Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.
Presentists standardly conform to the eternalist’s paradigm of treating all cases of property-exemplification as involving a single relation of instantiation. This, we argue, results in a much less parsimonious and philosophically explanatory picture than is possible if other alternatives are considered. We argue that by committing to primitive past and future tensed instantiation ties, presentists can make gains in both economy and explanatory power. We show how this metaphysical picture plays out in cases where an individual exists to partake in (...) facts about its past and future, and also in cases where that individual no longer exists, and proxies (or surrogates) for that thing must be found. (shrink)
This book espouses an innovative theory of scientific realism in which due weight is given to mathematics and logic. The authors argue that mathematics can be understood realistically if it is seen to be the study of universals, of properties and relations, of patterns and structures, the kinds of things which can be in several places at once. Taking this kind of scientific platonism as their point of departure, they show how the theory of universals can account for probability, laws (...) of nature, causation, and explanation, and explore the consequences in all these fields. This will be an important book for all philosophers of science, logicians, and metaphysicians, and their graduate students. The readership will also include those outside philosophy interested in the interrelationship of philosophy and science. (shrink)
Frank Jackson often writes as if his descriptivist account of public language meanings were just plain common sense. How else are we to explain how different speakers manage to communicate using a public language? And how else can we explain how individuals arrive at confident judgments about the reference of their words in hypothetical scenarios? Our aim in this paper is to show just how controversial the psychological assumptions behind in Jackson’s semantic theory really are. First, we explain how Jackson’s (...) theory goes well beyond the commonsense platitudes he cites in its defence. Second, we sketch an alternative explanation of those platitudes, the jazz model of meaning, which we argue is more psychologically realistic. We conclude that the psychological picture presupposed by Jackson’s semantic theory stands in need of a much more substantial defence than he has so far offered. (shrink)
Humean supervenience is the doctrine that there are no necessary connections in the world. David Lewis identifies one big bad bug to the programme of providing Humean analyses for apparently non-Humean features of the world. The bug is chance. We put the bug under the microscope, and conclude that chance is no special problem for the Humean.
Traditionally, forces are causes of a special sort. Forces have been conceived to be the direct or immediate causes of things. Other sorts of causes act indirectly by producing forces which are transmitted in various ways to produce various effects. However, forces are supposed to act directly without the mediation of anything else. But forces, so conceived, appear to be occult. They are mysterious, because we have no clear conception of what they are, as opposed to what they are postulated (...) to do; and they seem to be hidden from direct observations. There is, therefore, strong initial motivation for trying to eliminate forces from physics. Furthermore, as we shall explain, powerful arguments can be mounted to show that theories with forces can always be recast as theories without them. Hence it seems that forces should be eliminated, in the interests of simplicity. We argue, however, that forces should not be eliminated--just differently construed. For the effect of elimination is to leave us without any adequate account of the causal relationships forces were postulated to explain. And this would remain the case, even if forces could be identified with some merely dispositional properties of physical systems. In our view, forces are species of the causal relation itself, and as such have a different ontological status from the sorts of entities normally considered to be related as causes to effects. (shrink)
The world contains not only causes and effects, but also causal relations holding between causes and effects. Because causal relations enter into the structure of the world, their presence has various modal and probabilistic consequences. Causation and “necessary and sufficient conditions” do often go hand in hand. Causation, however, is a robust ingredient within the world itself, whereas modalities and probabilities supervene on the nature of the world as a whole, and on the resulting relations between one possible world and (...) others. Some modalities, therefore, are essentially causal; but causation is not essentially modal.19. (shrink)
Probability measures can be constructed using the measure-theoretic techniques of Caratheodory and Hausdorff. Under these constructions one obtains first an outer measure over "events" or "propositions." Then, if one restricts this outer measure to the measurable propositions, one finally obtains a classical probability theory. What I argue is that outer measures can also be used to yield the structures of probability theories in quantum mechanics, provided we permit them to range over at least some unmeasurable propositions. I thereby show that (...) nonclassical probability theories can be seen to arise naturally within the framework of possible worlds semantics. (shrink)
An association between a pair of variables can consistently be inverted in each subpopulation of a population when the population is partitioned. E.g., a medical treatment can be associated with a higher recovery rate for treated patients compared with the recovery rate for untreated patients; yet, treated male patients and treated female patients can each have lower recovery rates when compared with untreated male patients and untreated female patients. Conversely, higher recovery rates for treated patients in each subpopulation are consistent (...) with a lower recovery rate in the total population when data are aggregated. The arithmetical structures that underlie facts like these support surprising applications of them that invalidate a cluster of arguments that many people, at least initially, take to be intuitively valid. E.g., despite intuitions to the contrary, the following argument is invalid. (shrink)
This paper concerns the semantics of belief-sentences. I pass over ontologically lavish theories which appeal to impossible worlds, or other points of reference which contain more than possible worlds. I then refute ontologically stingy, quotational theories. My own theory employs the techniques of possible worlds semantics to elaborate a Fregean analysis of belief-sentences. In a belief-sentence, the embedded clause does not have its usual reference, but refers rather to its own semantic structure. I show how this theory can accommodate quantification (...) into belief-contexts. I close with skirmishes against the threat posed by the Liar Paradox. (shrink)
Vectors, we will argue, are not just mathematical abstractions. They are also physical properties--universals. What make them distinctive are the rich and varied essences of these universals, and the complex pattern of internal relations which hold amongst them.
