This essay is based on ideas from A. J. Ayer’s book Language, Truth, & Logic. The first two sections detail my understanding of some concepts from this book, and the final section shares a short reflection.

Two Kinds of Knowledge

We can divide knowledge into two distinct types: a priori knowledge, or that which we know indpendent of experience, and experiential knowledge, or that which we know through experience. For example, we know that the statement “All men are mortal” is true prior to observing any evidence that might substantiate it, and therefore this statement constitutes a priori knowledge. The reason that we can know that this statement is true is becuase mortality is a necessary condition in the definition of “man”, enabling us to logically deduce its truth, rather than needing to observe that every man has eventually died. Experiential, or empirical knowledge is acquired through the senses: signals of reality as interpreted by our brains. An example of this kind of knowledge is that the sky is blue.

Truth

One might then wonder how we come to know that a proposition is true, and the answer depends on whether we are considering an a priori proposition or an empirical proposition. A priori propositions can be verified or refuted by logical deduction alone. Logical deduction can be understood as the process of sequentially manipulating symbols, as permitted by a set of substitution rules, to traverse the space of possible propositions along paths of equivalent propositions. For example, we can pass from proposition A. to proposition B. by substiting the phrase “bachelors” for its definition, arriving at a tautology which then validates the truth of A.

A. “All bachelors are unmarried men” -> B. “All unmarried men are unmarried men”.

It is interesting to note that this verification method for a priori propositions implies that observation has no bearing on their truth or falsehood.

Verifying empirical propositions requires quite a different procedure. In this case, we must start with hypotheses about the nature of the world. If we observe that our hypothesis accords with nature, then our confidence in this hypothesis may increase, and similarly if we observe that the hypothesis contradicts natrue our confidence may decrease. We may then hypothesise that our empirical proposition is true, and we may be confident in its truth because we have observed it to be true many times, but we can never be certain that it is true. Indeed, absolute certainty is reserved for a priori statements, tautologies.

We can say then that of scientific laws, as they are empirical propositions, we may only ever be highly confident, and never certain.

Connecting the A Priori and the Experiential

The book has exposed an interesting distinction between mathematics, which consists of a priori propositions, and science, which consists of empirical propositions. I found this surprising, because maths is so heavily used in science, and science is used so often as an inspiration for new maths. I question how it can be that maths provides us which such useful analogies to the natural world, when it is in essence a tautological system whose validity can be neither confirmed nor denied by new observations of nature. The best answer I can think of for now is that the a priori – logic – arises from our human brains, which have been crafted by nature. Logic can then be seen as a tool which our brains have developed to help us make predictions about the natural world, and then a priori deduction can be seen as a kind of exploration of an internal world which has been modelled on the natural world.