David Kelley
David Kelley

The Free Radical Online - Perigo vs. Nola

Six: David Kelley Responds

Here, David Kelley, head of the Institute for Objectivist Studies in New York, comments on the debate.

I would like to enter several comments into the Perigo-Nola debate regarding validity, truth, and reality in logic.

1. The forms of legitimate inference can be abstracted from any specific content (premises), and stated as abstract formal rules applicable even to non-factual premises. Thus the categorical syllogistic form "All M are P, and all S are M, therefore all S are P" is valid regardless of what actual terms we put in place of S, M, and P; and thus valid regardless of whether the resulting premises (or conclusion) are true or false. The same goes for the conditional inference "If p then q, and p, therefore q." Nola is correct that this is standard doctrine in logic, and in my view the point is perfectly compatible with Objectivist views about knowledge. [See my response below. -LP ]

2. It does not follow, however, that "the validity of the rules of logic has nothing to do with reality, i.e., with the stock of true claims about the history of the world," as Professor Nola asserts (TFR, 31, p. 35), nor that "the certification of the validity of the rules of logic is not done by an appeal to reality" (TFR, 32, p. 20). The forms described above can be stated as principles and as such they are claims about the world. For example, the categorical inference form can be stated as the classical dictum de omni:

Whatever is true of all M (i.e., that it is P) is true of whatever is M (i.e., all S).

Why should we accept this principle, and reason in accordance with the associated syllogistic form? Is the principle true because of arbitrary conventions we have stipulated for the use of words like "all" and "is," as the logical positivists claimed? Is the principle true because it reflects an innate structure that the human mind imposes on the material of experience, as Kantians claim? Both of these are subjectivist theories because they ground the laws of logic in the subject, the knower, rather than in the world. The Objectivist view is that the laws of logic are objective: they are truths about the world, made true by the facts. Not, of course, by specific facts about the history of specific things or events in the world's history, but by metaphysical facts about the nature of existence as such.

3. The same is true of the laws of identity and non-contradiction. In Rand's view, these are not axioms in a formal system for deriving theorems of logic, as Professor Nola assumes. They are metaphysical claims about the world: that any existent is something specific (A), that its specificity consists partly in its differences from other things (non-As) along various qualitative and quantitative dimensions, and that such differences cannot be conflated in the form of a contradiction (A is non-A). The forms of valid inference are grounded in these laws in the sense that the forms tell us how to avoid making contradictory claims about things.

4. The fact that laws of logic are grounded in reality does not mean that the validity of a valid syllogism with false premises is somehow ersatz, as Mr. Perigo suggests at several points (e.g., in saying that a valid syllogism with false premises "imitates" the correct procedure "but I don't call that logic" (TFR 32, 21).) A good analogy here is the law of gravity. If I drop the pen I am holding, it will fall. That statement is perfectly true, and is made true by the law of gravity, even if I don't drop the pen. It is a statement about the causal potential of the pen, regardless of whether that potentiality is actualized. In the same way, a syllogism with false premises can be seen as a true statement about metaphysical potentiality. An apple is not a kite, for example; that is not its actual identity. But if being a kite were the apple's identity, then by the law of identity (as reflected in the dictum de omni) anything true of kites must be true of apples.

5. I would agree with Mr. Perigo in the following respect, however. Potentialities, whether causal or metaphysical, exist only in the context of actual things, with their actual identifies and actions. It is only because objects do fall, or otherwise act in accordance with the law of gravity, that we can say with confidence what would happen if an undropped object were to be dropped. In the same way, the laws of identity and non-contradiction are made true by the actual identities of actually existing things — that's all there is in reality.

As for how the laws of identity and non-contradiction, and other laws of logic, are learned and validated, the Objectivist epistemology does not have a well-developed theory. Rand's own remarks in Introduction to Objectivist Epistemology are only a preliminary. But a cardinal principle of epistemology is that questions about how we know cannot be taken to discredit what we know. That the laws of logic are true — true in the ordinary sense, as identifications of facts — is implicit in the realist view of knowledge as being of an independent, objective reality. I have no idea what it would mean to grasp such a reality if our primary tool for doing so were an arbitrary construction.

David Kelley, PhD
Executive Director
Institute for Objectivist Studies
New York

If you enjoyed this, why not subscribe?