The authors argue, against Frank Jackson, that weakness (and strength) of will involves higher-order mental states. The authors hold that this is compatible with a decision-theoretic belief-desire psychology of human action.
Frank Jackson argued, in an astronomically frequently cited paper on 'Epiphenomenal qualia '[Jackson 1982 that materialism must be mistaken. His argument is called the knowledge argument. Over the years since he published that paper, he gradually came to the conviction that the conclusion of the knowledge argument must be mistaken. Yet he long remained totally unconvinced by any of the very numerous published attempts to explain where his knowledge argument had gone astray. Eventually, Jackson did publish a diagnosis of the (...) reasons why, he now thinks, his knowledge argument against materialism fails to prove the falsity of materialism [Jackson 2005. He argues that you can block the knowledge argument against materialism - but only if you tie yourself to a dubious doctrine called representationalism. We argue that the knowledge argument fails as a refutation of either representational or nonrepresentational materialism. It does, however, furnish both materialists and dualists with a successful argument for the existence of distinctively first-person modes of acquaintance with mental states. Jackson's argument does not refute materialism: but it does bring to the surface significant features of thought and experience, which many dualists have sensed, and most materialists have missed. (shrink)
Reality and Humean Supervenience confronts the reader with central aspects in the philosophy of David Lewis, whose work in ontology, metaphysics, logic, probability, philosophy of mind, and language articulates a unique and systematic foundation for modern physicalism.
I. Logic, rationality and ideology Herbert Marcuse once claimed that the ‘“rational” is a mode of thought and action which is geared to reduce ignorance, destruction, brutality, and oppression.’ He echoed a widespread folk belief that a world in which people were rational would be a better world. This could be taken as an optimistic empirical conjecture: if people were more rational then probably the world would be a better place (a trust that ‘virtue will be rewarded’, so to speak). (...) However, it is also worth considering a stronger hypothesis: that if something did not reduce ignorance, destruction, brutality, and oppression then it would not constitute rationality. On this view there is no mere correlation between rationality and a propensity toward reduction in ignorance and the rest, it is the propensity to reduce ignorance, destruction, brutality and oppression which in part constitutes rationality. Call this a broad conception of rationality, because it expands beyond the epistemic goal of reducing ignorance, and reaches out to moral concerns like oppression. (shrink)
Holton, we acknowledge, has given a good counter-example to a theory, and that theory is interesting and worth refuting. The theory we have in mind is like Smith's, but is more reductionist in spirit. It is a theory that ties value to Reason and to processes of reasoning, or inference - not to the recognition of reasons and acting on reasons. Such a theory overestimates the importance of logic, truth, inference, and thinking things through for yourself independently of any ideas (...) about where you might end up. Now it might well be thought that any Kantian theory of value would need to be tied to just such a conception of Reason. But while the theory behind The Moral Problem is Kantian in some very salient respects, the survival of Smith's analysis of value in the face of Holton's argument is very instructive. It teaches us a memorable moral: that a Kantian theory like Smith' s does not need to be tied - even loosely - to an overly intellectualised, logocentric conception of Reason. (shrink)
Throughout his career, Barry Taylor argued for several key theses in semantics and in epistemology. He calls these theses “Antirealism”. I will suggest, however, that a “Realist” could, and perhaps should, accept these semantic and epistemic theses. Doing so would not, I argue, conflict with the core this of philosophical Realism, properly so-called, since this thesis is not semantic or epistemological, but “ontological”. A Realist about (say) badgers is just someone who believes that there are badgers. And Taylor’s semantic and (...) epistemological theses are not intended to entail any denial that there are (say) badgers. However, Taylor argues that the core theses of “realism” cannot be any such merely ontological theses. I will defend a simplistic, “ontological” understanding of “realism” against Taylor’s arguments. Taylor also usefully identifies something that others have called “Common-sense Realism”. But this so-called “Realism”, Taylor argues, is not properly described as any kind of “realism” at all – because it does not affirm Taylor’s key theses in semantics and epistemology. Yet I say it is realism – provided only that it does not also take a perverse stand on a realist’s “Euthyphro” question: Do (say) badgers exist because our ways of talking and knowing would ideally converge on an affirmation of the sentence “Badgers exist”? Isn’t it, rather, the case that, insofar as our ways of talking and knowing would ideally converge on an affirmation of the sentence “Badgers exist”, this is so at least in part because badgers exist? (shrink)
Given Quine's views on philosophical methodology, he should not have taken the axioms of classical mereology to be "self-evident", or "analytic"; but rather, he should have set out to justify them by what might be broadly called an "inference to the best explanation". He does very little to this end. In particular, he does little to examine alternative theories, to see if there might be anything they could explain better than classical mereology can. I argue that there is something important (...) that needs to be explained, namely, the way that properties "travel around in clusters" (eg. we often know that "when and where there is something with such-and-such property, there is also something with so-and-so other property", and so on). I argue that these clusterings of properties can be given various subtle (broadly "commonsense") explanations using a version of mereology that denies the classical axiom of "extensionality" (that is, denying that two distinct things must have distinct parts). I offer a challenge to the Quinean metaphysics: to show that these "non-extensional" explanations can be replaced by better explanations that use only classical, extensional mereology and set theory. (shrink)