This House Believes That Synthetic A Priori Knowledge Exists!

I want to make clear that the three arguments my opponent cited me as giving are, for all intents and purposes, accurate. Let me begin with my rebuttles, then. <strong> In reply to “On Synthetic Truths”: </strong> As I explained in my previous round, the fatal mistake with arguments of this kind is that the “essence” of a concept is conflated with the concept as a whole. It is true that all conceptual referents of a certain kind must have those attributes which are unique to the concept, but this does not mean that all other characteristics of those referents can be ignored. The fact that an <em> individual </em> man is a rational animal does not mean that he is not also two-eyed, to use the example I gave previously. If this is so, and if a concept only consists of the individual concretes (potential or otherwise) it subsumes, then the fact that that individual man has two eyes directly means that it would not be incorrect to say that men have two eyes (for this is valid by looking at the example man given – a conceptual referent which is wholly in-the-concept). In the same way, since some individual and concrete children have and do wear hats (i.e. they have the quality of “hat-wearing”, and thus hats are included in the concept of children), it is true that “children wear hats” by virtue of the concept of “child”. The issue at hand is my opponent’s insistence on viewing concepts not as collections of concretes, but as existing in some ethereal realm of essences. This view has been shown to be false, however, by way of the fact that, if I think of something with the quality “manness”, for example, I necessarily refer to an entity with other qualities (such as a body which takes up space, a brain, etc), and entities of this kind can have even more unessential qualities (such as weight or hair colour). These unessential qualities are <em> just as real </em> as the quality of being a “rational animal”, as a being can be a rational animal while holding other qualities. Therefore, if it is true that concepts refer only to essences, it would only be fair to conclude that we should think only of disembodied essences when the concepts are evoked – this is known to not be the case by anyone who has any knowledge of unessential qualities existing in a conceptual referent. <strong> In reply to (3.4): </strong> My opponent ignores that the concept “7”, <em> by the fact of equaling 12 when added with five </em>, includes in it the quality as just stated. If it is taken to be true that 7 + 5 = 12, then it is true of 7 that, when five is added to it, it equals 12. The same logic I have given before on the idea on concepts being made of concrete referents shows that, if it is observed that an instance of the above equation is true, then it is true not only of that individual “7”, but of all “7s” in like scenarios, that 5 added equals 12. 7 automatically subsumes “+ 5 = 12” by virtue of it being 7 – as such, it cannot be considered a synthetic truth that 7 + 5 = 12. In other words, since it is true that 7 + 5 = 12, it is true of the concept “7” that 7 + 5 = 12, and, as such, it is not a synthetic truth. This same logic can be cross-applied to any expression to show that none can be truly synthetic. In response to “Space”: “In fact my opponent just proves my argument: s/he states that Space is necessary and is used in sense experience. I completely agree, the idea of Space is a condition of sense experience, and so it makes sense experience coherent. Then if Space is required for any sense experience, and space could only be concluded from sense experience, then it follows directly that Space is a priori. “ “[Kant’s quote]” I want to clarify something: I argued that knowledge of space is necessary <em> in gaining sense-experience only</em>, not necessary when sense-experience is not concerned. As such, I never argued that space could be understood without sense-experience. The misinterpretation comes, however, when my opponent assumes that space being necessary to understand sense-experience means that it is <em> prior </em> to sense-experience. That is the position I argued against in my previous round, and I showed, not that understanding of space was prior to sense experience, but rather that knowledge of space and sense-experience come at one and the same time, in an intertwined manner. For if nothing is sensed, space cannot be understood, and is space is not understood, things cannot be sensed – this shows that space is inseparable from sense-experience, not that one is prior to the other. An accurate conclusion is that space is not a priori, as for space to be a priori it would be necessary for it to be known before things are sensed, which is absurd. They must, then, occur simultaneously, and not one without the other (meaning that sense experience is a prerequisite for knowledge of space – the exact definition of the a posteriori). <strong> On “Mathematics”: </strong> “For the first part, we should note that no method, nor framework, no system, to be said, has been outlined in any way which would explain how Mathematics is born out of experience.” I have showed that any consideration of Mathematics without the concept of units built from sense-experience is absurd, and, as such, the above accusation by my opponent is false. (5.2) My opponent seems to equate ta Matheta with Mathematics, and by extension with units. The simple reply to whether "is it possible to create and recognize units without sense-experience?" is a yes. Let us bconsider the example of Algebra, or really any Mathematics (take Differential Equations). There is no empirical experiment to verify Calculus per say, it was developed as a theoretical discipline and has run such. We use Mathematics to identify, and make equations for Quantum Mechanics, an entire field which cannot be experimentally verified. My opponent, here, makes the claim that, for a thing to be founded and based on sense-experience, it must be able to be verified by experiment. He says that things such as QM and Calculus cannot be verified through experiment, and, as such, must be based in a priori knowledge (and, as a result, not on sense-based units). He ignores, however, the fact that higher-level Maths are rightfully dependent on those fields below them, and are mere logical extentions of the basic groundwork, in the same way as the top floors of a skyscraper are dependent on those below them. Since logical deduction, I assume, will be given as a valid system, and since things are as they are (A is A), it can be seen that, even if the logical arguments used to build these fields are “untestable” themselves, the things that they are deduced from can be compared with reality. As I showed in my last round (and my opponent has not refuted this outright – he just tried to give an example of a system that does not rely on sense-experience), if the concept of units is formed via sense-experience, then anything deduced from them is, by extension, based in sense-experience. “Sense experience does not possess a necessity, my opponent agrees that all senses provide subjective knowledge, and so I ask him how is it that Mathematics provides objective answers. To anyone who undrstands this, 7+5 will always be 12. There is no man who can show it to be otherwise, and if they do try to do so, they shall do so with paper, they shall not align people in a row and count (for that would also require an idea of 12 a priori) but they will use reason.“ As referenced earlier, the Law of Identity governs all things, perceptions alike. If I sense something, it can only be so that I sense a real thing (as unreal things do not exist and cannot invoke sensations). As such, any concepts which have their root in sense-experience have their root in an outside world that is sensed – and if this is so, the veracity of any claim based in so-called “subjective” perception can be found by comparing the conclusions drawn from the sensations to the actual world. If two men sense an apple, for example, the apple acts on their sense organs such that they feel certain sensations. It is true that both feel different sensations, but neither is <em> incorrect </em> - they are merely different because of the two different sensors. The outside reality is still the same for both, meaning that, by application of logic to sense-experience, non-contradictory (with reality) conclusions can be reached that are the same for all observers. On to you, Ajab! This is fun!