I haven’t done a philosophy post for a while, so
let’s rectify that with a blog about Kant’s synthetic a priori. To start us
off, here’s a useful reminder of my summary of epistemology in 400 words.
Make any statement about reality and it will be incomplete in some way. If it is a statement that you can prove with logic or mathematics then it falls short of describing anything conclusive about any reality outside of mathematics or logic; if it is a statement about physical reality then it falls short of anything that can be conclusively proven to apply in all cases (in the black swan sense); if it is a statement of fact then it cannot be established by logic or by reason prior to initial experience; if it is a logical proposition then its subject/predicate content must be verified outside of the proposition; if it is an allusion to an inner concept then it is not knowledge (justified true belief) of the perceivable world; if it is an allusion to an inner perception of outside reality then it escapes your certainty; and if it is a statement about a metaphysical interpretation then in its proprietary form it is entirely subjective.
Everything is derived from experience (this is the basis of Hume’s fork – everything is classified as either Relations of ideas and Matters of fact), but in distinct ways: a priori is knowable without having to consult experience, except initially to understand the terms (“all bachelors are male”); a posteriori is only knowable by consulting experience (“London has a higher population than Birmingham”); analytic statements (A is A) are true by virtue of the meaning of the terms, synthetic statements (A is B) are true by virtue of meanings in relation to facts; physical statements are in relation to the material world (“the chair has four legs”), metaphysical statements are subjective ideas formed as a result of relation to the objective world (“Love and grace triumphs justice and revenge”); and necessity and contingency are related to whether or not a statement is conditioned by how the world happens to be.
Relations of ideas and Matters of fact describe everything, including all the notions like a priori and a posteriori, necessity and contingency, the physical and the metaphysical and the analytic and synthetic distinctions – they are part of our matters of fact derived through experience, and our relations of ideas that result from that experience.
Every possible distinct description of experience is covered above, because everything is either a fact (an impression) derived from experience, or a relation of ideas based on those impressions from experience.
Regarding Kant, the general historical method is that we identify all the possible mental configurations with the class of analytical and synthetic truths, and ascertain our success in tailoring models to reality. Because there is a quite seamless blend regarding the way experience requires an up and running interpretation component and how perception naturally integrates with the outside rules of nature, analytical truths and synthetic truths are really just different interpretations of the same empirical structure built from experience.
To that end, I’ve never really understood why Kant made such a mountain out of the synthetic a priori so-called problem in philosophy. I think if he’d have been steeped in 300 years of empiricist science and philosophy, as we are today, he wouldn’t have exhausted so much of his time over it.
Kant's analytic-synthetic distinction was posited to identify two types of knowledge related to our experiences of the world. In the Kantian terms, analytic statements are statements in which the concept of the predicate is included in the concept of the subject - so for example 'All triangles have three sides' or 'All bachelors are unmarried' are analytic statements because the predicate is found in the subject (i.e. a triangle, by definition, must have three sides, and a bachelor must be unmarried). Synthetic statements do not have the predicate found in the subject - so for example 'All life on earth is carbon based' cannot be shown to be true by the subject and predicate alone, it must be constituted as knowledge by external evaluation and repeated experience of the world.
The easiest way to put this to bed is to say that we cannot have any knowledge without attaining that knowledge through experience of the world. Although there is a secondary distinction regarding experience of the world that remains useful; a mind needs to experience reality to acquire all our knowledge and familiarity with patterns in that reality, so the issue of whether something can be worked out without needing to consult external facts or ideas was a pertinent philosophical question. This is where Kant’s famous example of 7 + 5 = 12 was considered as a synthetic a priori judgement. It is a priori in that we do not need to consult the world and experience 7 things and 5 things grouped together to know that they are 12 things, but it is synthetic in that there is nothing in the concept of 7 or in the concept of 5 that implies twelve; it is only when the two are combined (synthesised) that we can get twelve.
Understanding this an as empirical landscape deadens the mystery Kant was trying to illuminate. In subjecting our mind to Kant’s arithmetic, we would have these ideas formed without experience of the world, but equally at a secondary level we need not consult external facts to know that 7 + 5 = 12, so this is why the analytic-synthetic model works on those two levels.
I do not think Kant’s ideas or definitions were
strong enough to capture fully the relationship between definitions and their
relations regarding predication, but it wouldn’t have been so problematic to
him if he was writing under a stronger empiricist framework. Our dealing with
reality and our ideas about causal relations are very much grounded in both
perception, experience and ideation, so they are not mutually contradictory -
they are complementary, and can give a fairly accurate signpost towards sound
epistemology.
A priori knowledge is claimed to be knowledge which is known not through experience. But it’s better to think of all knowledge as being acquired by experience, and analytic propositions as describing a way of knowing but not extending knowledge already acquired. The primary distinction is about how they are determined; we always discern the analytic judgment by extension to what is contained in the proposition, but it's the structure we are determining, not what it contains. That’s why structurally 'All triangles have three sides' works the same way as 'All bachelors are unmarried' even though the subjects are different. Kant’s issue with synthetic, a priori knowledge seems to me to be a twofold combination of him not fully developing why it was supposed to be a problem and, as a consequence, not reaching the conclusion that it isn’t a problem.
