Best Logic

The edition's new Previews connect a section's content to real-life scenarios, using everyday examples to "translate" new notions and terms into concepts that readers unfamiliar with the subject matter can relate to. He is married to Dr. Linda Peterson, who retired from teaching philosophy at the University of San Diego in 2015.

Introducing philosophical issues along with logic by being philosophical about logic and logical about philosophy. It’s here both to satisfy the advanced student’s curiosity and to sell the approach of this book to prospective teachers who may question its emphasis on Aristotelian rather than symbolic logic, by justifying this choice philosophically.). Almost four hundred years before Christ, Aristotle wrote the world’s first logic textbook. (1) The first and most important one is that the new logic really is superior to the old in efficiency for expressing many long and complex arguments, as Arabic numerals are to Roman numerals, or a digital computer to an analog computer, or writing in shorthand to writing in longhand. However, longhand is superior to shorthand in other ways: e.g. it has more beauty and elegance, it is intelligible to more people, and it gives a more personal touch. Even though symbolic language is superior in sophistication, it depends on commonsense logic as its foundation and root. Strong roots are the key to healthy branches and leaves for any tree. Mathematics is the only totally clear, utterly unambiguous language in the world; yet it cannot say anything very interesting about anything very important. (2) A second reason for the popularity of symbolic logic is probably its more scientific and exact form. In fact, Ludwig Wittgenstein, probably the most influential philosophical logician of the 20th century, admitted, in Philosophical Investigations, that “because of the basic differences between natural and artificial languages, often such translations [between natural-language sentences and artificial symbolic language] are not even possible in principle.” “Many logicians now agree that the methods of symbolic logic are of little practical usefulness in dealing with much reasoning encountered in real-life situations” (Stephen N. Thomas, Practical Reasoning in Natural Language, Prentice-Hall, 1973). (The following summary should not scare off beginners; it is much more abstract and theoretical than most of the rest of this book.). Hume drew the logical conclusion of skepticism from Locke’s premise. Once he limited the objects of knowledge to our own ideas, Hume then distinguished two kinds of propositions expressing these ideas: what he called “matters of fact” and “relations of ideas.”. What Hume called “relations of ideas” are essentially what Kant later called “analytic propositions” and what logicians now call “tautologies”: propositions that are true by definition, true only because their predicate merely repeats all or part of their subject (e.g. “Trees are trees” or “Unicorns are not non-unicorns” or “Unmarried men are men”). What Hume called “matters of fact” are essentially what Kant called “synthetic propositions,” propositions whose predicate adds some new information to the subject (like “No Englishman is 25 feet tall” or “Some trees never shed their leaves”); and these “matters of fact,” according to Hume, could be known only by sense observation. Hume argued that particular facts deduced from these only-probable general principles could never be known or predicted with certainty. And we certainly do not see (with our eyes) the universal “principle of causality.” So Hume concluded that we do not really have the knowledge of objective reality that we naturally think we have. Kant accepted most of Hume’s analysis but said, in effect, “I Kant accept your skeptical conclusion.” He avoided this conclusion by claiming that human knowledge does not fail to do its job because its job is not to conform to objective reality (or “things-in-themselves,” as he called it), i.e. to correspond to it or copy it. (Kant distinguished three such levels of imposed meanings: the two “forms of apperception”: time and space; twelve abstract logical “categories” such as causality, necessity, and relation; and the three “ideas of pure reason”: God, self, and world.). The term “epistemological idealism” is sometimes is used in a different way, to mean the belief that ideas rather than objective reality are the objects of our knowledge; in that sense, Locke and Hume are epistemological idealists too. For instance, according to epistemological idealism, general “categories” like “relation” or “quality” or “cause” or “time” are only mental classifications we make, not real features of the world that we discover. But for Aristotle a “genus” is the general or common part of a thing’s real essential nature (e.g. “animal” is man’s genus), and a “species” is the whole essence (e.g. “rational animal” is man’s species). Another place where modern symbolic logic merely manipulates mental symbols while traditional Aristotelian logic expresses insight into objective reality is the interpretation of a conditional (or “hypothetical”) proposition such as “If it rains, I will get wet.” Aristotelian logic, like common sense, interprets this proposition as an insight into real causality: the rain causes me to get