Online research in philosophy

In this paper, it will be shown that Peirce was of two minds about whether his scientific fallibilism, the recognition of the possibib'ty of error in our beliefs, applied to mathematics. It will be argued that Peirce can and should hold a theory of fallibilism within mathematics, and that this position is more consistent with his overall pragmatic theory of inquiry and his general commitment to the growth of knowledge. But to make the argument for fallibilism in mathematics, Peirce's theory of fallibilism must be reconceived to incorporate two different kinds of fallibilism, which correspond to two different kinds of truth claims.

This paper explores the question of how the epistemological thesis of fallibilism should best be formulated. Sections 1 to 3 critically discuss some influential formulations of fallibilism. In section 4 I suggest a formulation of fallibilism in terms of the unavailability of epistemically truth-guaranteeing justification. In section 5 I discuss the claim that unrestricted fallibilism engenders paradox and argue that this claim is unwarranted.

It is well known that probabilistic support is not transitive. But it can be shown that probabilistic support is transitive provided the intermediary proposition screens off the original evidence with respect to the hypothesis in question. This has the consequence that probabilistic support is transitive when the original evidence is testimonial, memorial or perceptual (i.e., to the effect that such and such was testified to, remembered, or perceived), and the intermediary proposition is its representational content (i.e., to the effect that the such and such occurred).

John Post has argued that the traditional regress argument against nonfoundational justificatory structures does not go through because it depends on the false assumption that “justifies” is in general transitive. But, says Post, many significant justificatory relations are not transitive. The authors counter that there is an evidential relation essential to all inferential justification, regardless of specific inference form or degree of carried-over justificatory force, which is in general transitive. They respond to attempted counterexamples to transitivity brought by Watkins and Salmon as well as to Post’s, arguing that none of these counterexamples apply to the relation they are describing. Given the revived transitivity assumption using this relation, the regress argument does indeed demonstrate the need for foundational stopping points in inferential justification.

Conceptualists have it that the representational content of perceptual experience is determined by the concepts a subject applies in having such an experience. Conceptualists like Bill Brewer [1999] and John McDowell [1994] have laid particular emphasis on demonstrative concepts in trying to account for the fact that subjects can perceive and discriminate very many specific shades of colour in experience. Against this, it has been objected that such demonstrative concepts have incoherent conditions of extension and/or of individuation, due to the fact that chromatic indiscriminability is non-transitive. In this paper, I consider three different versions of this objection and show why each fails.

I argue that, contrary to widespread philosophical opinion, phenomenal indiscriminability is transitive. For if it were not transitive, we would be precluded from accepting the truisms that if two things look the same then the way they look is the same and that if two things look the same then if one looks red, so does the other. Nevertheless, it has seemed obvious to many philosophers (e.g. Goodman, Armstrong and Dummett) that phenomenal indiscriminability is not transitive; and, moreover, that this non-transitivity is straightforwardly revealed to us in experience. I show this thought to be wrong. All inferences from the character of our experience to the non-transitivity of indiscriminability involve either a misunderstanding of continuity, a mistaken interpretation of the idea that we have limited powers of discrimination, or tendentious claims about what our experience is really like; or such inferences are based on inadequately supported premisses, which though individually plausible are jointly implausible.

Let R be a binary relation on some domain. Use R∗ for the reflexive transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is reflexive and transitive. Use R+ for the transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is transitive. Use I for the identity relation on the domain. Let n range over natural numbers. Define Rn as follows, by induction: R0 := I Rn+1 := R ◦ R..

In this paper, I argue that those who accept the conceptualist view in the philosophy of perception should reject the traditional view that colour indiscriminability is non-transitive. I start by outlining the general strategy that conceptualists have adopted in response to the familiar ‘fineness of grain’ objection, and I show why a commitment to what I call the indiscriminability claim seems to form a natural part of this strategy. I then show how together, the indiscriminability claim and the non-transitivity claim –the claim that colour indiscriminability is non-transitive –entail a further, suspicious-looking claim that I call the problematic claim. My argument then splits into two parts. In the first part, I show why the conceptualist does indeed need to reject the problematic claim. Given that this claim is jointly entailed by the indiscriminability claim and the non-transitivity claim, the conceptualist is then left with a straight choice: reject the indiscriminability claim, or reject the non-transitivity claim. In the second part, I then explain why the conceptualist should choose the latter option.

Fallibilism about knowledge and justification is a widely held view in epistemology. In this paper, I will try to arrive at a proper formulation of fallibilism. Fallibilists often hold that Cartesian skepticism is a view that deserves to be taken seriously and dealt with somehow. I argue that it turns out that a canonical form of skeptical argument depends upon the denial of fallibilism. I conclude by considering a response on behalf of the skeptic.

I argue in this paper that the existence of sorites series of color patches – series of color patches arranged so that the patches on each end look different in color though no two adjacent patches do – shows that the relation of same phenomenal charac­ter as is not a transitive relation. I then argue that the intransitivity of same phenomenal character as conflicts with certain versions of intentionalism, the view that an experiences phenomenal character is exhausted, or fully determined by its intentional content. Lastly, I consider various objections to the arguments and reply to them.