English Question (philosophy)

On Critical Thinking and the Nature of Logic

In this course we seek to know what constitutes knowledge, how to acquire it, and how to represent it to others. Our study resembles that of epistemology more than rhetoric. We do not seek to persuade anyone of anything unless it be the truth; vero nihil verius (nothing is truer than truth) is our law. Recognizing or determining what is true requires critical thinking, the subject of our study, and representing such truths as we can discover in writing requires great skill and practice. The use of logic has long been thought to illuminate the road to truth, so it behooves us to begin our journey by looking into how and why that is. The word “logic” comes into English from Old French but seems to be a combination of two Greek words: logos (word, reason) and techne (art, craftsmanship). From an etymological standpoint, then, “logic” names the art (or process, or technique) of reasoning. We find the term “logos” first in the writings of Heraclitus, a Greek who wrote before the time of Plato. Exactly what Heraclitus means by the term has long been a matter of debate, but he seems to use it to name what might be called “the world process”: the most basic thing in the universe. Subsequent to Heraclitus, but still prior to Plato, the Pythagoreans used the term “logos” to name their most characteristic idea: the universe is an ordered thing, and the order can be found in and described by numbers. These days, when we say or think that something or other is “logical,” what we mean is that it is characterized by clear thinking or that it is a natural consequence of the circumstances. One is tempted, then, to describe logic as a mental thing that follows or piggybacks on the universe outside of us. The Greeks, however, considered logic to be the order of the universe, not simply a mental process in humans. So, to the extent that we are thinking logically, we are directly imagining the shape and order of the universe. Viewed in this way, logic would seem to be a very powerful tool for imagining what the universe is really like: the truth of the universe. From these considerations, logic would seem to be the truest arrow in the quiver of our critical thinking. The concept of logic espoused here is a Greek one. It is implicit in the ideas attributed to Thales, but informs the writings of nearly all of the thinkers that we call Greek philosophers, finding its most systematic expression in the works of Aristotle. It assumes a universe separate from and anterior to human consciousness. Logic, then, may be described as the study of the most basic characteristics of the universe that is inhabited by all of us. It provides us with the landscape for correct reasoning in that correct reasoning is understood to be grounded in the nature of things. Logic contains the basic principles for studying “being as being” as Aristotle has it. Logic provides the ground rules for all critical thinking and expression, which must be accepted by all in order to avoid what logicians Cohen and Nagel call the

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stultification of all thought. Among these ground rules are the laws of thought and some common inferences that apply to all things that are or may be. A possibly unsatisfactory aspect of some of these ground rules is that they cannot be proved as such because there are no more basic assumptions that can be formulated into premises from which they can be drawn as conclusions. We simply agree to agree to them so that discourse can proceed. If by discourse we mean broadly a connected series of utterances, which may in some cases be written down, then we might ask what “connected” actually means. If, for instance, you were relaxing at home some evening, and a knock at the door caused you to open it to a man who was uttering a series of animal names, you would be puzzled and perhaps frightened because you might not know how these actions connected to anything else in your life. But if you opened your door to a neighbor who informed you that the house next door was on fire, your puzzlement and fright might lead you to think of calling 911 or of stepping outside to assess the situation. In the first instance, the animal names do not constitute a claim or complete thought, so there is no consciousness of anything’s being true or false, and no consciousness of anything else’s being true or false as a consequence. In the second instance, the truth of the claim that the house next door is on fire would mean that other things were true. Among these might be that smoke is present or that your own house is in danger of igniting. Precisely in that space between the utterance of “the house next door is on fire” and the next event that takes place is where we must search for logic. Our search consists of exploring the relationship between the truth of one claim and the truth of another. That relationship is limited: if one claim is true, then the next claim can be true, or false, or unknown. Let us consider the claim, “The current month is January.” If this claim is true, then we can find the truth of the claims, “Next month is February,” “Last month was April,” and “Next month it will be cold.” These claims are respectively true, false, and unknown (the last is unknown because we do not know the relevant geographical area). One of logic’s most important areas of study is the relationship of implication or entailment. Cohen and Nagel claim that logic just is the study of implication. We do not necessarily have to agree with that claim to understand the importance of the relationship, so let us consider it. We say that one claim implies or entails a second claim if and only if it is impossible for the first claim to be true and the second claim to be false. Consider two claims: (1) “My sister lives in Syracuse” and (2) “I am not an only child.” If it is true that my sister lives in Syracuse, then it must be true that I am not an only child. We say that claim (1) implies claim (2), or claim (1) entails claim (2), or claim (2) necessarily follows from claim (1).

