Socratic Logic: A Logic Text PDF

# Socratic Logic: A Logic Text Using Socratic Method, Platonic Questions & Aristotelian Principles ## Edition 3.1 **By Peter Kreeft** **Edited by Trent Dougherty** ### A Logic Text Using - Socratic Method, - Platonic Questions, & - Aristotelian Principles Modeling Socrates as the ideal tea...

# Socratic Logic: A Logic Text Using Socratic Method, Platonic Questions & Aristotelian Principles ## Edition 3.1 **By Peter Kreeft** **Edited by Trent Dougherty** ### A Logic Text Using - Socratic Method, - Platonic Questions, & - Aristotelian Principles Modeling Socrates as the ideal teacher for the beginner and Socratic method as the ideal method Introducing philosophical issues along with logic by being philosophical about logic and logical about philosophy Presenting a complete system of classical Aristotelian logic, the logic of ordinary language and of the four language arts, reading, writing, listening, and speaking. ### VIII. The Third Act of the Mind: Reasoning #### Section 1. What does "reason" mean? (P) "Man is a rational animal." That was the classical definition of man. The modern mind tends to object to two things in this definition: (1) its larger meaning of "man" and (2) its larger meaning of "rational." (1) In all books written in English until fairly recently we find the larger, or inclusive, use of "man" to mean both men and women equally. But current feminist fashion insists on an exclusively masculine meaning to "man," which this author would call not "inclusive" but "exclusive," in fact "male chauvinism." They would use not "man" but "humanity" to designate both males and females equally. But this is a confusion, because "humanity" is an abstract term, designating a quality, as in "humanity vs. divinity," while "man" is a concrete term, as in "God and man" or "a man or an animal." The new usage, which is exclusive and "sexist," calls itself "inclusive" and it accuses the traditional inclusive usage of exclusivism and sexism!? (2) The larger, older meaning of "rational" includes wisdom, intuition, understanding of the nature or essence of a thing (the "first act of the mind"), self-knowledge, moral conscience (awareness of good and evil), and the appreciation of beauty, as well as reasoning and rational calculation (the "third act of the mind"). Even in this larger, ancient sense of "reason," human reason has weakness as well as power. Compared with angels (pure spirits), we are like slowly crawling insects: we must gather all our data from our five senses, and we must usually proceed slowly, step by step, deducing or inducing one thing from another. In these two ways our rational knowledge is indirect: it depends on prior sense experience and it depends on prior knowledge. Angels, in contrast, have something like direct mental telepathy with the mind of God, or at least with the essences of things as God knows them, immediately and intuitively. #### What does "reason" mean?/The ultimate foundations of the syllogism On the other hand, the human mind has a remarkable power compared with even the highest animal intelligence. Human reason surpasses animal intelligence in at least three ways: First, though all human knowledge begins in experience, we can acquire knowledge beyond experience, and even with certainty, through deductive reasoning. For instance: * If we know that everything that has atoms must be able to reflect light, * And if we know that all little green men on Mars have atoms (i.e. if there are little green men on Mars, they must have atoms), * Then we know with certainty that all little green men on Mars (if there are any) must be able to reflect light, even though we have never seen little green men on Mars, and even though we do not know whether or not there are little green men on Mars. This is quite remarkable. Second, we can know not only particular truths beyond our immediate experience, but also universal truths, such as "2+2=4" or "all men are mortal." This power presupposes the first power, the power to know beyond experience, for experience never presents universals, only particulars. We can know universals by abstracting them from the particulars that we experience, e.g. "human nature" from human beings or "life" from living things. Third, we can know necessary and unchangeable truths; we can know not only that such and such happens to be the case, but also that it must necessarily and always be the case. If A is B and B is C, then A must necessarily be C. This is even more than the power to know universal truths. Not all universal truths are necessary. "All human babies come from human mothers" is a universal truth (so far) but not a necessary truth, and it will cease to be true when someone clones a human being. "All my ties are four-in-hand" is true but not necessarily true, since I could have had some bow ties too, and probably will have some in the future. But "all men are mortal" or "all triangles have 180 degrees in the sum of their three interior angles" are not only universal truths (true of all men or all triangles) but also necessary truths, truths that must be so and cannot ever cease to be so. #### Section 2. The ultimate foundations of the syllogism (P) The power of deduction to give us certain knowledge, as expressed in a syllogism such as the classic "All men are mortal and² Socrates is a man, therefore Socrates is mortal," comes from the inherent, self-evident, and necessary truth of the following principles: We are not assuming the existence of angels, or of God, but using the concept of an angel to understand the nature of human reason by contrast. 