The A Priori

The original proof of the four-color theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depend heavily for their soundness on large amounts of computation-intensive custom-built software. Contra Tymoczko, we argue that the justification provided by certain computerized mathematical proofs is not fundamentally different from that provided by surveyable (...) proofs, and can be sensibly regarded as a priori. We also show that the aforementioned impression is mistaken because it fails to distinguish between proof search (the context of discovery) and proof checking (the context of justification). By using mechanized proof assistants capable of producing certificates that can be independently checked, it is possible to carry out complex proofs without the need to trust arbitrary custom-written code. We only need to trust one fixed, small, and simple piece of software: the proof checker. This is not only possible in principle, but is in fact becoming a viable methodology for performing complicated mathematical reasoning. This is evinced by a new proof of the four-color theorem that appeared in 2005, and which was developed and checked in its entirety by a mechanical proof system. (shrink)

[Robert Stalnaker] Saul Kripke made a convincing case that there are necessary truths that are knowable only a posteriori as well as contingent truths that are knowable a priori. A number of philosophers have used a two-dimensional model semantic apparatus to represent and clarify the phenomena that Kripke pointed to. According to this analysis, statements have truth-conditions in two different ways depending on whether one considers a possible world 'as actual' or 'as counterfactual' in determining the truth-value of the statement (...) relative to that possible world. There are no necessary a posteriori or contingent a priori propositions: rather, contingent a priori and necessary a posteriori statements are statements that are necessary when evaluated one way, and contingent when evaluated the other way. This paper distinguishes two ways that the two-dimensional framework can be interpreted, and argues that one of them gives the better account of what it means to 'consider a world as actual', but that it provides no support for any notion of purely conceptual a priori truth. /// [Thomas Baldwin] Two-dimensional possible world semantic theory suggests that Kripke's examples of the necessary a posteriori and contingent a priori should be handled by interpreting names as implicitly indexical. Like Stalnaker, I reject this account of names and accept that Kripke's examples have to be accommodated within a metasemantic theory. But whereas Stalnaker maintains that a metasemantic approach undermines the conception of a priori truth, I argue that it offers the opportunity to develop a conception of the a priori aspect of stipulations, conceived as linguistic performances. The resulting position accommodates Kripke's examples in a way which is both intrinsically plausible and fits with Kripke's actual discussion of them. (shrink)

The topic of a priori knowledge is approached through the theory of evidence. A shortcoming in traditional formulations of moderate rationalism and moderate empiricism is that they fail to explain why rational intuition and phenomenal experience count as basic sources of evidence. This explanatory gap is filled by modal reliabilism -- the theory that there is a qualified modal tie between basic sources of evidence and the truth. This tie to the truth is then explained by the theory of concept (...) possession: this tie is a consequence of what, by definition, it is to possess (i.e., to understand) one’s concepts. A corollary of the overall account is that the a priori disciplines (logic, mathematics, philosophy) can be largely autonomous from the empirical sciences. (shrink)

In the history of epistemology, discussions of the a priori have been bound up with discussions of necessity and analyticity, often in confusing ways. Disentangling these confusions is an essential step in the study of the a priori. This will be the aim of my introductory remarks. The goal of the remainder of the paper will then be to try to develop a unified account of the a priori, dealing with the notions of intuition and a priori evidence, the question (...) of why intuitions qualify as evidence, and the question of how they can be a reliable guide to the truth about a priori matters. (shrink)

The aim of this article is twofold. First, we shall review and analyse the neo-kantian justification for the application of probabilistic concepts in science that was defended by Hans Reichenbach early in his career, notably in his dissertation of 1916. At first sight this kantian approach seems to contrast sharply with Reichenbach’s later logical positivist, frequentist viewpoint. But, and this is our second goal, we shall attempt to show that there is an underlying continuity in Reichenbach’s thought: typical features of (...) his early kantian conceptions can still be recognized in his later work. (shrink)

I examine Reichenbach’s theory of relative a priori and Michael Friedman’s interpretation of it. I argue that Reichenbach’s view remains at bottom conventionalist and that one issue which separates Reichenbach’s account from Kant’s apriorism is the problem of mathematical applicability. I then discuss Hermann Weyl’s theory of blank forms which in many ways runs parallel to the theory of relative a priori. I argue that it is capable of dealing with the problem of applicability, but with a cost.

