This House Believes That Synthetic A Priori Knowledge Exists!

I thank bossyburrito for accepting. I want to give a fair warning to everyone, this is no mean debate, if you lack philosophical expertise, please abstain from voting. Once more I'd like to state that there is a 2, 000 Elo Minimum requirement for voting. I cannot define every term, so should anyone want to acquaint themselves with the complex terminilogy used, I suggest a reading of the Introduction of the Critique of Pure Reason by Immanuel Kant, or a reading from Stanford Encyclopedia of Philosophy. I should like to clarify my position. I am not advocating for rationalism, nor am I denying sensory knowledge. This debate is to decide whether alongside with sensory knowledge, humans also possess synethetic a priori, or pure rational knowledge independent of any sense experience. I am arguing for a Kantian view where empiricism, and rationalism go hand in hand. My opponent will be arguing that pure rational knowledge (if substantive a.k.a synthetic) does not exist, and all knowledge is empirical. I may have the onus in proving the existence of a priori knowledge, but my opponent needs to do more than poke holes, they must not ask questions, but must support an anti-thesis with reason. I hope the readers enjoy, and I wish bossyburrito (from now Gabriel or Gabby) the best of luck. Once more please understand terms such as a priori, a posteriori, synthetic, analytic, and empirical before continuing. Accompanying texts to explain ideas have been cited.1. Of Mathematics:(1.1) In all Mathesis that constitutes ta Mathemata, the judgements that form follow an apodictic order, and it is true, as it is in all apodictic systems, insofar as they refer to themselves by incontrovertibility from establishment of non-contradiction. Presented then, is a two-fold judgement: that such, and by extension all wissenschaft possess, insofar as they are limited to being Mathesis, an ontological conceptualization of necessity, and that the aforementioned must be binded by non-contradiction, in contradistinction to being naturally so.[1](1.2) It may, due to non-contradiction seem that Mathematics may be analytic. In an anamnistic tone, knowledge which of itself would declare itself to be analytic must possess self-reference. As Kant says: 'Either the predicate B belongs to the subject A; or B lies outside the concept A, though connected with it. In the former case I call the judgements analytic, in the latter synthetic.'[2] Taking Kant's paragon, consider 7+5=12. It is a simple arithmetic equation. It should be evident that the judgement we form here is "12". Consider the judgement 12, which was born out of the knowledge of 7, and 5, with the knowledge of addition. Neither 5, nor 7 indepdentently contain the knowledge of 12, unlike "all bachelors are unmarried" where the term "bachelors" in itself implies unmarried. Since the judgement does not belong to the predicate, but rather exists outside it, we may safely say ex ve termini that all judgements matheta are synthetic.(1.3) We can say for Mathematics, what we cannot for numbers, for since numbers in themselves are not judgements, nor are they ontological creations, any ontic of such sort will remain esoteric so far as enumeration of predication within boundaries of synthetic or analytic are concerned. Though we may discuss this later, as for now they this does not concern us immediately.(1.4) To satisfy ourselves of Mathematics being a priori, we have laid the foundation a priori (haha). Let us first know the buissness of Mathematics, as Kant says: 'the buissness of Mathematics...is that of combining, and comparing given concepts of magnitudes, which are clear and certain, with a view to establishing what can be inferred from them.'[3] Then so long as we know that these concepts and judgements are exhibited in concreto of intuition our task becomes easier. For our first proof we say that Mathematics possess, precisely for its being an apodictic system, de jure a conceptualization of necessity. It is then contradictory to state that Mathematics is empirical, for firstly it is a form of judgement, and secondly that this judgement is necessarily objective. I shall, hopefully, reach the same Mathematics judgement as anyone else with the same predicates. Simply then since Mathematics provides objective truths, and no empirical means can provide such empirical truths, for they arise only of the intuition, we may safely deduce that Mathematics is a priori. Is it clear then? Simply because Mathematics possess the conceptualization that is lacking in empirical sciences we may safely conclude thus.[5] We assume empirical judgements being subjective as principia probant non probantur. (1.5) If this were not enough though we shall present a second proof to our above thesis. We know from Godel's Incompleteness Theorem that Mathematics cannot be axiomised. By extension of the Second Theorem we know that T cannot be the proof of its own consistency. Thereby any judgement of Mathematics, or more precisely, the order of the judgement must be proven by another order. This means that a basic arithmetic equation, that goes on to prove others, cannot be proven. Thereby 1+1=2 (this is a hypothetical example, as the actual example is too technical to post here) may not be proved. This works equally well, because there is indeed no proof to this statement. I must have the idea of both 1, and 2 a priori for this to make any sense to me: it bases itself de jure out of intuition. 2. Space:(2.1) Human cognition represents to itself objects, to which it attributes certain dimensions, and relations. This quality of possessing such dimensions has hitherto been known as Space. It is our wish then to show that these objects which are given this quality, are done so because of an external sense. It is then out duty to postualte that Space could not have been gauged by the senses and if we can show this, seeing how essential Space is to the understanding and collection of empirical knowledge we will have shown that at the base of the pillars of empiricism, lie purely theoretical postulates, one such being Space. (2.2) Space then must exist as a foundation a priori for in order for me to recieve certain sensations from external objects, or them from me Space must exist as a foundation. For I could not be represented to them, nor them to I had the idea of Space not been inherent. Consequently then the knowledge of space could not be gained from the experience of external phenomenon, rather on the contrary this external experience is only made possible, the cognition can only address it if the said foundation of Space is antecedent to experience. I believe the point is made rather clearly, in simpler words I mean to state that the knowledge of Space could not be borrowed from experience for experience has the condition of having the knowledge of Space as a foundation a priori. This is made quite clear by the fact that while we can imagine Space devout of an object, our cognition falls into dogma when it practices to imagine a phenomenon where an object does not possess Space. (2.3) Space must also then be a priori for we cannot imagine the concept of pure Space, rather we can only take it as a quality certain objects possess. A coin may possess Space, as may a chair or a lamp however the idea of Space as a seperate entity alludes us, and it would not be so had space been a concept a posteriori. For the general concept of Space, had it been taken from experience would be subject to the scrutiny of human cognition, but this is not so, for we cannot imagine Space lest we imagine an object which possess Space. It is also then that we have possess only one Idea of Space, which would not be so if we have gauged it from experience. While to different objects we give the different variations of Space it is clear that these are only the make ups from the original conception of Space. Whether we view a tiny object, or a large one, even though both objects possess different Space and therefore should be a posteriori we know that they are only parts of the all encompassing original Idea of Space for we can apply this Idea of Space to concepts purely unknown. It then follows that Space must be purely a priori. For from our above premise it directly follows that our Idea of Space may be taken to infinity, where an infinity amount of objects may be studied, each varying, through the same conception of Space, something impossible if Space were a posteriori. For if such a case would have occured then it is simple enough to assume that a different view of Space would be taken for different quantities, and in no way could one Idea of Space be applied so apportionately to all other phenomenon, and an infinite number of representations would be impossible. Therefore it is quite clear that Space is an intuition a priori. There shall be more, but I'm very tired right now. I wish Gabby once more, the best of luck. He's my boo.