After presenting my paper on rationalism and empiricism in Comus and Lamia, I spent a good half hour or so speaking with an atheist from my class about the reasons why I am a rationalist. He didn’t seem to know how to answer me, so it wasn’t productive in terms of actually having a debate, but it did get me thinking about a number of other, equally important issues. These are some preliminary considerations I hope to further flesh out at some later point in time.
1. Inductive reasoning assumes that property-sharing entities belong in sets. This assumption cannot be arrived at via inductive reasoning. In other words, inductive reasoning proceeds on the basis of an a priori axiom apart from which inductive reasoning cannot be performed.
1a. Consequently, inductive reasoning begins with an a priori axiom (the axiom of induction, from here onward) by which entities are either classed together or not. This process of classification is a deductive process, expressible in the syllogism:
(p1.) All property sharing entities belong to a set.
(p2.) X and Y are property sharing entities.
(c.) Therefore, X and Y belong to a set.
Inversely, if X and Y are not property sharing entities, they do not belong to a set. Thus, prior to inductive reasoning, there is not only an axiom of induction but a syllogistic chain of deductive reasoning by which entities are either classed together or not.
2. Inductive reasoning, therefore, can only function in the service of deductive inference from at least one a priori axiom, viz. The axiom of induction. Of course, the axiom of induction, as it is the criterion by which sets are defined, is an extension of the law of identity, which is itself an axiom which cannot be inductively inferred, and which implies two other axioms which also cannot be inductively inferred, viz. The laws of non-contradiction and excluded middle.
2a. Consequently, the following a priori axioms necessarily precede inductive reasoning: (i.)axiom of identity (A:A), (ii.)axiom of non-contradiction (~[A : ~A]), (iii.)axiom of the excluded middle (A v ~A), and (iv.)axiom of induction ( [x⊃A & x⊃B] → [A&B⊃Sx] ).
2b. Furthermore, deductive inference from the axiom of induction precedes inductive reasoning.
2c. Therefore, pure materialist and empiricist epistemologies are false. For if a priori axioms precede induction, then at the very least the mind is ready-made with these axioms without which even the most elementary processes of induction cannot begin.
3. Numerical difference between two qualitatively identical entities, as it differentiates A from B via spatio-temporal quantification, is not derivable from observation. Given a universe of qualitatively identical entities, numerical differentiation would entail not simply the difference between A and B as regards their relation to one another spatio-temporally, but spatio-temporal relations themselves. Problematically, however, materialism assumes that quantificationally distinct entities are all that exist. Therefore, materialism is self-referentially absurd, for if the only things that differ are quantificationally distinct entities, the only difference between any two entities, as well as between them and the secondary medium of differentiation (viz., spatio-temporality), is quantitative and not qualitative, and hence immaterial. Therefore, if materialism is true, then it is false.
3a. My friend Cain Pinto has recently reformulated this argument (#3) and posted it to his blog. It is a First Order demonstration of the absurdity of materialism’s assumption that all that exists is matter. If you aren’t familiar with First Order Logic, then jump right in and try to follow his argument! You can view it here.