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On Showing Invalidity

Published online by Cambridge University Press:  01 January 2020

Thomas J. McKay
Thomas J. McKay*
Affiliation:
Syracuse University
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Extract

In studying logic, one learns how to establish that a conclusion follows from a set of premises. Those arguments that exhibit one of the valid forms of the deductive system under study are valid. There may be questions about what forms are exhibited by various arguments - Is this English conditional (or any other) really truth-functional? Is this disjunction really inclusive? Are the English predicates used with uniform meaning? - but none of these problems undermine the claim that if an argument exhibits a valid form of a system for deductive logic, then that argument is valid.

When we move on to study invalidity, however, we find that the situation is not parallel. Every argument is an instance of some invalid argument forms, and we cannot say that every instance of every invalid form is invalid.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 14 , Issue 1 , March 1984 , pp. 97 - 101
Copyright
Copyright © The Authors 1984

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References

1 Every argument with two premises, for example, is an instance of the invalid form

p

q

Therefore r.

A more detailed analysis, however, may reveal that a particular argument is an instance of some valid form as well.

2 The Fallacy behind Fallacies,’ Midwest Studies in Philosophy, 6 (1981) 489-500. In this paper Massey develops themes introduced in ‘Are there any Good Arguments that Bad Arguments are Bad?’, Philosophy in Context, 4 (1975) 61-77.

3 Bencivenga's, Ermanno discussion (‘On Good and Bad Arguments,’ Journal of Philosophical Logic, 8 (1979) 247-59)CrossRefGoogle Scholar criticizes Massey's views on the wrong grounds, since it relies upon a criticism of the claim of logical (as opposed to pragmatic) asymmetry of validity and invalidity judgments. My conclusion is that the logical asymmetry does not have the consequences that Massey claims for it, not that there is no logical asymmetry.

4 Copi, Irving Introduction to Logic (New York: Macmillan 1978)Google Scholar and Fogelin, Robert J. Understanding Arguments (New York: Harcourt Brace Jovanovich 1978)Google Scholar

Not all dogs are brown.

Some dogs are dogs.

Therefore, some dogs that are dogs are not brown.

Not all men are mortal.

Some men are non-mortal.

Therefore, some men that are non-mortal are non-mortal.

6 This instruction is used in Copi, Introduction to Logic, fifth edition (New York: Macmillan 1978), 365. The same instruction is used for exercises involving arguments and for exercises involving argument forms. The discussions of invalidity, pp. 288-9, 330, and 361-5, misleadingly suggest that formal methods apply directly to arguments (rather than to argument forms).

7 At one point Massey makes a remark that is quite puzzling. He says that those arguments ‘that upon close scrutiny seem invalid are best set aside unless and until their composers or admirers supply cogent evidence of their validity.’ This seems exactly right, but Massey also seems to want to take away from us the resources we have for closely scrutinizing arguments. If we don't scrutinize them by trying to find the logical features that might be relevant to validity and then checking to see if we can show that arguments with these features are valid or that these features don't suffice for validity, then how should we scrutinize them? How does Massey scrutinize them?

8 Massey's case against text-book treatments of fallacies rests largely on his claim that there is no systematic study of invalidity. For example, one idea of a formal fallacy - i.e., of an argument that is fallacious because it is an instance of an invalid argument form - does succumb to Massey's criticism. But a related idea - that of an argument that is judged to be fallacious because it has logical features that are not validity-making and about which there is no expectation of uncovering more subtle validity-making features - stands unaffected.

9 I thank Irving Copi for his helpful comments on a version of this paper.