A Priori: Peikoff's Misconception

Classical philosopher Immanuel Kant theorized two types of knowledge; a priori and a posteriori knowledge. Basically, a priori knowledge is something that we can know intuitively, one that does not require experience. Meanwhile, a posteriori knowledge is something we can obtain by observing reality with our senses. A pretty harmless conjecture, but then, the rise of the Objectivist movement, eager to prove itself in the philosophical realm, boldly challenged the philosophies of old. Leonard Peikoff, the so-called intellectual heir of Ayn Rand, contested Kant's theory about the nature of knowledge. 

In the Ayn Rand Lexicon, a priori knowledge as explained by Peikoff is as follows:

Any theory that propounds an opposition between the logical and the empirical, represents a failure to grasp the nature of logic and its role in human cognition. Man’s knowledge is not acquired by logic apart from experience or by experience apart from logic, but by the application of logic to experience. All truths are the product of a logical identification of the facts of experience.

Peikoff claims that logic cannot be separated from experience, and that truth can only be attained by applying logic to experience. A bold assertion, but a dangerously flawed one. 

Yes, knowledge can be gained by applying logic to experience. This is called induction. Scientists have applied induction in their scientific research. Thanks to Francis Bacon and Galileo Galilei, induction from its primitive form (applied by Ancient Greeks like Aristotle) developed into a highly systematic methodology, something we now call the scientific method.

But Peikoff's argument fails to acknowledge another manner of acquiring knowledge; deduction. And as most philosophers would know, knowledge (or truth) from induction is probabilistic, while the knowledge (or truth) acquired from deduction is necessary. Take the mathematical form of modus ponens for starters. 

P ⊃ Q

P

∴ Q

This is read as: P implies Q; P, therefore Q.

This is a standard logical syllogism in mathematical logic. But how did we come to know this? How do we know it's valid? By Peikoff's argument, we knew this because we applied logic to experience.

But then proving this by induction would be a heavily arduous task, since deduction is known to produce necessary truths. This means that modus ponens must be true for anything, and must have no counter-instance. So, should we examine every causal relationship that occurs in this universe? Can you even do that? If we can't do this, then we fail to establish Peikoff's argument that knowledge is attained only by applying logic to experience.

So what becomes of Peikoff's definition?

Well, how about we disregard deduction altogether, since it doesn't fit with Objectivism? Why, that would be disastrous. Recall that inductive reasoning is obtaining a generalization from a specific data. Meanwhile, deduction is defined as obtaining a specific data from a generalization. If we disregard deduction as a body of knowledge, then what would become of all the scientific predictions our civilization has come up throughout the years? 

To illustrate this cataclysm, consider this simple scientific knowledge we have gathered from our early years. This is one of my professor's favorite examples.

So a caveman observed the sun every morning, and noticed that every time he sees the sun rise, it rises from the east. Months have passed and he sees the same thing; the sun always rises from the east. The caveman then made a leap of faith (or reason), and asserted this thing; the sun always rises from the east. He has successfully applied inductive reasoning; from a set of specific data (he sees that the sun rises from the east everyday), he was able to formulate a generalization (the sun always rises from the east). 

However, another thing can be done from this generalization; prediction. The caveman can assert that tomorrow, if the sun rises, it will rise from the east. This is deductive reasoning; from a generalization, he was able to formulate a specific data; a prediction. We also know that mankind has been able to predict countless things by deductive reasoning.

However, by Peikoff's definition, what the caveman did is wrong. He hasn't experienced tomorrow yet, therefore his prediction is not true knowledge. He was able to relate an unseen to the seen, an immaterial to the material, a potential to the actual; this is intuitive knowledge at work... an a priori knowledge, but then Objectivism asserts that a priori is not true. So how do we settle this dilemma?

How about we assert that knowledge from deduction is not necessary, but probabilistic, just like induction? Since knowledge is either inductive or deductive, such an assertion gives us an interesting conclusion; all knowledge is probabilistic. What then, becomes of arithmetic?

I'd love to have Objectivists say that 1 + 1 = 2 is probabilistic.

Oh, and besides that, I'd love to have them assert that man is man is probabilistic. Oh, but they can't; man is man, that is their ethical axiom! 

Perhaps, in the Objectivists' zeal to demolish Kant's philosophy (they seem to hate Kant very much), they have walked into a subtle trap; self-contradiction. They themselves are guilty of using necessary truths and knowledge to prove their points, but then they accuse someone who points that out of being evil and dishonest.

Perhaps the administrators of Ayn Rand Lexicon should take a look at how they define Kant's theory of knowledge. After all, for a group who claims to despise intellectual dishonesty, for a group who claims to uphold objectivity, such an action is, needless to say, expected.