This paper will present my position on a priori knowledge. As Pollock states, the source of such knowledge is "quite mysterious" and "comprises one of the most problematic areas" in philosophy (11). Chisholm begins his treatment of the topic with Leibniz's statement that, "There are also two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary, and their opposite is impossible. Those of fact, however, are contingent, and their opposite is possible" (26). Chisholm then offers a general definition of a priori truth as those "propositions that are necessarily true and such that, once one understands them, one sees that they are true" (Ibid). A set of such propositions is the axiom which is traditionally taken to be "incapable of proof"; that is, there is no proposition which is better known. (Ibid, 27) This understanding of axiom naturally implies then that the axiomatic proposition is "better known" to us than any demonstration thereof. This implication is reflected in Thomas' claim that "those who have knowledge of the principles [i.e., the axioms] have a more certain knowledge than the knowledge which is through demonstration" (Posterior Analytics, quoted in Ibid, 29). Upon such axioms a greater body of a priori knowledge is then established.
This understanding of a priori knowledge troubles me for two reasons. First, it claims a complete independence from actual states of affairs, that which Leibniz refers to as "truths of fact" or Thomas as "demonstrations". Secondly, the claim is then made for the superiority in quality as knowledge of the axiomatic over the actual or particular. Though over simplistically outlined here, I do believe these two claims characterize particular traditional views of a priori knowledge.
I would argue, however, that rather than an independent status, such axioms are more primarily descriptive of actual states of affairs and to the degree our reality operates uniformly, they may be said to be prescriptive. One might object that this seems to imply that the relationships to which such axioms refer (such as non-contradiction) are contingent and subject to change should facts change. Though theoretically possible, it is our experience that such facts do not change, but in fact, operate consistently and uniformly. To say that the law of gravity primarily describes actual states of affairs does not necessarily imply it is contingent or transient.
Axioms describe relationships which will always adhere among particulars within our reality. To state simply that such axioms are "truths of reason" would seem to imply that such axioms are laws of reason or of thought and as such do not depend upon external fact. But as Russell rightly points out, belief in, for example, the law of contradiction is to be distinguished from the law of contradiction itself. On the distinction, he writes,
- "The belief in the law of contradiction is a belief about things, not only about thoughts. It is not, e.g., the belief that if we think a certain tree is a beech, we cannot at the same time think it is not a beech; it is the belief that if the tree is a beech, it cannot at the same time be not a beech. Thus the law of contradiction is about things, and not merely about thoughts; and although belief in the law of contradiction is a thought, the law of contradiction itself is not a thought, but a fact concerning the things in the world" (89).
Though time does not here allow an adequate justification of my reasoning, I would, through the position outlined above disagree with Thomas' claim that knowledge of the axiom is a more certain knowledge than the knowledge which comes through demonstration. As Russell alluded to earlier, the certainty in our knowledge of the axiom is grounded in the axiom's correspondence to reality. Thus, I personally doubt that an observation of the actual relationship is less vivid or less certain than our belief or knowledge that such a relationship would adhere (or will adhere in potential scenarios). This disagreement, however, raises the issue of the role of such axioms within reason. It is not the case, as we have seen, that these are "axioms of reason" in the sense that the mind is naturally compelled to adhere to them. And yet it remains that such axioms serve as a standard whereby thought or reason itself is rightly deemed truthful or erroneous. Logic itself consists of such axioms and the inferences drawn from them. Thus the role of such axioms differs greatly from, for instance, our earlier example of the law of gravity. Although Aristotle adhered to logic or right reasoning, his conclusion that "it is the nature of all bodies to seek a state of rest" does not correspond to reality.
In contrast, the axioms of which we speak are not subject to erroneous thinking in the same sense. One might disbelieve or dispute their universal application, but to do so, we might say, seems unreasonable. It is precisely for this reason that these axioms have been traditionally deemed "basic truths".
How is it that these axioms operate in such a distinct manner within reason? On the one hand we have said that these axioms are not simply "laws of thought", that they refer to real things. And yet they do indeed operate as principles, even laws necessarily adhered to in any right reasoning. Several answers to this question are possible depending on how one wishes to account for the origin of the axioms. Some view such axioms as belonging to the very nature of God such that God himself and all he creates necessarily adhere to them. All of God's dealings with humanity demonstrates adherence to the axioms and so the conclusion is possible that they stem from God's nature. It is clear that if this understanding is correct, then Thomas' claim would be quite reasonable, since knowledge of the axiom is then knowledge of an aspect of God's nature and as such is easily superior to knowledge derived from material objects. This understanding would also support the very clear distinction traditional views have maintained between matters of fact and reason. Given the location of the axioms within the divine nature, and given the belief that rationality is an aspect of the imago dei, the relation between axiom and reason is made independent of actual states of affairs. One difficulty with such a stance is that it subjects the divine nature to the same consistency we see in the created order such that God is said to necessarily abide by all such axioms including, for example, mathematics. (This is Plantinga's conclusion in Does God Have a Nature?)
An alternative to this explanation and one I am more inclined to accept is that which views such axioms as inherent in the order of creation as designed by God, though without concluding that such design necessarily stems from the divine nature. It is evident that our reality consisting of material bodies and three dimensions necessarily adheres to certain axioms such as the law of contradiction. For us, reality could not conceivable act in any other manner. But this inability to conceive otherwise does not preclude God from acting otherwise, in the same way our utter inability to conceive a five dimensional object in no way precludes the possibility of its existence. This alternative explanation allows the type of dependence of "a priori" knowledge upon actual states of affairs I have proposed in this paper. It also accounts for the unique role such axioms play in regard to reason itself, by relating the axioms to the actual context, the state of affairs within which both reality and reasoning take place. The difficulty with this position is, of course, that it does not lend itself to statements regarding the nature of God or his thoughts. It does not necessitate God's adherence to the axioms he employed to construct our reality. Instances of God's adherence to such axioms as found in God's communicated affirmations and negations in the form of human language would be explained in terms of the necessary conditions for human understanding rather than the necessary conditions for divine communication.
As to whether or not God always abides by such axioms remains unanswerable according to this view. One might suggest that God's nature is qualitatively different such that the law of contradiction does not apply in any way to God outside of his voluntary use of it in communicating to humanity. Or one might suggest that a quantitative difference exists such that God's nature is understood to operate at an infinitely higher capacity such that those axioms which constitute our "basic truths" are in fact circumscribable by him in some way. Neither of these positions is necessitated by the proposal put forth in this paper, nor is one more likely than the other without reference to other discussions, though the latter is to be preferred for reasons not mentioned here.
Such a brief argument as this undoubtedly leaves too many generalizations and unanswered objections. It serves only to indicate the direction I find myself moving.
Chisholm, Roderick M. Theory of Knowledge. (New Jersey: Prentice Hall; 1989)
Pollock, John L. Contemporary Theories of Knowledge. (Maryland: Rowman & Littlefield Pub.; 1986)
Russell, Bertrand. The Problems of Philosophy. (New York: Oxford Univ Press; 1997)