'And' often indicates a relation between two premises. #### The ultimate foundations of the syllogism ##### Tautologies A "tautology" is a proposition that does not need to be proved because it is logically self-evident. It "proves itself," so to speak, because if you deny it, you must contradict yourself. Examples are: "Frogs are frogs," "Whatever animal has teeth and claws, has claws," "If I exist, I exist," and "Nothing that is divisible is indivisible at the same time." A tautology can be defined in three ways: (a) a proposition that is true because of its logical form, whatever its content, (b) a proposition whose contradictory is self-contradictory, or (c) a proposition whose predicate is necessarily contained in its subject. Though a proposition may be self-evident objectively, in itself, it may not be self-evident subjectively, to a given human mind. For instance, "angels are not confined to space" and "whatever has color must have size" are both self-evident in themselves, but not to a person who does not understand the nature of angels and space, color and size well enough to know that these connections are necessary. Sometimes the term "tautology" is used for any objectively self-evident proposition, but more usually it is used in a narrower sense, only for propositions that are explicitly self-evident, verbally self-evident, independent of the meaning of the terms. If we use this narrower sense, "All red ties are red," "All red X's are X's," and "All red gloms are gloms" are tautologies, but "no angels have bodies" and "All men have bodies" are not. What about a proposition like "You will pass this course if you work hard enough?" This is a tautology if "hard enough" means "hard enough to pass"; for then the proposition means "If you work hard enough to pass, you will pass," or "If you pass because you work hard enough, then you will pass." And that is clearly a tautology. However, if "hard enough" means "hard enough to satisfy the teacher," then it is not a tautology. A tautology tells us no new information. "This candidate will be elected if there is sufficient support" is a tautology, like "you will pass if you work hard enough," though it sounds as if it is saying something informative. It says only that if there is sufficient support for him to be elected, then there will be sufficient support for him to be elected. If you contradict the proposition, you contradict yourself: it cannot be true that the candidate will be elected even if there is not sufficient support for him to be elected. Tautologies are necessarily true. Their contradictories are necessarily false, logically impossible. Other propositions are true (or false) only because of some other things being true; that is, they are contingently true (or false). "Water runs downhill" is contingently true, true only because of gravity. In a universe where matter repels instead of attracts, it would not be true. Necessary truths are truths that are true in all possible worlds. We cannot imagine or conceive the opposite of a necessary truth. For instance, we cannot imagine, or conceive, or tell a story about, a world in which 2+2=5. We can, however, imagine the opposite of any contingent truth if we have lively enough imagination – like a world without gravity. "Dead bodies decay (when there is normal heat and air) and do not come back to life" is a truth about all dead bodies; but it is a contingent truth, and we can imagine (and even believe) a miracle happening, in which a dead body does not decay but comes back to life. That would be a violation of physical law, but physical laws are only contingent truths, true only because something else is true in this particular world, which might not be true in some other possible world. But we cannot even conceive, and therefore we literally cannot believe, any violation of a logical law, since logical laws are necessary truths, true of all possible worlds, so that a proposition that violates a logical law is strictly meaningless. For instance, "A man walked on water" may be a miracle, but it is not a self-contradiction. "A man walked on water and didn't walk on water at the same time" is a self-contradiction, if there is no ambiguity in the terms. (Of course, surfers walk