Radical Empiricism is Preferable to Radical Rationalism

This is being written from my phone, so I apologize for any format problems. To simplify, I will drop the "radical" from before each term. Included in the category of experience is reflection, which can be categorized as "ongoing introspective experiences of my own specific conscious mental states and processes" -Laurence BonJour. Reflection was employed by Locke and Hume and explains how complex ideas such as dragons can be taken from simpler impressions. Correspondence and Abstractions For something to be true it must correspond to an aspect of reality in some way. In order to discover some truth we thus have to verify that it agrees with reality. No truth can be independent of reality, so the correspondence principle is clearly correct. Experience gives us a clear access to reality. By observing something we know it's part of reality. It's clear how empiricism provides us with the necessary insights into reality. It's more difficult to see how rationalism can. The senses are our only possible connection with reality. Knowledge gained before experience is not really knowledge at all because it lacks an established connection with reality. Rationalists might disagree and say that mathematics and logic (hereby conflated as math) constitute a reality that rests in the domain of a priori knowledge. I will show why this is false. First for math to count, it itself must be an independent realty and escape the need for empirical confirmation. For example, by positing mathematical Platonism. The problem is that math is not an abstract reality. It is in fact abstract but only a tool created by humans in order to make sense of the physical world and make useful applications. Math (and logic) can be considered inventions used to articulate facts of the world and not alternative realities themselves. We know that math only provides approximations of reality. Math employs numbers and geometric shapes in absolute terms. Can we say squares and ones and equalities actually exist independent of us? Not really. Through experience we gain concepts of lines and figures and form idealized notions of squares and triangles that don't truly match up to anything in our world of crooked shapes. Nothing is equal to anything else in the physical world because everything is unique, and equivalence is just a concept. It is the mind, through the concepts gained from experience that categorizes, labels and divides objects. I won't make more arguments here since I don't yet know my opponent's position. My claim is that mathematical notions arise from experience and require experience in order to be termed knowledge. So even if math is an a priori construct-which I deny-it is still a human creation- not an abstract reality-and thus requires empirical confirmation since there's no other way to establish its correspondence to reality. The rationalist might ask, well what about pure math? Is applied math really the only math we can know? Pure math doesn't exist because logical notions stem from experience, and thus all math rests in experience. Still, the rationalist will likely say that I must admit a priori notions must be employed in some aspects of math even if combined with empirical parts. For example, the series of positive integers can be gained from experience, but how can the empiricist prove that the series is endless; that no number is so large that one cannot be added to it? What is empirical about that? Well, as shown the power of reflection allows us to parlay complex notions out of simple ideas. So we can build on math without acquiring new data. Moreover, out of language we make definitions which match a concept with all samples of a certain aspect of reality. For example, we say that H2O is water, so we know that everything that is H2O is water and everything that is not H2O is not water. Similarly, we invoke sets and integers and derive the fact from their definitions that the set of integers does not terminate. These facts are true because we've said they are, not because they're a priori. Since knowledge claims must establish correspondence to reality and because abstractions are not part of this reality, abstractions do not count as knowledge in themselves. They must meet the correspondence criteria, which is done through matching abstractions to reality. Our only known reality is the physical world and our only means of perceiving this reality is sense experience. Thus, sense experience provides us with the only possible means of meeting the correspondence criteria and thus the only means for gaining knowledge. Concepts without Precepts Pure a priori knowledge is impossible for the simple reason that-if we grant the existence of a priori concepts-the use of such concepts on their own does not amount to knowledge. For example, if we agree with some rationalists that we posses a priori the principle of sufficient reason, what basis do we have for accepting other than our mere opening it? That it exits in our mind surely cannot be sufficient justification. The PSR is a useful example because, during the period when the rationalism-empiricism debate dominated philosophy, pre- Kant, it was held by rationalists that the PSR was an example of innate or a priori knowledge. With modern science, however, we've empirically found the principle to be erroneous. Quantum particles behave in inconceivable fashion. Virtual particles in a vacuum wink in and out if existence as if from nothing, and radioactive decay is random. This is the perfect example of an alleged a priori principle proven wrong empirically. So how can we be confident of any alleged a priori claim that hasn't been empirically proven? It seems we need experience to justify all knowledge claims. This argument refutes most of rationalism, but not all the the theses. However. I only need to show empiricism as better. This argument is in itself enough.