wet. (See Chapter II, Section 3, “The Problem of Universals.”). The opposite of realism is “nominalism,” the belief that universals are only man-made nomini (names). William of Ockham (1285–1349) is the philosopher who is usually credited (or debited) with being the founder of nominalism. Aristotelian logic assumes both epistemological realism and metaphysical realism because it begins with the “first act of the mind,” the act of understanding a universal, or a nature, or an essence (such as the nature of “apple” or “man”). “Aristotle never intended his logic to be a merely formal calculus [like mathematics]. He tied logic to his ontology [metaphysics]: thinking in concepts presupposes that the world is formed of stable species” (J. Lenoble, La notion de l’experience, Paris, 1930, p. 35). If we should begin to speak and think only in nominalist terms, this would be a monumental historic change. It would reverse the evolutionary event by which man rose above the animal in gaining the ability to know abstract universals. It would be the mental equivalent of going naked on all fours, living in trees, and eating bugs and bananas. While it may be “extremist” to suggest it, such a mental “devolution” is not intrinsically impossible. To most modern minds, those last seven words sound almost as archaic as alchemy or feudalism. These critics dislike categories because they “feel that” (that phrase is a category confusion, by the way) classifications, and universal statements about classes such as “Hittites could not read Hebrew,” constitute “prejudice,” “judgmentalism,” “oppression,” or even “hate speech.”. Logic and social change are not unrelated. Instead, we think about how we feel about things, about how we can use them, how we see them behave, how they work, how we can change them, or how we can predict and control their behavior by technology. The higher animals too have feelings, and things to use, and sight, and action, and even a kind of technology of behavior prediction and control. Logic is deeply related to moral and ethical changes in both thought and practice. All previous societies had a strong, nearly universal, and rarely questioned consensus about at least some basic aspects of a “natural moral law,” about what was “natural” and what was “unnatural.” There may not have been a greater obedience to this law, but there was a much greater knowledge of it, or agreement about it. Today, especially in the realm of sex (by far the most radically changed area of human life in both belief and practice), our more “advanced” minds find the old language about “unnatural acts” not only “politically incorrect” but literally incomprehensible, because they no longer accept the legitimacy of the very question of the “nature” of a thing. Issues like homosexuality, contraception, masturbation, pedophilia, incest, divorce, adultery, abortion, and even bestiality are increasingly debated in other terms than the “nature” of sexuality, or the “nature” of femininity and masculinity. .” ethics of calculating consequences – essentially, “the end justifies the means” (though that formula is somewhat ambiguous). For its basic unit is the term, a subject (S) or a predicate (P) within a proposition (p); and its basic judgment is “all S is P” – a statement of universal truth about the nature of S and P. The very nature of reason itself is understood differently by the new symbolic logic than it was by the traditional Aristotelian logic. “Reason” used to mean essentially “all that distinguishes man from the beasts,” including intuition, understanding, wisdom, moral conscience, and aesthetic appreciation, as well as calculation. Out at sea there between Scylla and Charybdis, it reveals by contrast the double tragedy of modern thought in its alienation between form and matter, structure and content, validity and meaning. For example, in a logic text book misleadingly entitled Practical Reasoning in Natural Language, the author takes six full pages of symbolic logic to analyze a simple syllogism from Plato’s Republic that proves that justice is not rightly defined as “telling the truth and paying back what is owed” because returning a weapon to a madman is not justice but it is telling the truth and paying back what is owed. Another single syllogism of Hume’s takes eight pages to analyze (pp. The new logic is like typically modern movies: strong on “special effects” but weak on substance (theme, character, plot); strong on the technological “bells and whistles” but weak on the human side. The Problem of “Material Implication” The following issue is quite abstract and difficult, though I shall try to make it as simple as possible. It is included because I believe it shows that “something is rotten in the state of Denmark” at the very heart of the new logic. Logic is most especially about reasoning, or inference: the process of thinking by which we draw conclusions from evidence, moving from one proposition to another. A logically valid argument is one in which the conclusion necessarily follows from its premises. The conclusion (“Lassie is a dog”) may be true, but it has not been proved by this argument. If that assumption is naïve and uncritical, unfashionable and unintelligent – well, welcome to Logic for Dummies.

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