on water in a sense. But though that may be almost as wonderful as what Jesus did, it's not quite the same.) "God can give man free choice, so that man is free to choose between good and evil, and at the same time withhold free will from man, so that man never chooses evil" is a self-contradictory and thus strictly meaningless proposition. It does not become meaningful because it is predicated of God. God, if He exists and created the physical universe, can override its physical laws; but even God cannot violate logical laws, because these laws are not dependent on the temporal nature of the creation but on the eternal nature of the Creator. If there is no God; but in any case they are eternal, unchangeable, necessary truths. If God exists, these laws are descriptions of the nature of God. This is a useful explanation of the distinction between necessary and contingent truths even for atheists, for it is the meaning of "God," or the concept of God, that is relevant here. The distinction holds conceptually whether there is a real God or not. #### Section 3. How to detect arguments We can evaluate arguments as valid or invalid only after we find them. Not all written or spoken discourse contains arguments, and discourse that does contain arguments is usually like a tide pool containing crabs: you have to hunt for them to find them. Detecting arguments is like crabbing. Suppose we are fishing for crabs with a net. We must (1) first detect the presence of a crab before we can hope to (2) get it into our net; and we usually must get it into our net before we can (3) tell whether it is one of the edible kind of crabs or not. These three steps apply to arguments as well as crabs. The critical question about any argument is (3) whether it is logically valid or not, whether the mind can accept it, whether it is mentally edible, so to speak. But before we can determine that (3), we must first (2) be clear about what the argument is saying, and we do this by putting it into logical form, especially the form of a syllogism. That corresponds to the net. (Advanced fishermen might do without a net, and advanced logicians can bypass the step of putting ordinary-language arguments into logical form, but beginners in logic definitely need to put an argument into logical form before they can see whether it is valid or not, just as beginning crabbers need to get the crab in the net before they can see whether it is edible or not.) But even before we can do this (2), we must first (1) detect the presence of an argument, as we detect the presence of a crab. If we wave our net of syllogism randomly, we will probably not find an argument in it. For there is much more in human linguistic communication than arguments, just as there is much more in the sea than crabs. Detecting the presence of an argument is not something that can be taught mechanically. It is intuitive "seeing." There are mechanical principles for testing the validity of an argument, and we will learn these shortly; but there are no mechanical principles for testing for the presence of an argument. However, there are indicators. One is the presence of the essential structure of an argument, and another is certain key words. (1) The essential structure of every argument consists of a relationship between its two parts: premises and conclusion. The conclusion is what you are trying to prove; the premises are your reasons, your evidence, your proof. The relationship between them can be put in different ways: we can say that the conclusion "follows from" the premises, or that the premises "entail" the conclusion, or "prove" the conclusion, or that the premises are the "reasons" for the conclusion, or that the conclusion is true because the premises are true, or that (in a deductive argument but not an inductive one) if the premises are true, then the conclusion must be true. In "All men are mortal and Socrates is a man, therefore Socrates is mortal," the conclusion is "Socrates is mortal" because that is what you are trying to prove; and the premises are "All men are mortal" and "Socrates is a man" because that is your reason for believing that Socrates is mortal, that is your proof that Socrates is mortal, that is your evidence that Socrates is mortal. The word "therefore" asserts your claim that the premises have this logical relation to the conclusion, that they prove the conclusion to be true. (2) There is usually a key word indicating this premise-to-conclusion relation. "Therefore" is the formal, proper word, but there are many others. The following is a list of "conclusion indicators." The proposition that follows these words is usually the conclusion of an argument; and the proposition that precedes these words is usually a premise (thus argument-indicator words usually indicate both the conclusion and a premise): - "therefore" - "hence" - "it follows that" #### Section 5. Truth and validity (B) Arguments are either