This House Believes That Synthetic A Priori Knowledge Exists!

I can most certainly believe that Gabby is delirious from lack of sleep, for I know him to not give unsupported claims. After all, seeing the number of baseless arguments, one would have concluded by themselves that Gabby was not in a fair state of mind (I love you Gabby, don't you forget it babe <3).I shall start off by re-stating the three arguments presented by my honorable opponent. 1. There exists no synthetic truths. 2. That Mathematics is based on "unit values" and these values in themselves are taken a posteriori, therefore Mathematics is a posteriori. 3. That Space is a posteriori because the knowledge of Space is theoretically useless without sensory experience. To begin, I realize my round was techincal, but by being technical it was also clear. My opponent's round suffers from delirium in so far as it hardly makes any coherent sense. Its also more than half a copy of my rounds with some Randian commentary. The first argument was given in a general format, so I shall attack it in a general format, and therein I shall address the issues in relation to Mathematics, and Space. In contradistinction to spelling them out individually, for I feel they will only be rhetorical. 3. On Synthetic Truths:(3.1) You will recall the Kantian definition of "synthetic truths" we gave in our previous round. So long as the predicate exists outside the subject, the said judgement should be synthetic. This can be easily determined in numerous ways. For this let us first determine that said qualities of a particular subject are limited to those which are positive; in simple terms a subject cannot possess a negative quality. If I were to say the Spaghetti Monster possess the negative quality of non-existence, it would be absurd. Similarly in all qualities that we attribute to Dasein, an Ontological (or in contradistinction an Ontical quality is non-Dasein being) would be presupposed to be a positive quality. We must also remember that we must not limit ourselves to inquiries pertaining to attributes alone, for our chief scrutiny is placed on judgement and judgement alone, by that judgement so far as it is knowledge. (3.2) Consider then similarly that something must "be" for it to possess a property, for property is an afterthought to being. For if there is no existence then the property cannot also exist, however we have already considered the negative property of "non-existence", one which would directly contradict being. Thereby we have determined that to consider a negative property is an absurd thesis all together. All properties must be positive in nature. (3.3) Take then the example of "children wear hats". It is for all purposes a synthetic proposition, for no where in the concept of children, is the concept of a hat to be found, but we may relate them with each other through the mind. It will not do to say that from the idea of children we have the idea of head, which possess the idea of a hat. Absurd! While the idea of a head correlates to an idea of a hat, it in no way possess it. We must differentiate between that which is "from a concept" and that which is "of a concept". While in analytic judgements the relation is "from" the concept itself: such as "all bodies are extended", in synthetic truths the relation is "of" a concept, and the relation must be made. (3.4) Similarly in all Matheta, insofar as Mathematics itself is concerned my opponent says that within the number 7, is the concept that it is less than 12 by 5, and so addition of 5 will make it 12. My dear readers, even now the number 7 is empty (in this case) without the number 5, and without the connective of "addition". It is quite simple then, that without the other number to support it, without the relation of addition we could not go from 7 to 15. Think of it this way, from 7, and 7 alone we could not derive the entire judgement. Contrast this to "all bachelors are unmarried" where if we were given "bachelors" alone we could derive "unmarried" without using any negative with other terms. 4. Space:(4.1) As far as Space is concerned, I in no way stated that Space is unconnected with the physical world. In the words of Kant himself: 'But although all our knowledge begins with experience, it does not follow that it arises from experience'[4] With regards to Space the knowledge is used in an a posteriori fashion, but we are not debating how knowlege is used. This debate is about the origins of said knowledge, and that knowledge, Space, is born a priori. I am not a rationalist, I simply wish to discuss where the birth of the concept of space came from. That I have shown must be a priori, and see no refutation from my opponent. 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. (4.2) In Immauel Kant's own words: "Space is a necessary a priori representation which underlines all outer intuitions. It is impossible to have a representation of there being no space, though one can very well think of space without objects to fill it. Space is therefore regarded as the condition of the possibility of appearences, not as a determination dependent upon them. It is an a priori representation which necessarily underlines all outer appearences."[5] This answers all of Gabby's refutations. 5. Mathematics: (5.1) I have already previously answered any claim of Matheta, and by extension ta Mathemata being analytical. I shall not solely focus on the bold statements which claim that such apodictic systems are a posteriori, and developed from experience. 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. This is a problem our opponent should remedy immediately. (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 consider 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. (5.3) This aside if Mathematics does depend on sense experience then how is it that Mathematics, and all such systems follow with a conceptualization of necessity? What I find warm, you may find hot. Surely a person who lives in Greenland will find the climate of Pakistan in the winters as pleasent, when one from Africa may find it extremely chilly. 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. Mathematics, or more precisely ta Matheta (so we may limit it to Pure Mathematics) is a purely theoretical discipline, and while it may be used in physical cirumstances I have already informed the readers of how we are discussing the birth of such knowledge, not its applications. In such Mathematics is an a priori discipline. [4]Critique of Pure Reason, Introduction by Immanuel Kant [5]Critique of Pure Reason, Metaphysical Exposition of the Concept of Space by Immauel Kant Over to bossy then! :)