Logical and Conceptual Principles

Logical and Conceptual Principles 14.1 Logical principles From the point of view of formal logic, there is an even deeper level at which our reasoning depends on principles. Although we are not currently engaged in the study of formal logic, it is both interesting and important to understand why this is so. To begin consider the following reasoning: 1. Bob is friendly. 2. Sally is feisty. 3. Bob is friendly and Sally is feisty. You will recall that this is not the sort of reasoning that particularly interests us from a practical point of view. This is because while 1 and 2 do logically imply the conclusion, they seem to have no evidential or explanatory significance. Put differently, it is very strange and unhelpful to say that the reason (or the reason we believe that) Bob is friendly and Sally is feisty is that (1) Bob is friendly and (2) Sally is feisty. From a practical point of view we are inclined to say that the relation between the premises and conclusion in the reasoning above is completely trivial. But this is actually incorrect. From the point of view of formal logic, this inference is not at all trivial, and our ability to perform it depends on a logical principle, otherwise known as a rule of inference. The rule is this: • If the sentence 'P' is true and the sentence 'Q' is true, then the sentence 'P and Q' is true. Once you understand this rule, you may be tempted to say that it is so obvious that it is hardly worth mentioning. But it's obviousness does not it any way make it trivial or unimportant. The recognition that inference depends on these rules has been absolutely critical to the development of formal logic, which in turn has had enormous influence on the development of fields like mathematics, linguistics, computer science and electrical engineering. Rules of inference validate certain forms of reasoning by generalizing on the sentences themselves rather than the things the sentences are referring to. These rules underwrite all of our valid reasoning, but they are ordinarily hidden even more deeply than the principles we think of as connecting reasons to conclusions. Since this is not a course in formal logic, these rules will, for the most part, remain hidden from us. However, it is important to take a moment to understand how logical principles function beneath the surface of the reasoning that we are analyzing. The rationales we construct can easily be put in the same form as the example above. For instance, if you are given the reasoning. • Phil fell ill because he caught a chill. you would reconstruct as an explanation as follows But you could also reconstruct it in the traditional way as follows. 1. Phil caught a chill. 2. If person x becomes chilled, then x falls ill. 3. Phil fell ill. We think of premise 2 as the principle that provides the connection between 1 and 3. But the truth is that this principle does not connect 1 to 3 all by itself. The connection is itself facilitated by a few different rules of inference. The main one is this: • If sentence 'P' is true and sentence 'If P, then Q' is true, then sentence 'Q' is true. This inference rule is known as "affirming the antecedent" and has been known for centuries by the Latin phrase modus ponendo ponens, or just modus ponens for short. In the above example, premise 1 would correspond to P, premise 2 would correspond to 'If P, then Q' and the conclusion, sentence 3, would correspond to Q. So even though we will continue to speak as if 2 connects 1 to 3 all by itself, the truth is that this connection depends on a more fundamental logical principle that permit this kind of inference in the first place. 14.2 Logical principles vs. empirical principles Most of the principles we will attribute to people's reasoning are empirical in nature. They contain information about how the world works. Logical principles are different. They tell us specifically about how logical inference works. Because of this, there is an absoluteness to logical principles that is not characteristic of empirical principles. This absoluteness can be expressed in two different ways. First, logical principles do not have any exceptions. There is, for example, no exception to the rule of modus ponens. By contrast, almost all of the empirical principles we use in everyday contexts do have exceptions. This holds even for highly reliable scientific principles. The reason is very simply that where the real world is concerned, there is usually some way that it is at least theoretically possible to prevent the antecedent conditions represented in a principle from producing the conditions represented in the consequent. For example, it is a highly reliable principle that if you jump off of a very tall building you will die on impact. But this can be prevented in any number of ways: a parachute, a net, a strong updraft, or dumb luck. Second, logical principles are necessarily true. In other words, logical principles do not just express facts about the world that might have been different, or might actually be different in some other possible world. Rather, logical principles are true in every possible world. Logical principles are such that to deny them leads to some fundamental absurdity. This is not the case with empirical principles. We say that empirical principles are contingently true, which means that if certain fundamental features of the world were different, then the principle would simply no longer hold. The difference between logical and empirical principles is something that will occupy us later when we study a particular kind of logical error called a priorism. This error consist in treating an empirical principle, which may have exceptions, and which may actually be false, as if it were a logical principle, which is necessarily true. 14.3 Conceptual principles Empirical principles, which concern how various aspects of the world are related, may be distinguished from conceptual principles, which concern how concepts are related. Logical principles are conceptual principles; they are principles about how logical concepts are related. But there are principles pertaining to all of the concepts that we use, not just logical concepts. For example, the following are conceptual truths: • • • • • If x is an even number that x can be divided by two. If x is a planet, that x is in orbit around a star. It x is a chair then it is designed to be sat in. If x is an eye, then it is sensitive to light. If x is a game that it requires players. Conceptual principles are sometimes represented as if they have the absoluteness of logical principles, though this is not obviously correct. At any given time it may seem that a conceptual principle is such that it would be absurd to deny it. But conceptual principles often are denied with fruitful results. For example all of the following were once were regarded as conceptual truths:. • • • • • • The earth is the center of the universe. There is no number less than zero. Space has three dimensions. The mind is distinct from the body. Species do not evolve. Waves require a medium. None of these are now held to be true. Scientific inquiry is constantly challenging our conceptual truths, though it does not appear to have the same capacity to challenge our logical truths. This is because logical truths underwrite the possibility of scientific inquiry itself. 14.4 The practical significance of conceptual and logical principles Although both conceptual and logical principles tend to operate at a deeper level then we are typically concerned with when analyzing reasoning for practical purposes, these principles do occasionally come into the foreground. For example, it is a conceptual principle that an object can't be at two places at once. You would be using this principle if you reasoned as follows: • Mitchell can't be at Ann's house because he's at the movies with Courtney. Purely logical principles are a little more reluctant to be brought out into the open, but it does happen on occasion. For example, it is a logical principle that if something actually happens, then it is possible for it to happen. You would be using this principle if you reasoned as follows: • I know it's possible for someone to survive a fall from a ten story building because it's actually happened before. Here is another example of reasoning that appeals to a purely logical principle. • Raj was going to come by here either late last night, or early this morning. He didn't come by last night, so I guess he'll be here this morning. This logical principle is the principle we use whenever we reason by a process of elimination. The classical name for it is "disjunctive syllogism." It is interesting to reflect on the fact that the reason in the above rationale does seem to satisfy an evidential function even though it is connected by a principle only slightly less obvious than the one we used above to infer the conjunction 'P and Q' from the individual sentences 'P' and 'Q'.