logically valid or logically invalid. If they are logically invalid, they contain a logical fallacy. The word "fallacy" has a specific and narrow meaning in logic. Not every mistake is a fallacy. An error of fact, like the belief that the earth is flat, is not called a fallacy in logic, though sometimes it is called that in ordinary language. Only an argument can be fallacious, not a proposition. A fallacy is a mistake in reasoning. A fallacy makes an argument logically "invalid." An argument without any fallacies is logically valid: its conclusion follows necessarily from its premises. To review the threefold structure of logic once again: - Terms are never true or false, and never logically valid or invalid (fallacious), but only clear or unclear (ambiguous). - Propositions are never valid or invalid (fallacious), but only true or false. - And each term within a proposition is either clear or unclear. - Arguments are either valid or invalid (fallacious). Each proposition in an argument is either true or false, and each term is either clear or unclear. So a good argument is one whose terms are all clear, whose propositions are all true, and whose logic is valid. A bad argument is one with an unclear term or a false proposition or a logical fallacy. Truth is a relationship between a single proposition and the real world, or the nature of things, or "objective reality," or what is "outside of" (independent of) the proposition and the mind that expresses it. Validity is a relationship between propositions: between the premises of an argument and the conclusion of the argument. We have already studied "material fallacies," fallacies of content, wrong uses of the content in arguments. We are now about to study "formal fallacies," fallacies of logical form. Logical form is the relationship between, or arrangement of, terms and propositions (that is, the content, or matter) in an argument. #### Truth and validity To understand what makes an argument invalid, we need to understand what makes one valid. An argument (we speak only of a deductive argument here) is valid if the premises necessitate the conclusion, if they prove the conclusion, if their being true makes it necessary that the conclusion be true. So in a valid argument, the premises cannot be true without the conclusion being true. If we know that the premises are true, we can be sure that the conclusion is true. This is the point of "validity": it assures us that it is safe to move to the conclusion if we have already moved to, or occupied, the premises – like a step across a river in a battle. A valid argument gives us certainty about its conclusion. It is not absolute certainty but relative certainty, that is, certainty relative to the premises. It is conditional certainty or hypothetical certainty: certainty that if the premises are true, then the conclusion must be true. But it is certainty, which is a currently unfashionable thing; it is "rigid" and iron and awful and unchangeable. If all A is B and all B is C then all A must be C, necessarily and everywhere, for everyone and forever. At no time or place or culture or world can it change. Changes might take place in the laws of physics: water might run uphill tomorrow, or a galaxy of antimatter and antigravity might be discovered; but in all possible worlds the fundamental laws of logic must hold. Miracles might happen; the fundamental laws of the universe might be set aside by the Creator of the universe; but even the Creator cannot violate logical laws. If God exists, logical laws are the laws of the divine nature. Even God cannot both exist and not exist at the same time. A meaningless self-contradiction does not suddenly become meaningful because you add the words "God can do this" to it. And this is so not because we say so, because the human mind has legislated these laws. The laws of logic are not invented, they are discovered; they are objective truths. (Of course, the language systems we use to formulate them are invented, and our process of coming to learn them is subjective.) In a previous chapter, we made the point (which some will find startling and even offensive) that it is very easy to define "truth." However, it is far from easy to find it, and to be sure when you have found it. We now make another point some will find surprising: it is easy to know with certainty whether an argument is valid. However, this is not enough: an argument is totally satisfactory only if it meets three criteria, and it is far from easy to know whether an argument is good by the other two criteria: whether all the terms are unambiguous and whether all the premises are true. In any deductive argument, assuming the logic is valid and the terms are clear, there are four possibilities: - The premises are true and the logic is valid. - The premises are true and the logic is invalid. - At least one of the premises is false and the logic is valid. - At least one