noted.

Given that the steps of an argument are thematically coherent, we are then set to determine whether the claims are true. Recall that the two principal formal standards, deductive validity and non-deductive strength, both specified the formal strength of arguments in terms of truth: in arguments that meet these standards, we have good reason to believe that the conclusion is true given that the premises are true. The conditional nature of both standards is tied to the flow of truth—when a certain condition, identified in terms of truth, is satisfied, then we have good reason to believe that truth flows to the conclusion. Thus, full assessment of an argument requires determining whether the premises are in fact true so that our hypothetical appreciation for the conclusion can become categorical.

Premises come in one of two forms: either they are obviously true, or they are not. If they are obviously true, they are either true because they are a first principle and so make a claim that we all find intuitively true in virtue of our status as rational beings, or they are true because they are trivial. (Perhaps there is not a real difference between these?) First principles are hard to come by—Descartes thought he found one, but there are many who believe that he should have thought harder. As for the second sort, we have claims like the conclusion above, "The handbook is here or it isn’t here." These claims are known as tautologies, and the truth of these claims is guaranteed by their form, regardless of their specific subject matter. As a result, they are trivial claims that add nothing to arguments that contain them. (Of course, tautologies in the wild are almost never as obvious as this, even though they are no more informative or any less trivial.) Thus, most of the premises that really pack a punch will be claims that are not obviously true. These will come in many forms and will concern as many things as concern us, and a good many of them will find their support in additional argumentation. To be sure, we will be able to read the truth values of some of these off of the world directly, via observation, but often premises in one argument will be conclusions of supporting arguments and will depend on those supporting arguments for their force. As a result, the task of determining the truth of such a premise will depend on the nature of the subject matter it concerns. It is at this point that logic and formal methods give way to the facts and methods characteristic of specific subject areas. For instance, a full assessment of an argument in organic chemistry requires familiarity with the details of organic chemistry, assuming of course that the form of the argument withstands scrutiny. Thus, in addition to formal facility, critical thinking requires subject knowledge, and the range of contexts in which one can apply critical thinking skills will increase in direct proportion with the number of subjects one knows.

If the premises of a formally strong argument emerge as true, the argument must be regarded as establishing its conclusion. If it is deductive, we say that it is sound in this case, where soundness requires both validity and true premises. There is no corresponding term for the non-deductive case, although most arguers will accept compelling in its place.

V. Context Analysis

But wait! The analysis is not yet complete. It is an accomplishment to craft an argument that measures up to both formal and subject matter analysis, but such an argument may nevertheless fail to have the intended effect. Outside of critical thinking classrooms, people do not argue in a vacuum—arguments are typically adduced in the service of achieving broader goals, e.g., creating consensus, advancing one’s research agenda, creating community, getting one’s way, etc. Given this, there remains one level of analysis to discuss, viz., context analysis. How does the argument fit into its context? If it fails to fit the context, it likely will not compel even though it is unobjectionable when considered by itself. If it fits its context, then it should have its intended effect, assuming a certain level of rationality on the part of the audience.

What counts as context is a vexed philosophical question, and it seems likely that there are no necessary and sufficient conditions for delimiting it. The relevant frame for conducting this sort of analysis of an argument will change given the subject matter, the participants, the location of the argument, the surrounding political climate, etc. etc. We are quite adept at intuitively recognizing what is relevant and what is not in specific circumstances, but identifying a small set of generalizations that systematize these elements is a very tall order, and one I am in no position to fill. Nevertheless, there are a few common contextual dimensions that recur regularly and warrant mention here. They correspond to elements in a typical argument episode, and are listed here in connection with those.

  1. Discourse Context: Arguments are typically supplied in a discourse, where that could be a conversation or a temporally extended dialogue that takes place in scholarly journals, among many other things. In fact, a given argument might have a place in a number of overlapping discourses, and it may be evaluated differentially according to its different place and function in these discourses. The other arguments that figure into these discourses will influence how one regards the argument under scrutiny. For instance, if a given confirmation argument ends in a conclusion that is repeatable, or buttressed by other results that also lend confirmatory support to the background claims, then the argument under analysis will be strengthened. Think here of a tripod, where the arguments figuring into the discourse serve as the legs; the individual legs in the tripod would collapse if they were not supported by the others, and the same is often true of arguments. Alternatively, a given argument, while sound on its own, may be an isolated voice in a wilderness of counter arguments that are equally compelling. In such a case, the analyzed argument will suffer in this context. (Keep in mind that the first volleys in an intellectual revolution are arguments in such a context, so while the argument suffers it needn’t die, and what begins as a lonely cry may in retrospect be regarded as a call to arms.) Thus, when one analyzes an argument along this contextual dimension, the focus is on the company that the argument keeps.

  2. Intentional Context: An argument is advanced by an arguer, and the arguer usually does this with some goal in mind. However, it isn’t always the case that the argument fits with the goal—the arguer may be somewhat confused, or perhaps misled about what is required to achieve that goal. In such a case, there is dissonance or perhaps inconsistency between the argument taken individually and the broader argumentative plan of which it is a part. As a result, a perfectly good argument might fail in its context because it isn’t relevant to the goals of arguer. Contextual analysis along this dimension can reveal this, assuming that enough information about the surrounding plan is available to support it.

  3. Practical Context: Even if an argument fits into the plan of the arguer responsible for it, that may not be enough if the plan itself fails to fit the overall discourse in which the argument fits. For instance, someone may have an agenda that they pursue in a conversation that, unbeknownst to them, fails to mesh with the issue at hand, perhaps again because of confusion. (Think here of Rosanne Rosanna Danna, of Saturday Night Live fame.) In such a circumstance, contextual analysis will reveal the failure of fit, and this failure should influence one’s critical reaction to the argument.

There are other dimensions, but these three stand out as more or less general and, where they are found, critical. An argument that runs the gauntlet of analysis, avoiding pitfalls of form, subject matter, and context, will stand out as compelling and will have a deserved claim on the beliefs of those who value rational consistency.

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