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Now consider two further claims: (3) “My sister lives in New York” and (4) “I can easily visit my sister.” Is it possible for claim (3) to be true, and claim (4) to be false? It would certainly be possible if I made the claim from Tokyo or jail. So, we cannot say that claim (3) entails claim (4). When two claims are related by implication or entailment, then, like Sherlock Holmes, we can make a deduction from one to the other. We can deduce from the truth of “My sister lives in Syracuse” that “I am not an only child.” But, we cannot deduce from “My sister lives in New York” that “I can easily visit my sister.” The relationship of implication or entailment is strict and formal. It only holds if it is impossible for one claim to be true and another claim to be false. It is not sufficient that the second claim be highly likely. The truth of “the sun rose this morning” does not imply the truth of “the sun will rise tomorrow morning” even though every day in human memory has affirmed the likelihood of the latter. It is conceivable that the sun could go nova or that something could interfere with the earth’s rotation, making it false that the sun will rise tomorrow. The relation of implication depends on the thing being implied’s being part of the meaning of the thing implying. If I have a sister living in Syracuse, then I cannot be an only child because the meaning of “only child” is that a person has no brother or sister. The most basic rules governing relationships such as implication are three in number and are often referred to as the laws of thought (though, as Cohen and Nagel point out, they are not about thought at all, but the universe itself). The first is the law of identity: a thing is equal to itself. In terms of discourse, if a claim is true, then it is true. The second is the law of non-contradiction: a thing cannot be itself and not itself at the same time. In terms of discourse, a claim cannot be true and false at the same time. The third is the law of the excluded middle: a thing exists, or it does not exist; there is nothing in between these two states. In terms of discourse, a claim is true or it is false. Logic, to sum up these points, can be seen as the description of the most general qualities of things in the universe and the study of the most basic relationships among them. Critical thinking employs logic, as well as other tools, to determine and communicate truths about a shared universe that exists independent of the thinker. We make claims about this universe such as “today is warmer than yesterday,” and according to the law of the excluded middle, these claims are either true or false. Thinking might be described as the process of moving one’s attention from one claim to another. In doing so, one evaluates the truth or falsity of some claims in an effort to determine the truth or falsity of others. This is the process of inference. When the relationship between the claims under consideration is one of implication, then we are making a valid inference, which is completely reliable because it is necessary or truth preserving. Such inferences are very useful for finding and expressing truths, but they are limited to a small number of forms.

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The best known of these forms is the modus ponens. A modus ponens is a valid or deductive inference that takes the form “If P, then Q; P is true; therefore Q is true” (where P and Q can stand for any proposition). In plainer English: If I run a mile, then I get tired. I run a mile; therefore, I get tired. A related inference is the modus tollens. It is also a valid or deductive inference, and it takes the form “If P, then Q; Q is not true; therefore P is not true.” In natural English: If it rains, then the corn grows tall. The corn does not grow tall; therefore, it doesn’t rain. The modus ponens and modus tollens are valid argument forms in addition to being valid inferences. They each consist of two propositions (a proposition can be thought of as the meaning or content of a sentence that is either true or false) that offer reasons to ascribe truth to a third proposition. The propositions offered in support are called premises and the proposition being supported is called the conclusion. An argument, for our purposes, consists of at least two propositions (the number is theoretically infinite); the truth of at least one of which is supported by the others. While arguments containing valid inferences, deductive arguments, are extremely effective in elucidating truths, they are not the only kind if argument. Other arguments contain inferences that support the truth of their conclusions but do not guarantee it the way that deductive arguments do. The inferences in these arguments rather than being necessary are only probable inferences. An example of such an inference is “There are low, dark clouds in the sky, so there will be a thunderstorm.” Can we think of a situation in which it is true that there are low, dark clouds in the sky, but no thunderstorm occurs? If the answer is yes (which it is), then we cannot claim a relationship of implication or entailment between these propositions, and we cannot claim that the second one is necessarily true. The first proposition offers only probable support for the second, so we cannot call the inference a deduction. We must call it a probable inference or an induction. We are now in a position to clarify what critical thinking means in the context of this course. Critical thinking is a mental search for what is true. It manifests itself in the use of verbal or written arguments, containing deductive or probable inferences offered in support of some claims. Critical thinking is never demonstrated by those who offer only conclusions or answers without premises or reasons. Slogans shouted at demonstrations, no matter how loudly, or painted on signs or billboards, no matter how boldly, cannot be analyzed or evaluated for their truth value until the premises are made explicit and the inferences characterized according to the time-honored principles of the study of logic.

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