of the premises is false and the logic is invalid. Only in the first case can we know that the conclusion is true. In the other three cases, we do not know whether the conclusion is true or false. ### LOGIC **VALID** **INVALID** **PREMISES** TRUE | Conclusion true | Conclusion unknown FALSE | Conclusion unknown | Conclusion unknown We can also know that an argument whose conclusion is false and whose logic is valid must have at least one false premise. ### LOGIC **VALID** **INVALID** **CONCLUSION** TRUE | Premises unknown | Premises unknown FALSE | At least one premise must be false | Premises unknown This is equally important for practical purposes, since we often argue "backwards," so to speak, proving that a premise must be false from the fact that the conclusion is false (if the logic is valid), instead of "forwards," proving that a conclusion must be true from the fact that the premises are all true (if the logic is valid). These are the two most usual strategies in arguing: reasoning backwards, or "upstream" from pollution downstream (a false conclusion) to pollution upstream (a false premise); or reasoning forwards, or "downstream" from unpolluted (true) premises to an unpolluted (true) conclusion. And both strategies depend on this principle about the relationship between truth and validity in an argument. We cannot validly argue in any other way. E.g., we cannot validly argue that if the premises of a valid argument are false, then the conclusion must be false too; that pollution upstream proves pollution downstream, so to speak; that if the argument is consistent, false premises must lead to a false conclusion just as surely as true premises lead to a true conclusion. That mistake comes from thinking of an argument as a sort of mathematical equation, with the premises on one side and the conclusion on the other. But a mathematical equation is reversible, while an argument is not. (Neither is a proposition simply reversible, as we have seen previously (page 140): the subject and the predicate are not interchangeable, but perform different functions.) In a valid argument, true premises entail a true conclusion (arguing "downstream"), but a true conclusion does not necessarily entail true premises. And a false conclusion entails false premises (arguing "upstream") but a false premise does not necessarily entail a false conclusion. The conclusion might be true by accident. So only the two following inferences are correct: 1. If the argument is valid and the premises are true, then the conclusion must be true. (This is one mode of correct argument; we could call it "arguing forward.") 2. If the argument is valid and the conclusion is false, then at least one premise must be false. (This is the other mode of correct argument; we could call it "arguing backward.") Here are two examples of valid arguments with false premises but a true conclusion: - All evil spirits are birds. - And all sparrows are evil spirits. - Therefore all sparrows are birds. In both cases above, the premises are false, and the argument is valid, yet the conclusion happens to be true (by accident). - The earth is a star. - And no stars are fish. - Therefore the earth is not a fish. The practical point of this is that you do not refute a conclusion by showing that it follows from false premises. Suppose someone has just given a logically valid argument for a conclusion you disagree with, but this argument has one or more false premises in it. You point out these false premises. What have you accomplished? Something, but not everything. You have refuted his argument but not his conclusion. You have only shown that your opponent's argument has not proved his conclusion, as he claimed. His argument is inconclusive because it has a false premise. The conclusion is still in doubt. It is neither proved to be true, as your opponent has claimed, nor is it proved to be false. And just because a valid argument has a true conclusion, that does not mean it has true premises. We must be careful not to think of an argument as a reversible equation. Like a river, an argument carries us in one direction, downstream: we can move from true premises to a true conclusion - we can know that if the premises are true, then the conclusion be true - but we cannot reverse this and know that if the conclusion is true the premises must be true. (We can, however, deduce that if the conclusion is false, at least one of the premises must have been false, just as we can deduce that if garbage is flowing down the river, someone must have unloaded it upstream.) The practical point in strategy of arguing here can be summed up as the following: 1. You do not prove that a premise is true by showing that from it a true conclusion logically follows. 2. You do not prove that a conclusion is false by showing that it logically follows from a false premise. 3. You do prove that a premise is false by showing that from it a false conclusion logically follows. 