Logic

To Think Clearly Use reason, instead of relying on instinct alone What is Logic? – “the art of reasoning” – The study of truth – The ethics of thought and belief – The linguistic and structural relationships of diction and syntax Therefore, logic is concerned with thought, with language, and with truth.

Logic Aristotle's logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. Aristotle's logical works contain the earliest formal study of logic that we have. It is therefore all the more remarkable that together they comprise a highly developed logical theory, one that was able to command immense respect for many centuries

Syllogisms (Formal Logic) All Aristotle's logic revolves around one notion: the deduction (sullogismos). What, then, is a deduction? – Aristotle says: – A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. (Prior Analytics I.2, 24b18-20) Each of the "things supposed" is a premise (protasis) of the argument, and what "results of necessity" is the conclusion (sumperasma).

Syllogisms The core of this definition is the notion of "resulting of necessity" (ex anankês sumbainein). This corresponds to a modern notion of logical consequence: X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true. We could therefore take this to be a general definition of "valid argument".

Syllogisms In modern usage, ‘syllogism’ means an argument of a very specific form. Thus, precise language where connections are explicit or logically suggested. Contains three categorical positions, must affirm or deny the predicate of the subject: – If A is predicated of all B (major premise) – And B is predicated of all C (minor premise, or middle term) – Then A is predicated of all C. (conclusion) The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises. Example – All humans are mortal. – Aristotle is human. – Therefore, Aristotle is mortal.

Enthymeme A “truncated syllogism” since either the major or minor premise of a syllogism is left implied – Informal logic – Within an enthymeme, inferential deductions are made, a logical assumption based on the available information Example: – We cannot trust this man, for he has perjured himself in the past. What is missing? – Major premise omitted: Those who perjure themselves cannot be trusted.

Enthymeme Syllogism Broccoli is a vegetable. All vegetables are delicious. Therefore, broccoli is delicious. Enthymeme I like foods that are delicious. (premise) All vegetables are delicious. (premise) I like all vegetables. (Inferred premise) Broccoli is a vegetable.(premise) Therefore, I like broccoli. (conclusion inferred)

What is a logical fallacy? A “fallacy” is a mistake, and a “logical” fallacy is a mistake in reasoning. In logic, the term “fallacy” is used in two related, but distinct ways. 1.“Argumentum ad Hominem is a fallacy.” 2.“Your argument is a fallacy.” Arguments should not be characterized as fallacies. Instead: – “Your argument commits a fallacy. It is fallacious.”

What is a logical fallacy? To be a fallacy, a type of reasoning must be potentially deceptive—must be likely to fool some of the people some of the time. History: – Aristotle was both the first formal logician and informal logician. Named type of logical error and categorized within: On Sophistical Refutations. – Plato, too, as Aristotle’s teacher, deserves credit for being the first philosopher to collect examples of bad reasoning: “Euthydemus” collection of fallacious arguments in dialogue form. Two sophists enact exaggerated examples – Exaggerated arguments are sometimes called “sophisms” and bad reasoning “sophistry”

Why study logical fallacies? 1.Even if you could count on reasoning correctly 100% of the time, you cannot count on others doing so. In logical self- defense, you need to be able to spot poor reasoning, and— more importantly—to understand it. To be able to correct others’ mistakes, or to refute them convincingly, you need to understand why they are wrong. 2.Studying formal logic and the rules of correct reasoning is like having a road map that show how to get from point A to point B. However, even the best navigators sometimes get lost, and it helps if the roads that go nowhere are clearly labeled “DEAD END,” “WRONG WAY,” or “DO NOT ENTER.”

Politics and Logical Fallacies Political campaigns are compounded with fallacious arguments—despite the sincerity of candidates in their belief that they are the best person for the job. Unlikely that they use fallacies unintentionally. Reasons for using fallacies: 1.The candidate believes the argument will be effective, whether fallacious or not 2.The candidate believe a particular demographic will find the fallacy appealing in itself.

Logical Fallacy Defined as flawed logic, or reasoning. What is wrong with the following syllogism? – All humans are mortal. – Aristotle is mortal. – Therefore, Aristotle is human. It follows Aristotle’s prescribed form, yet why is it flawed? Review “So You Think You Know All the Answers”