The dog's argument has an implicit inference which has to be made explicit:

All cats have four legs.That argument can also be stated, equivalently, as follows:

All creatures that have four legs are cats.

I have four legs.

Therefore I am a cat.

If the animal is a cat then it has four legsWell our canine shouldn't be heartbroken at all for discovering she's actually a feline. Instead she should be depressed she's committed the

I'm an animal with four legs.

Therefore, I'm a cat.

*fallacy of illicit conversion*.

The fallacy occurs when given "all p are q" we infer that the converse "all q are p" is also true. Likewise when given "if p then q" and we conclude that "if q then p," then we've committed an illicit conversion. The "if - then" case may be more familiar when stated as follows:

If p then qThat's the well known fallacy of

q

Therefore p.

*affirming the consequent*and is an example of an illicit conversion. (p is known as the

*antecedent*and q the

*consequent*.) An argument in this form is

*invalid*.

The thing to remember is that "all s are r" or "if p then q" do not necessarily imply "all r are s" or "if q then p." The converse is is not necessarily implied but it might be true. For instance, in causal arguments, if p causes q, and if p is both

*necessary*and

*sufficient*to cause q, then the converse is also true:

If a sheet of paper is heated to its combustion temperature and oxygen is present then it will burn.Both statements are true. This is called a

If paper is burning then it's been raised to its combustion temperature and oxygen is present

*biconditional*--the conditional (i.e., the if - then statement) is true both ways. If p then q and if q then p. To formalize the relationship between temperature/oxygen and paper we would say:

Paper will burnThe phrase "if and only if" indicates this is a biconditonal statement.if and only ifits temperature is raised to its combustion point and oxygen is present.

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Print References:

Bennett, Deborah J..

*Logic made easy: how to know when language deceives you*. New York: W.W. Norton & Co., 2004. p. 108-110, 116-117, 130.

Vaughn, Lewis.

*The power of critical thinking: effective reasoning about ordinary and extraordinary claims*. New York: Oxford University Press, 2005. p. 287-289.

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