The purpose of this article is to show that the truthmaker solution to the Gettier counter-examples can solve the Russell case of the stopped clock (other standard cases have already been analysed). The solution amounts to this: the truthmaker for the claim that it is, say, 2.00 pm, is a combination of natural and non-natural determinants. The latter are created by stipulation, but having been so made make it is a perfectly objective matter as to whether it is 2.00 o'clock. (...) To know that it is 2.00 pm is to have the evidence for one's belief evidence of the very state of affairs that make the belief true. Thus, in the Russell case one does not have knowledge, in accord with intuition. (shrink)

The indistinguishability of bosons and fermions has been an essential part of our ideas of quantum mechanics since the 1920s. But what is the mathematical basis for this indistinguishability? An answer was provided in the group representation theory that developed alongside quantum theory and quickly became a major part of its mathematical structure. In the 1930s such a complex and seemingly abstract theory came to be rejected by physicists as the standard functional analysis picture presented by John von Neumann took (...) hold. The purpose of the present account is to show how indistinguishability is explained within representation theory. (shrink)

In a number of influential articles published since 1972, Dorothy Grover has developed the prosentential theory of truth. Brought together and published with a new introduction, these essays are even more impressive as a group than they were as single contributions to philosophy and linguistics. Denying that truth has an explanatory role, the prosentential theory does not address traditional truth issues like belief, meaning, and justification. Instead, it focuses on the grammatical role of the truth predicate and asserts that (...) “it is true” is a prosentence, functioning much as a pronoun does. Grover defends the theory by indicating how it can handle notorious paradoxes like the Liar, as well as by analyzing some English truth-usages. The introduction to the volume surveys traditional theories of truth, including correspondence, pragmatic, and coherence theories. It discusses the essays to come and, finally, considers the implications of the prosentential theory for other theories. Despite the fact that the prosentential theory dismisses the “nature of truth” as a red herring, Grover shows that there are important aspects of traditional truth theories that prosentential theorists have the option of endorsing. (shrink)

Cesario misrepresents or ignores data on real-world racist and sexist patterns and processes in an attempt to discredit the assumptions of implicit bias experimentation. His position stands in stark contradiction to substantive research across the social sciences recognizing the widespread, systematic, and structuring processes of racism and sexism. We argue for centering the relationship between structural racism and individual bias.

The Received View of particles in quantum mechanics is that they are indistinguishable entities within their kinds and that, as a consequence, they are not individuals in the metaphysical sense and self-identity does not meaningfully apply to them. Nevertheless cardinality does apply, in that one can have n> 1 such particles. A number of authors have recently argued that this cluster of claims is internally contradictory: roughly, that having more than one such particle requires that the concepts of distinctness and (...) identity must apply after all. A common thread here is that the notion of identity is too fundamental to forego in any metaphysical account. I argue that this argument fails. I then argue that the failure of individuality and identity applies also to macroscopic physical objects, that the problems cannot be constrained to apply only within the microscopic realm. (shrink)

"This reviewer had to be restrained from stopping people in the street to urge them to read it: They would learn something of the way science is done,...

I argue that the suppositional view of conditionals, which is quite popular for indicative conditionals, extends also to subjunctive or counterfactual conditionals. According to this view, conditional judgements should not be construed as factual, categorical judgements, but as judgements about the consequent under the supposition of the antecedent. The strongest evidence for the view comes from focusing on the fact that conditional judgements are often uncertain; and conditional uncertainty, which is a well-understood notion, does not function like uncertainty about matters (...) of fact. I argue that the evidence for this view is as strong for subjunctives as it is for indicatives. (shrink)

