This House Believes That Synthetic A Priori Knowledge Exists!

A disclaimer: I finally finished this round at 8:43 AM, and I think I've started to get delirious from a lack of sleep. I first want to start with my conclusion, in order to allow the reader the knowledge of where the following train of logic is headed. I am to argue that a so-called synthetic truth (i.e. a truth which is true not because of the concepts involved, but rather the concepts’ relationships to those things not included in the proposition) is self-contradictory. I intend to show that the main quality which my opponent ascribes to analytic truths (“self-reference”) must be present in any truth, so that the idea of a non-self-referential truth (a synthetic truth) could be discarded.A concept is a mental construct created to organize sense-data according to similar and dissimilar characteristics. For instance, if a young child saw three cars, he might recognize that they all have four wheels, headlights, etc. These would be the defining characteristics, or the essences, of cars, and any entity that did not have these characteristics would not be said to be a car. The concept covers all potential instances of concretes with those qualities, but it must be noted that concepts can only refer to legitimate and concrete existents (else the concept would refer to non-existents, and would have no value). For instance, if it is said that the sentence "Humans have two eyes" is synthetic, it is proposed that "two-eyedness" is not a part of the concept of man - which ignores that concepts refer to specific referents that are just categorized because of similarities. To *only* look at these similarities (the essences of the things) would be to ignore the fact that concepts subsume individual existents, meaning that any existent that falls under a concept falls under it as a whole - the "essence" of something is not separate from the thing itself. Therefore, ignoring that the fact that some individual men have two eyes and claiming that that quality is not part of "manness" is to say that concepts do not reference existents, which invalidates the idea of conceptual abstraction altogether. If it is said that the knowledge is based on something outside of the concept under which the referent is subsumed, it is said that knowledge is based on what an existent is not – i.e. the opposite of the real.Since all existents have qualities, and all qualities are subsumed by their respective concepts, then all concepts (and, as a result, all existents) can be said to be equal to themselves – all knowledge, then, can be reduced to tautologies in the form of A = A. The only way for synthetic knowledge to exist is for an existent to have a quality that its concept, by virtue of its identity, does not – which, if what I have said holds true, is impossible. 1. Of Mathematics:“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.”While this reasoning might seem sound at first glance, a closer look shows the flaws in this reasoning. An example of a (supposedly) analytic statement is given: “all bachelors are unmarried”. This is compared with the statement “7+5=12”. My opponent argues as follows: the word “bachelor”, in itself, implies that any bachelor is unmarried, while none of the terms of the math equation given, in themselves, imply that the equation given should be true. Since, he says, 7+5=12, if the previous assumption holds true, the equation must be an example of synthetic knowledge – knowledge that does not come from the concepts in question themselves. If, though, it is shown that “7+5=12” can be known from an analysis of concepts only, it holds that math is analytic.If it is true that the concept of a bachelor is taken to be equal to the concept of an unmarried man (by virtue of identical definitions), then it can be said that all unmarried men are unmarried. This is because any bachelor has the same qualities as any unmarried man in the context of their being unmarried. In other words, since “bachelor” is synonymous with “unmarried man”, it holds that either could be substituted for each other. The only prerequisite is that both terms being substituted have the same meaning when placed in the same roles in the proposition – “salmon” and “the fish with qualities x, y, z (which are unique to salmon and are the defining characteristics of salmon)” are synonymous in the sentence “___ has the particular qualities x, y, z. “Now, let us apply this to the math equation. It is true that the number seven is equal to the number seven, is counted as seven units, etc. It is also true that the number seven is five short of twelve. Likewise, it is true that it is a quality of the number five that it is seven short of twelve, and it is true that twelve, when seven and five are taken from it, is equal to zero. As explained earlier, these qualities are contained within the concept of these numbers, as concepts subsume all potential referents. So, if it is true that “seven” is equal to “a number five short of twelve” (as shown by the fact that, in the equation 7 + 5 = 12, either incarnation of “seven” would result in the validity of the equation), and if it is true that, by analyzing these synonymous (i.e. undoubtedly conceptually self-contained and equal) ways of stating each number, the equation 7 + 5 = 12 can be proved (by way of definitional analysis of the fully-substituted equation, five less than twelve in addition to seven less than twelve is equivalent to the sum of five less than twelve in addition to seven less than twelve), it has been made clear that math is, in fact, non-synthetic.“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.” As my opponent has admitted, he has taken for granted that sense-experience is, by nature, subjective (and, by extension, can only produce subjective results). This means that he has done nothing but arbitrarily assert that math is a priori, as a result of his unsupported premises. Regardless, I will try to show that math is, in fact, dependent on sense-experience.Via the Kantian definition supplied by my opponent, it can be seen that math is based on units with specific values. This is all that is needed to make progress in the field, but there is a question which needs to be answered to determine if math can be known a priori: is it possible to create and recognize units without sense-experience? The answer seems fairly self-evident – the use of any unit presupposes the concept of units themselves. Any unit must be, in order to be comprehendible to man, be able to be a unit of something. A unit, contemplated by a mind in which the only experience with said units is in a vacuum, would be inconceivable – any such unit would be divorced from any substance or definition, as there is nothing to define it by. It would be a floating abstraction, detached from anything physical, and, as such, would not be able to be used or even understood (Unless, of course, “innate knowledge” can be unknowable).“Thereby 1+1=2 (this is a hypothetical example, as the actual example is too technical to post here) may not be proved […] out of intuition.”It is certainly true that any attempt to understand something such as 1+1=2 requires knowledge of all the concepts involved, but, as I have explained, the concepts of units must be formed a posteriori. My opponent has given no reason to believe that this is otherwise, especially in light of the concerns I have raised over his (unsupported) position. 2. Space: “Space then must exist as a foundation […] 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 can be shown to be false quite simply by imagining a world in which sense-organs did not exist. If space is an a priori concept, it could be understood without any help from sense-perception. The problem, then, is that space can only be understood if things which take up space are perceived – in a world in which there is no way to know that anything exists via a posteriori means, the concept of space (which you claim is a priori because sense-experience depends on it) would be meaningless to any man. This is because space is, as you pointed out, a result of human methods of cognition, or, in other words, completely intertwined with sense-experience. Space is one of the attributes of the result of the world being sensed by man – this, if anything, means that knowledge of space is clearly not a priori.“For if such a case [...] Space is an intuition a priori.”There are two issues with this: firstly, the concept of space can be applied to every potential referent just as any other concept can do the same – the fact of the matter, though, is that, since there is a finite number of representations of space at any given time (the potential is infinite only because, at any point when counting, you can count to a higher number – much like slicing a cake into smaller and smaller pieces, although you could theoretically keep going forever, whenever you do stop you’ll have a finite number of slices), and, again, the concept of space is meaningless without sense experience.