Nietzsche on the Synthetic A Priori

¨How are synthetic judgments a priori POSSIBLE?" Kant asks himself--and what is really his answer? "BY MEANS OF A MEANS (faculty)"--but unfortunately not in five words, but so circumstantially, imposingly, and with such display of German profundity and verbal flourishes, that one altogether loses sight of the comical niaiserie allemande involved in such an answer."

"But such replies belong to the realm of comedy, and it is high time to replace the Kantian question, "How are synthetic judgments a PRIORI possible?" by another question, "Why is belief in such judgments necessary?"--in effect, it is high time that we should understand that such judgments must be believed to be true, for the sake of the preservation of creatures like ourselves; though they still might naturally be false judgments! Or, more plainly spoken, and roughly and readily--synthetic judgments a priori should not "be possible" at all; we have no right to them; in our mouths they are nothing but false judgments. Only, of course, the belief in their truth is necessary, as plausible belief and ocular evidence belonging to the perspective view of life."

Friedrich Nietzsche- Beyond Good and Evil

Friedrich Nietzsche takes on Kant's attempt to derive universal laws of thought from which we can derive new knowledge about the world, in response to Hume's skepticism.

A priori knowledge is before experience, a posteriori is after experience. 

Analytic truths are those which are true by definition and synthetic truths are true by their relation to the world. 

Hume had only analytic a priori and synthetic a posteriori truths: only knowledge from experience tells us about different things in the world. 

Kant's response was that mind has universal conditions which make knowledge possible and so enter into all judgements, making a priori synthetic knowledge possible because we, "by a means", always use them with regards to experience so there's no absolute wall between reason and experience. And so there are universal necessary truths from which we derive knowledge about the world, even if we have to restrict them to what humans can perceive of the world in itself. 

Nietzsche's response is that such necessary conditions of thought are only necessary for our purposes as living beings and it doesn't matter if they relate to the real world. It is our activity which makes the a priori synthetic, as we are ultimately sensual beings in the world. The a priori itself is only our belief in our own judgements. We need synthetic a priori knowledge to serve our own purposes and it doesn't matter if it is universal either to our thoughts or to the world. It is relevant to our specific needs. 

We need not consider this a form of truth though, and so Hume is right.

David Hume on Necessary Existence

"I shall begin with observing, that there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable."

Hume's argument against attempts to demonstrate the existence of God through reason from Dialogues Concerning Natural Religion.

The only thing one cannot conceive of as not existing and be in contradiction is existence itself, but everything else can be conceived not to exist without contradiction if there is no matter of fact to its existence.

Something either exists or it doesn't. Any notion we have of something is derived from sense experience or is an idea culled from sense experience, and so to infer the existence of something from our ideas will only give us another idea of something which can either be detected in the sensual world or it can't. Just because one conceives of a being doesn't mean it exists, just that an idea exists which is a synthesis of ideas from sense experience.

When it comes to existence, one either experiences something or not, but anything more cannot be inferred with necessity. That something exists rather than nothing at all is the only necessity in the universe. The universe exists and it couldn't be otherwise, but the existence of anything else is contingent on facts.

Notice Hume says distinctly conceivable, which implies some self-fabrication or some particular contingent thing.