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Lesson 10

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Lesson 10: Logic Introduction

 

The formal discipline of logic is ascribed to Aristotle and can be defined as the study of arguments. Classical logic should be familiar to most, but later developments such as symbolic logic and computer logic have surged to the forefront in recent years. This lesson will discuss the basic concepts of classical logic and touch briefly on the more recent development of symbolic logic.

 

Classical Logic

            As in the areas of ethics, aesthetics, and metaphysics, Aristotle is generally considered the authority on classical logic. In his work, Organon, he introduces the concept of syllogisms--a formal (that is, having a distinctive form) way of proposing and defending various propositions in a system of restricted judgments. In this case, "judgments" refers to the conclusions of said syllogisms.

            According to Aristotle, there were four possible outcomes in logic using syllogisms: (A) All X is Y, No X is Y, Some X is Y, and Some X is not Y. Examples of each would include: "All apples are fruit", "No apples are oranges", "Some apples are rotten", and "Some apples are not rotten".

            Of course, an argument can be valid (that is, it's form is good), but not be true(that is, the conclusion doesn't coincide with reality). Likewise, an argument's conclusion may be true, but the argument itself is not valid (that is, there an error with one or more of the premises). It is best to strive for both truth and validity in logical thinking.

 

Deduction or Induction?

            Within logic exist two different modalities of reasoning: deduction and induction. Briefly, deduction begins with a broad, general premise and works its way to a narrower, more specific conclusion. Induction begins with finite and specific observations and then draws a broader conclusion.

            Aristotle's syllogistic form is nearly ideal for deductive reasoning purposes:All humans are mortal. Jimmy is a human. Therefore, Jimmy is mortal. Here we see a specific, narrow conclusion derived from the very broad first premise that "all humans are mortal". Further, the conclusion is rather inescapable if one accepts the truth and validity of the first and second premises.

            Inductive logic is more useful for forming hypotheses and is well-suited for scientific inquiry, as it allows the thinker to use various pieces of evidence to form a broader conclusion. For example, Mouse A has four legs, Mouse B has four legs, Mouse C has four legs, and so on. Having observed this, it could be posited that "All mice have four legs".

 

Fabulous Fallacies

            The field of rational thinking has numerous pitfalls, called fallacies, that can lay waste to the most well-intentioned of arguments. Fallacies can be divided into several different categories: relevance, component, ambiguity, and omission. Here are some of the more common fallacies, their category is noted in parentheses.

            Ad hominem argument: Literally "to the man", this involves arguing against (or for) the person making the argument rather than against or for the issue involved. This is a very popular tactic in political debates, but remains a logical fallacy nonetheless. (Relevance)

            Ad populum: Making an argument that a position is valid simply because it is popular. While seemingly absurd on the face of it, this type of "reasoning" is used quite frequently, especially in commercial marketing: "All your friends and neighbors have the new Elephantron 3000 Baby Elephant Maker, so you should have one, too!" (Relevance)

            Appeal to force: This is literally a "might-makes-right" line of reasoning which, in many cases, is not a logical argument in the least. Relying on force or the threat of force, this fallacy attempts to force people to accept an argument's conclusion in order to avoid negative consequences. (Relevance)

            Argument from authority: This argues that people ought to support or oppose a given argument or course of action simply because someone in a position of authority supports or opposes it. For example, celebrity endorsements of a product do not make a convincing argument for the merits of the product, they simply urge you to buy based on the word of the celebrity involved. (Relevance)

            Argument from ignorance or lack of evidence: By arguing from a lack of evidence, a person claims that, just because an opposing point of view cannot be proven that their point of view must be true or vice versa. For example, "since you can't definitively disprove God exists, He must exist" or the opposite. (Omission)

            Circular reasoning/Begging the question: "Circular reasoning is an attempt to support a statement by simply repeating the statement in different or stronger terms.  In this fallacy, the reason given is nothing more than a restatement of the conclusion that poses as the reason for the conclusion.  To say, 'You should exercise because it's good for you' is really saying, 'You should exercise because you should exercise'" (Kennesaw State University, 2011). (Component)

            Complex or loaded question: This poses a question in such a way that the desired outcome is presumed true or false regardless of how it's answered. For example, "have you stopped beating your wife?" is a loaded question that implicates the person answering whether he answers yes or no. (Omission)

            Equivocation: This fallacy involves shifting back and forth between two or more different definitions of a single word or phrase that is crucial to the argument.For example, "buying government bonds is the right thing to do, therefore the government has a right to our money" (Ambiguity)

            Fallacy of composition: This error occurs when an argument focuses on the parts of a whole in order to make a generalization about the whole. For example, "each feather in a ton is very light weight, therefore a ton of feathers is lightweight". (Ambiguity)

            False dilemma/false dichotomy: This fallacy misrepresents a situation has having only two possible outcomes when, in fact, there may be more in order to force a choice. For example, "if you're not part of the solution, you're part of the problem" or "if you aren't with us, you are against us". (Component)

            Genetic fallacy: Typically, this fallacy involves arguing against a given position or argument because its origins are suspect (Pojman, 2000). Examples include "He's Italian, what good would his chicken lo mein be?" or "That person isn't an Ivy League graduate, they can't possibly win a nation-wide election!". (Relevance)

            Post hoc ergo propter hoc: From the Latin "after this, therefore because of this". This fallacy states that since event B followed event A, then event A necessarily was the cause of event B. For example, "It's raining today because I just washed my car!" or "Every time I need to go to the bathroom, the mail man shows up needing a signature." (Relevance)

            Non-sequitur: From the Latin, "does not follow". Literally, a conclusion that does not follow from the premises of an argument. (Relevance)

            Straw man argument: This fallacy is more often used in an intentional rather than accidental way and relies on a distortion of the opposing view's position. For example, Politician A believes reducing welfare payouts would help balance the budget in her state. Politician B argues that Politician A wants to cut off funds from those less fortunate and let them starve. (Component)

 

Symbolic Logic & Beyond

            Also known as mathematical logic, symbolic logic is a sub-discipline of philosophical logic as well as mathematics. It "...includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems" (Free Dictionary, 2011).

            Symbolic logic, emerging in the late 19th century, is generally divided into three fields of set theory: model theory, recursion theory, and proof theory (Free Dictionary, 2011). Early symbolic logicians such as Charles Pierce, George Boole, and George Peacock, extended traditional Aristotelian logic into the field of mathematics, paving the way for the interfacing of computers and classical logic.

            Since its inception, symbolic logic has lead to massive innovations in computer programming, logical systems (such as "fuzzy logic"), mathematics, and philosophy. Philosopher-mathematicians such as Bertrand Russell and Albert North Whitehead dealt extensively with the interface of math and logic, leading to increasingly more complex philosophies of the modern era.

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