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On the Nature of A Priori Knowledge, its methods for Justification and the Apriority of Mathematics

Steven Umbrello

Table of Contents

Introduction 3 The Token Forms of Apriority 3 The Objections to A Priori Knowledge 4 Putnam’s Contextual Apriority 6 The Necessity of Mathematical Apriority 8 Discussion 9 Conclusion 9 Works Cited 11

This short paper will evaluate whether or not a priori knowledge is possible. The questions regarding the objections to the possibility of a priori knowledge are discussed, as are the possible resolutions to such objections with a focus on Hilary Putnam’s theory of contextual apriority. The nature of apriority in mathematics will also be examined and its possible absolute a priori status. A short deliberation regarding whether or not apriority obtains will conclude this paper, but before these are discussed the meaning of a priori knowledge must be considered.

The Token Forms of Apriority A priori knowledge is generally understood as knowledge that is independent of our experience with it. Unlike a posteriori knowledge that requires experience to justify it, a priori knowledge can be referred to as ‘armchair knowledge, such that one need not remove himself from his seat to attain said knowledge. ‘All bachelors are unmarried men’ illustrates a token form of a priori knowledge, that being analytic. One can easily see that the knowledge

Steven Umbrello

Table of Contents

Introduction 3 The Token Forms of Apriority 3 The Objections to A Priori Knowledge 4 Putnam’s Contextual Apriority 6 The Necessity of Mathematical Apriority 8 Discussion 9 Conclusion 9 Works Cited 11

This short paper will evaluate whether or not a priori knowledge is possible. The questions regarding the objections to the possibility of a priori knowledge are discussed, as are the possible resolutions to such objections with a focus on Hilary Putnam’s theory of contextual apriority. The nature of apriority in mathematics will also be examined and its possible absolute a priori status. A short deliberation regarding whether or not apriority obtains will conclude this paper, but before these are discussed the meaning of a priori knowledge must be considered.

The Token Forms of Apriority A priori knowledge is generally understood as knowledge that is independent of our experience with it. Unlike a posteriori knowledge that requires experience to justify it, a priori knowledge can be referred to as ‘armchair knowledge, such that one need not remove himself from his seat to attain said knowledge. ‘All bachelors are unmarried men’ illustrates a token form of a priori knowledge, that being analytic. One can easily see that the knowledge

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