Traditionally, philosophers have used the analytic/synthetic, a priori/a posteriori, and necessary/contingent distinctions to categorize statements. And traditionally, philosophers have used these distinctions to categorize necessary statements as a priori statements. Yet certain statements seem better categorized as necessary and a posteriori. Examples of such statements include: Heat is the form of energy constituted by the motion of atoms and molecules in solids; Gold is the element with atomic number 79; and Water is H$\sb2$O. For while we believe that these statements (...) express empirical discoveries, we also believe that they express the essence of their subjects. ;I wish to justify the claim that these statements are both necessary and a posteriori. My justification includes a synthesis of the causal theory of reference with the network theory of meaning. But once this synthesis is carried out, we have a rather complicated notion of necessity. We no longer have one notion of necessity, but four notions. One notion is the logical positivist's. A statement is necessary if it expresses a linguistic convention. The second notion is the network theorist's. A statement is necessary if it is central to our theoretical network. The third notion is the causal theorist's. A statement is necessary if it is a singular statement of identity between two rigid designators. And the fourth notion is the essentialist's. A statement is necessary if the predicate expresses the essence of the subject. But this essence must be a structural property that plays an explanatory role within our theoretical network. Of these four notions of necessity, only the first must be a priori. The other three are ultimately a posteriori. Statements - fall under the fourth notion. And thus, they are necessary and a posteriori. (shrink)

This book is concerned with the alleged capacity of the human mind to arrive at beliefs and knowledge about the world on the basis of pure reason without any dependence on sensory experience. Most recent philosophers reject the view and argue that all substantive knowledge must be sensory in origin. Laurence BonJour provocatively reopens the debate by presenting the most comprehensive exposition and defence of the rationalist view that a priori insight is a genuine basis for knowledge. This important book (...) will be at the centre of debate about the theory of knowledge for many years to come. (shrink)

The dissertation maintains that a priori justification requires a non-experiential source of justification. Further, it is argued that a non-experiential source of justification involves only cognitive seemings as evidence to justify a belief. ;Chapter one considers the question, in what sense is a priori justification independent of experience? Three theses are considered, each expresses a sense of independence allegedly necessary for a priori justification: source independence, defeasibility independence, and causal independence. I argue that defeasibility independence is not a necessary condition (...) for a priori justification. I argue that source independence is a necessary condition for a priori justification. A priori justification must have a non-experiential source. Finally, I suggest that the issue of causal independence be deferred until the notion of a non-experiential source of justification has been clarified. ;Chapter 2 deals with several recent accounts of the nature of non-experiential sources of justification. The views of Philip Kitcher, John Pollock, and Laurence BonJour are presented and evaluated in an attempt clarify the notion of a non-experiential source of justification. ;Chapter three concerns the task of adequately distinguishing between experiential and non-experiential sources of epistemic justification. An argument against such a distinction is considered and rejected. Several proposals for distinguishing non-experiential sources of justification are considered. I put forth and defend the view that experiential sources of justification require sensory seemings while non-experiential sources of justification require only cognitive seemings. In light of this proposal, I suggest that a priori justification is independent in the sense required for the causal independence requirement introduced in Chapter one. ;Chapter four examines Laurence BonJour's recent claims that a priori justification is indispensable to reasoning and that only a rationalist epistemology successfully accounts for a priori justification. I argue that neither conclusion is adequately supported by BonJour's arguments. ;Finally, a concluding section summarizes the dissertation. (shrink)

The focus of this dissertation is the relationship between a priori knowledge and naturalized epistemology. I consider, by way of Paul Benacerraf's essay entitled "Mathematical Truth," the incompatibility between a priori knowledge and a causal theory of knowledge. The ideas in this essay are often invoked to support mathematical empiricism. I show that Benacerraf's own argument offers no conclusive reason to accept mathematical empiricism ;The argument given in Benacerraf's essay presupposes a causal theory of knowledge. A priori knowledge is incompatible (...) with a causal theory of knowledge. We must either reject one of these or fit a priori knowledge into some other epistemic framework. I argue that we can accommodate a priori knowledge within a reliabilist framework. One matter that appears to prevent including a priori knowledge into a reliabilist framework is the subjunctive conditional invoked by Fred Dretske and Robert Nozick. What would S believe if p were false? If S would believe p anyway, then S does not know that p. This conditional is met trivially in the case of necessary truths. And necessary truths, as a class of propositions, are alleged to be knowable a priori. So it appears that a priori knowledge meets this important conditional trivially. I argue that with suitable modification, we can construct an acceptable reliabilist framework that accommodates both necessary and contingent truths. ;I provide a definition of a priori knowledge that fits into a reliabilist and "externalist" theory of knowledge. However, it could be argued that this is inadequate, that one only knows p if one has internal or "cognitive justification" for p in addition to objective justification for p. Therefore, one knows a priori only if one's objective and cognitive justification is a priori. I argue that S knows a priori if S's objective justification is a priori. More than objective justification may be required for knowledge, but no more than one's objective justification being a priori is required for that knowledge to be a priori. (shrink)