There is a large literature on the issue of the lack of properties (i.e. accidents) in quantum mechanics (the problem of “hidden variables”) and also on the indistinguishability of particles. Both issues were discussed as far back as the late 1920’s. However, the implications of these challenges to classical ontology were taken up rather late, in part in the ‘quantum set theory’ of Takeuti (Curr Issues Quant Logic 303–322, 1981), Finkelstein (in Beltrametti EG, Van Fraassen BC (eds) Current issues in (...) quantum logic. Plenum, New York, 1981) and the work of Décio Krause (1992)—and subsequent publications). But the problems created by quantum mechanics go far beyond set theory or the identity of indiscernibles (another subject that has been often discussed)—it extends, I argue, to our accounts of truth. To solve this problem, i.e. to have an approach to truth that facilitates a transition from a classical to a quantum ontology one must have a unified framework for them both. This is done within the context of a pluralist view of truthmaking, where the truthmakers are unified in having a monoidal structure. The structure of the paper is as follows. After a brief introduction, the idea of a monoid is outlined (in Sect. 1) followed by a standard set of axioms that govern the truthmaker relation from elements of the monoid to the set of propositions. This is followed, in Sect. 2, by a discussion of how to have truthmakers for two kinds of necessities: tautologies and analytic truths. The next Sect. 3, then applies these ideas to quantum mechanics. It gives an account of quantum states and shows how these form a monoid. The final section then argues that quantum logic does not, despite what one might initially suspect, stand in the way of an account of quantum truth. (shrink)

The significance of Max Black’s indistinguishable spheres for the nature of particles in quantum mechanics is discussed, focusing in particular on the use of the idea of weak indiscernibility. It is argued that there can be four such Black spheres but that five are impossible. It follows from this that Black’s example cannot serve as a model for indistinguishability in physics. But Black’s discussion of his spheres gave rise to the idea of weak discernibility and it is argued that such (...) predicates are unsatisfiable in the way intended. The underlying problem with weak discernibility spreads out to also undermine the whole notion that indistinguishability rests on a notion of the permutation invariance of particles. A better foundation is indicated. (shrink)

Mathematics, as Eugene Wigner noted, is unreasonably effective in physics. The argument of this paper is that the disproportionate attention that philosophers have paid to discrete structures such as the natural numbers, for which a nominalist construction may be possible, has deprived us of the best argument for Platonism, which lies in continuous structures—in fields and their derived algebras, such as Clifford algebras. The argument that Wigner was making is best made with respect to such structures—in a loose sense, with (...) respect to geometry rather than arithmetic. The purpose of the present paper is to make this connection between mathematical realism and geometrical entities. It thus constitutes an argument against formalism, for which mathematics is merely a game with humanly set rules; and nominalism, in which whatever mathematics is used is eliminable in the final analysis, by often insufficiently specified means. The hope is that light may be cast on the stubborn mysteries of the nature of quantum mechanics and its mathematical formulation, with particular reference to spinor representations—as they have been developed by Andrej Trautman. Thus, according to our argument, quantum mechanics (QM) may appear more natural, as we have better reasons to take spinor structures as irreducibly real, a view consonant with the work of Trautman and Penrose in particular. (shrink)

That there is an edge at all is, of course, philosophically controversial; it would be denied by anti-realists of a verificationist stripe. However, we accept, since G¨odel, that there are true propositions of elementary arithmetic that are unprovable in arithmetic; just so, we should accept—by analogy—that there are true statements that are unknowable. An argument called the Fitch Argument tells us that it is so. Williamson has long argued that the Fitch Argument cannot by itself refute antirealism—because the anti-realist is (...) already committed to the denial of some of the principles of classical logic required to derive the anti-realist conclusion. The point is well made.1 In Knowledge and its Limits, however, Williamson looks at what the Fitch argument tells us if we adhere to classical logic: and that is that there are unknowable truths. (shrink)

The geometric mean is also called the mean proportional. This is how the mathematicians of the √ −1. 19th Century, such as Gauss, understood..

Fitch’s argument purports to show that for any unknown truth, p , there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual (...) situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge. (shrink)

It’s a truism of philosophy that Realists must not postulate more than we could reasonably hope to know, while Anti-Realists must not leave us with so little that all knowledge is impossible. But balance is not easily come by—and even less in philosophy than in life. So philosophy continues to struggle over the hard cases, with neither the Realist nor the Anti-Realist able to score an easy victory.

