Hilbert's program attempts to show that our mathematical knowledge can be certain because we are able to know for certain the truths of elementary arithmetic. I argue that, in the absence of a theory of mathematical truth, Hilbert does not have a complete theory of our arithmetical knowledge. Further, while his deployment of a Kantian notion of intuition seems to promise an answer to scepticism, there is no way to complete Hilbert's epistemology which would answer to his avowed aims.

Although the push to get universities to accumulate IP by commercializing their scientific research was a conscious movement, dealing with the blowback in the form of contracts over the transfer of research tools and inputs, called materials transfer agreements (MTAs), was greeted by universities as an afterthought. Faculty often regarded them as an irritant, and TTOs were not much more welcoming. One reason universities could initially ignore the obvious connection between the pursuit of patents and the prior promulgation of MTAs (...) was a legalistic distinction made between intellectual property and contract law, which of course is of direct concern to a lawyer, but should be less compelling for anyone trying to understand the big picture surrounding the commercialization of academic science. However, as a subset of scientists were increasingly drawn into the commercial sphere, they tended to attach MTAs to research inputs requested by other academics; and this began a tidal wave of MTAs which shows no sign of abating. Furthermore, many IP-related restrictions have been loaded into individual MTAs, including the stipulation that the existence and content of MTAs themselves be treated as secret and proprietary. The paper closes by looking at recent arguments that the growth of MTAs has not actually harmed the research process, and rejects them. (shrink)

In this wide-ranging study, Quinn argues that human moral autonomy is compatible with unqualified obedience to divine commands. He formulates several versions of the crucial assumptions of divine command ethics, defending them against a battery of objections often expressed in the philosophical literature.

Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantificrs, and then include further quantifiers which are modifications of such fractions (such as "almost ½ the S are P" and "Much more than ½ the S are P"). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes & Peterson (forthcoming) for proofs of the unsoundness and incompleteness (...) of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., "almost ¾ the S arc P'" is represented as " -(3(SP) » SP)". (shrink)

Argues i) that part of what it is to understand what is being asked, when we ask whether something is good, is being able to distinguish stopping points in a series of "Why?" questions, and ii) that this ability explains how we can reason from observable facts to conclusions about value.

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field${\mathbf {No}}$of surreal numbers was brought to the fore by the first author and employed to provide necessary and sufficient conditions for an ordered field (ordered$K$-vector space) to be isomorphic to an initial subfield ($K$-subspace) of${\mathbf {No}}$, i.e. a subfield ($K$-subspace) of${\mathbf {No}}$that is an initial subtree of${\mathbf {No}}$. In this sequel, analogous results are established forordered exponential fields, making use of a slight generalization of Schmeling’s conception of (...) atransseries field. It is further shown that a wide range of ordered exponential fields are isomorphic to initial exponential subfields of$({\mathbf {No}}, \exp )$. These include all models of$T({\mathbb R}_W, e^x)$, where${\mathbb R}_W$is the reals expanded by aconvergent Weierstrass system W. Of these, those we calltrigonometric-exponential fieldsare given particular attention. It is shown that the exponential functions on the initial trigonometric-exponential subfields of${\mathbf {No}}$, which includes${\mathbf {No}}$itself, extend tocanonicalexponential functions on theirsurcomplexcounterparts. The image of the canonical map of the ordered exponential field${\mathbb T}^{LE}$oflogarithmic-exponentialtransseries into${\mathbf {No}}$is shown to be initial, as are the ordered exponential fields${\mathbb R}((\omega ))^{EL}$and${\mathbb R}\langle \langle \omega \rangle \rangle $. (shrink)

Dmitri Mendeleev’s detailed prediction in 1871 of the properties of three as yet unknown elements earned him enormous prestige. Eleven other predictions, thrown off without elaboration, were less uniformly successful, thanks mainly his unbending adherence to the structure of his table and his failure to account for the lanthanides. At the end of his life he returned to his table without making the required changes, and added a theoretical discussion of elements lighter than hydrogen. The overall balance of success and (...) failure is nevertheless in his favour. There may now be a similar failure to understand the ultra-heavy elements because of adherence to the pattern of chemical groups. (shrink)

Some philosophers claim that there are certain laws that restrict what kinds of things we can perceptually represent. Those laws do not apply, however, to beliefs. To be a representationalist is to hold that there is a similarity between perception and belief. If this is the case, why do the laws apply to one kind of mental state, but not the other? I argue that the puzzle is not a puzzle for representationalists in general, but only for some forms of (...) representationalism that hold excessive analogies between perception and belief. I will consider three kinds of views: a view that identifies perception with belief; a view that claims that perception and belief share the same kind of content, viz. propositions; and the view that belief and perception are both intentional states, but do not share the same type of content. I will argue that the laws of appearance rule out views that identify perception with belief, and that consider propositions to be the contents of perception. (shrink)

Andrew Kania has attempted to argue for nihilistic fictionalism about musical works. This view combines an error theory about musical work discourse with the proposal that musical work discourse has a non-alethic value which warrants continued participation in it. In this paper, I argue that Kania fails to establish either component of nihilistic fictionalism. First, I elaborate and reject Kania’s attempt to establish fictionalism on the basis of a methodological proposal he calls ‘descriptivism’. I argue that the methodology is unpopular, (...) unappealing and that the interest in its implications is unclear. What is worse descriptivism does not support fictionalism. I then elaborate and reject Kania’s attempt to establish fictionalism as the best theory compatible with nominalism. I argue that, even by Kania’s standards, eliminativist nominalism, materialist nominalism and materialist fictionalism are preferable to nihilistic fictionalism. (shrink)

What if self-questioning could provoke an extreme attentiveness to a rich inner life? In pursuit of this question, a mixed group of highly fallible thinkers gather together in the north of England. Will they be able to respond to the actual events of their lives, and reinvent philosophy as a collective spiritual exercise?

I argue that bias can be reduced but never completely removed, owing to humanity’s incomplete knowledge. A proposal is thus made for research to have more than one paradigmatic approach in order ….

Deep convolutional networks exceed humans in sensitivity to local image properties, but unlike biological vision systems, do not discover and encode abstract relations that capture important properties of objects and events in the world. Coupling network architectures with additional machinery for encoding abstract relations will make deep networks better models of human abilities and more versatile and capable artificial devices.