Traditional philosophy has been under attack from several quarters in recent years. The traditional philosopher views philosophy as an armchair discipline relying, for the most part, on reason and reflection. Some philosophers doubt the legitimacy of this type of inquiry. Their arguments usually occur along two dimensions. Some argue that the primary data source for the armchair philosopher--intuition--does not provide evidence for philosophical theories. Others argue that conceptual analysis, which is the preferred method of inquiry for armchair philosophers, can't yield (...) the results the philosopher is looking for, since concepts like 'knowledge' or 'free-will' vary from culture to culture or even between persons within a culture. Finally, some philosophers argue that we should abandon the armchair program because philosophy should be an empirical enterprise continuous with the sciences. I argue that attempts to undermine intuition fail and that one can justify the evidential status of intuition in a non-question begging way. I then argue that attacks on the belief in shared concepts do not succeed because they often conflate the nature of scientific objects with those of interest to the philosopher. However, if concepts do vary from culture to culture, I show that the philosopher need not abandon the armchair. She can still do conceptual analysis but it will be only the entry point into the philosophical dialogue. I apply this approach to epistemology arguing that the central epistemic questions ought to be the existential and the normative. This approach helps to vindicate epistemic internalism. (shrink)

This volume collects articles of the late philosopher Tamara Horowitz. It includes four previously published and two unpublished articles. Though she had wide-ranging interests during her career, Horowitz was mostly concerned with what can be known as priori. She argued against too much confidence in philosophical intuition and argued for a more naturalist, scientific approach. Joseph Camp includes an editor's introduction to the collection of this important philosopher.

It is a natural assumption in mainstream epistemological theory that ascriptions of knowledge of a proposition p track strength of epistemic position vis-à-vis p. It is equally natural to assume that the strength of one’s epistemic position is maximally high in cases where p concerns a simple analytic truth. For instance, it seems reasonable to suppose that one’s epistemic position vis-à-vis “a cat is a cat” is harder to improve than one’s position vis-à-vis “a cat is on the mat”, and (...) consequently, that the former is at least as unambiguous a case of knowledge as the latter. The current paper, however, presents empirical evidence which challenges this intuitive line of reasoning. Our study on the epistemic intuitions of hundreds of academic philosophers supports the idea that simple and uncontroversial analytic propositions are less likely to qualify as knowledge than empirical ones. We show that our results, though at odds with orthodox theories of knowledge in mainstream epistemology, can be explained in a way consistent with Wittgenstein’s remarks on ‘hinge propositions’ or with Stalnaker’s pragmatics of assertion. We then present and evaluate a number of lines of response mainstream theories of knowledge could appeal to in accommodating our results. Finally, we show how each line of response runs into some prima facie difficulties. Thus, our observed asymmetry between knowing “a cat is a cat” and knowing “a cat is on the mat” presents a puzzle which mainstream epistemology needs to resolve. (shrink)

Originally published in 1966, this pivotal work of Mikel Dufrenne revises Kant’s notion of _a priori,_ a concept previously given insufficient attention by philosophers, to realize a rich understanding that finally does justice to one of Kant’s most troubling cruxes. Following the Husserlian analytics of phenomenology, Dufrenne postulates a dualistic conception of the _a priori_ as a structure that expresses itself outside the human subject, but also as a virtual knowledge that points to a philosophy of immediate apprehension or feeling. (...) A friend of Paul Ricoeur, with whom he was detained as a prisoner of war during World War II, Dufrenne’s work until now has been sorely overlooked by American philosophers. (shrink)

How is knowledge of the external world possible? How is knowledge of other minds possible? How is a priori knowledge possible? These are all examples of how-possible questions in epistemology. In this highly original book Quassim Cassam explains how such questions arise and how they should be answered.