In his essay ‘Laws and States in Quantum Mechanics’, John Forge presents a case for considering laws of nature to be privileged sets of states, trajectories in the quantum mechanical analogue of phase space. Having presented an argument to show that states have to be taken with full ontological seriousness, Forge then uses those states to undergird his favourite account of laws and explanation — called the Instance View. On this view laws are a special sort of pattern, a certain (...) kind of regularity, and explanations are instances of these regularities (so that you explain some phenomenon A by indicating that it is an instance of some regularity R). Forge then uses this account of laws and explanation to urge the acceptance of van Fraassen’s Modal Interpretation of Quantum Mechanics. (shrink)

Book synopsis: Vagueness is currently the subject of vigorous debate in the philosophy of logic and language. Vague terms-such as "tall", "red", "bald", and "tadpole"—have borderline cases ; and they lack well-defined extensions. The phenomenon of vagueness poses a fundamental challenge to classical logic and semantics, which assumes that propositions are either true or false and that extensions are determinate. Another striking problem to which vagueness gives rise is the sorites paradox. If you remove one grain from a heap of (...) sand, surely you must be left with a heap. Yet apply this principle repeatedly as you remove grains one by one, and you end up, absurdly, with a solitary grain that counts as a heap. This anthology collects papers in the field. After an introduction that surveys the field, the essays form four groups, starting with some historically notable pieces. The 1970s saw an explosion of interest in vagueness, and the second group of essays reprints classic papers from this period. The following group of papers represent current work on the logic and semantics of vagueness. The essays in the final group are contributions to the continuing debate about vague objects and vague identity. (shrink)

It is argued that the part-whole account of the relation between evidence and the larger state of affairs the evidence is evidence of—an account that was elucidated in the paper ‘Truthmaking, Evidence of, and Impossibility Proofs’ —provides a better basis for epistemology than causal relations between events. I apply this to a well-known phenomenon in physics which suggests that causal connectedness is not necessary for knowledge.

The article argues that Marx’s use of the concept of ideology in The German Ideology is incidental to a sustained critique of how those he described as the German ideologists think and reason about society and history and that this critique is not simply of an idealist theory that represents society and history as determined by consciousness but of methods of reasoning that treat concepts, even of those of political economy, as determinants. His view of how consciousness is determined historically (...) by our social being does not envisage some kind of mechanical transfer of class status to class consciousness. Rather, he works with an epistemology that takes the concepts foundational to political economy as expressions or reflections of the social relations of a mode of production. The difference between ideology and science is the difference between treating those concepts as the primitives of theory and treating them as sites for exploring the social relations that are expressed in them. Thus, the historical rather than further undermining claims to knowledge, provides both the conditions under which knowledge is possible and its limitations. (shrink)

An extensive survey by Heathcote et al. (in press) found that the Law of Practice is closer to an exponential than a power form. We show that this result is hard to obtain for models using leaky competitive units when practice affects only the input, but that it can be accommodated when practice affects shunting self-excitation.

The ArgumentA survey of 2901 genetics professionals in 36 nations suggests that eugenic thought underlies their perceptions of the goals of genetics and that directiveness in counseling after prenatal diagnosis leads to individual decisions based on pessimistically biaed information, especially in developing nations of Asia and Eastern Europe. The “non-directive counseling” found in English-speaking nations is an aberration from the rest of the world. Most geneticists, except in China, rejected government involvement in premarital testing or sterilization, but most also held (...) a pessimistic view of persons with genetic disabilities. Individual, but not state-coerced, eugenics survives in much modern genetic practice. (shrink)

Conditional judgements—judgements employing ‘if’—are essential to practical reasoning about what to do, as well as to much reasoning about what is the case. We handle them well enough from an early...

A proof is presented that a form of incompleteness in Quantum Mechanics follows directly from the use of unbounded operators. It is then shown that the problems that arise for such operators are not connected to the non- commutativity of many pairs of operators in Quantum Mechanics and hence are an additional source of incompleteness to that which allegedly flows from the..