4. You do prove that a conclusion is true by showing that it logically follows from true premises. #### These situations all concern valid arguments. Here are some other situations with invalid arguments: When you have an invalid argument, you know nothing about truth and falsity: (5) You do not prove that a conclusion is false by showing that the argument is invalid. An invalid argument can have a true conclusion: - The sky is blue - And grass is green - Therefore man is mortal (6) You do not prove that an argument is invalid by showing that its conclusion is false. A false conclusion can emerge from a valid argument if it has false premises: - All pigs are purple - And all purple things are immortal - Therefore all pigs are immortal (7) You do not prove a conclusion is true by showing that the argument is valid. The premises must also be true. The example above (6) is a valid argument but has a false conclusion. (8) You do not prove an argument valid by showing that its conclusion is true. Example (5) above has a true conclusion but it is an invalid argument. ### Arguing "Forward" If Premises Are... | And Argument Is... | Then Conclusion Is... ------- | -------- | -------- TRUE | VALID | TRUE TRUE | INVALID | UNKNOWN FALSE | VALID | UNKNOWN FALSE | INVALID | UNKNOWN ### Arguing "Backward" If Conclusion Is... | And Argument Is... | Then Premises Are... ------- | -------- | -------- TRUE | VALID | TRUE TRUE | INVALID | UNKNOWN FALSE | VALID | ONE FALSE FALSE | INVALID | UNKNOWN Imagine a spy trying to get out of East Berlin into West Berlin. In order to succeed in getting to West Berlin, he has to pass three checkpoints: Able, Baker, and Charlie. If he fails at any of one or more of the checkpoints, he fails to get out. The spy symbolizes an argument, and escape to West Berlin symbolizes proving its conclusion to be true. The three checkpoints are the three questions of logic, one for each of the "three acts of the mind" (see the charts on pages 32-33). Checkpoint Able checks for ambiguous terms. Checkpoint Baker checks for false premises. Checkpoint Charlie checks for logical fallacies. At least one, possibly more. #### Truth and validity We can know (1) that if the spy passes all three checkpoints, he succeeds (this is arguing "forward"); and that (2) if he does not succeed, he has failed at least one checkpoint (this is arguing "backward"). (3) We also know that if he has passed two of the three checkpoints and yet has not succeeded in getting to West Berlin, he must have failed the remaining checkpoint. Thus we know (1) that if an argument has no ambiguous terms, false premises, or logical fallacies, its conclusion must be true; and that (2) if the conclusion is not true, it must have failed at least one of the three checkpoints. (3) We also know that if the argument with the false conclusion has passed any two of the three checkpoints, it must have failed the remaining one. ## Exercises on the relationship between truth and validity: Which of the following statements can we know to be true, assuming unambiguous terms? (This is probably the dullest, most abstract, and least interesting exercise in this book.) 1. If a premise is false and the argument is invalid, the conclusion must be false. 2. If a premise is false and the argument is invalid, the conclusion must be true. 3. If a premise is false and the argument is valid, the conclusion must be true. 4. If a premise is false and the argument is valid, the conclusion must be false. 5. If a premise is false and the conclusion is false, the argument must be invalid. 6. If a premise is false and the conclusion is false, the argument must be valid. 7. If a premise is false and the conclusion is true, the argument must be invalid. 8. If a premise is false and the conclusion is true, the argument must be valid. 9. If the premises are true and the argument is valid, the conclusion must be true. 10. If the premises are true and the argument is valid, the conclusion must be false. 11. If the premises are true and the argument is invalid, the conclusion must be false. 12. If the premises are true and the argument is invalid, the conclusion must be true. 13. If the premises are true and the conclusion is true, the argument must be valid. 14. If the premises are true and the conclusion is true, the argument must be invalid. 15. If the premises are true and the conclusion is false, the argument must be valid. 16. If the premises are true and the conclusion is false, the argument must be invalid. 17. If the argument is valid and the conclusion is false, at least one premise must be false. 18. If the argument is valid, the conclusion is false, and one premise is true, the other premise must be false. 19. If the conclusion is false, then either the argument is invalid or a premise is false. 20. If one premise is false, the conclusion true, and the argument valid, the other premise must be true.