The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

In two recent papers, I criticized Ronald N. Giere's and Larry Laudan's arguments for 'naturalizing' the philosophy of science (Siegel 1989, 1990). Both Giere and Laudan replied to my criticisms (Giere 1989, Laudan 1990b). The key issue arising in both interchanges is these naturalists' embrace of instrumental conceptions of rationality, and their concomitant rejection of non-instrumental conceptions of that key normative notion. In this reply I argue that their accounts of science's rationality as exclusively instrumental fail, and consequently that their (...) cases for 'normatively naturalizing' the philosophy of science fail as well. (shrink)

Analysis of Emmy Noether's 1918 theorems provides an illuminating method for testing the consequences of coordinate generality, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether's first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father of (...) the whole business, A. Einstein. (shrink)

A critique of reflective equilibrium as an account of epistemic justification.

Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.

I respond to the insightful comments of L iu Liangjian, Stephen Angle, and Trenton Wilson.

A distinction should be made betweentwo types of ethical problems. A Type I ethicalproblem is one in which there is no consensusas to what is ethical. A Type II ethicalproblem is one in which there is a consensus asto what is ethical, but incentives exist forindividuals to behave unethically. Type Iethical problems are resolved by making,challenging, and reasoning through moralarguments. Type II ethical problems areresolved by changing the institutionalenvironment so that people do not haveincentives to behave unethically. Type Isolutions, however, (...) will not be effective insolving Type II problems. Examples inagriculture and elsewhere show howdistinguishing between Type I and Type IIethical problems will help in theidentification of solutions to ethical issuesin agriculture. (shrink)

Brown makes elegant use of sociological theory and of insights from language philosophy, literary criticism, and rhetoric to articulate a new theory of the human sciences, using the powerful metaphor of society as text.

The kinematical principle of Equal Passage Times (EPT) was introduced by Winnie in his 1970 derivation of the relativistic coordinate transformations compatible with arbitrary synchrony conventions in one-dimensional space. In this paper, the claim by Winnie and later Giannoni that EPT is a direct consequence of the relativity principle is questioned. It is shown that EPT, given Einstein's 1905 postulates, is equivalent to the relativistic (synchrony independent) clock retardation principle, and that for standard synchrony it reduces to an isotropy condition (...) for contraction (and dilation) effects. (shrink)

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

Dispositionalist accounts of colour concepts are now largely discarded. But a number of recent and influential objections to this type of theory can be readily answered providing the dispositionalist account contains the key elements it should---which actual versions in the literature do not. I explicate some of the conceptual components needed in such an account once we correctly understand the anthropocentricity of the colour concepts involved. When these components are incorporated into dispositionalism, including one crucial distinction in particular, some powerful (...) seeming objections against this revised dispositionalism fail. In addition, dispositionalism has extra advantages over the far more popular physicalist theories, and I therefore contend that we should explore vigorously this kind of enriched dispositionalist account. (shrink)

We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic.

We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).

Theories and Methods is the one compulsory unit on the AEB and Interboard syllabuses. This guide outlines the main sociological perspectives, and discusses three main approaches: positivism, phenomenology and critical social research. The topic-book format should be suitable for linear and modular courses, and there are sample questions and skills advice.

Gödel's definitive results and his essays leave us with a rich legacy of philosophical programs that promise to be subject to mathematical treatment. After surveying some of these, we focus attention on the program of circumventing his demonstrated impossibility of a consistency proof for mathematics by means of extramathematical concepts.

S. Adams, W. Ambrose, A. Andretta, H. Becker, R. Camerlo, C. Champetier, J.P.R. Christensen, D.E. Cohen, A. Connes. C. Dellacherie, R. Dougherty, R.H. Farrell, F. Feldman, A. Furman, D. Gaboriau, S. Gao, V. Ya. Golodets, P. Hahn, P. de la Harpe, G. Hjorth, S. Jackson, S. Kahane, A.S. Kechris, A. Louveau,, R. Lyons, P.-A. Meyer, C.C. Moore, M.G. Nadkarni, C. Nebbia, A.L.T. Patterson, U. Krengel, A.J. Kuntz, J.-P. Serre, S.D. Sinel'shchikov, T. Slaman, Solecki, R. Spatzier, J. Steel, D. Sullivan, S. (...) Thomas, A. Valette, V.S. Varadarajan, B. Velickovic, B. Weiss, J.D.M. Wright, R.J. Zimmer. (shrink)

For digraphs G, we write V(G) for the set of all vertices of G, and E(G) for the set of all edges of G. A digraph on a set E is a digraph G where V(G) = E.

The equation P = NP concerns algorithms for deciding membership in sets. The consensus is that P ≠ NP, although some prominent experts guess otherwise.

This distinction between logic and mathematics is subject to various criticisms and can be given various defenses. Nevertheless, the division seems natural enough and is commonly adopted in presentations of the standard foundations for mathematics.

Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.

To prove this, we fix P(x) to be any polynomial of degree ≥ 1 with a positive and negative value. We define a critical interval to be any nonempty open interval on which P is strictly monotone and where P is not strictly monotone on any larger open interval. Here an open interval may not have endpoints in F, and may be infinite on the left or right or both sides. Obviously, the critical intervals are pairwise disjoint.

(1995). Innovation and change in the production of knowledge. Social Epistemology: Vol. 9, Knowledge (EX) Change, pp. 211-232. doi: 10.1080/02691729508578789.

This paper responds to Kauffeld’s 2009 OSSA paper, considering the adequacy of his “commitment-based” approach to “ordinary presumptive practices” to sup-ply an account of presumption fit for general application in normative theories of argument. The central issue here is whether socially-grounded presumptions are defeasible in the right sorts of ways so as to pro-duce “truth-tropic” presumptive inferences.

Jim Garrison’s recent criticisms of what he refers to as ‘dangerous dualisms’ in my theory of critical thinking are unsuccessful. They fail, in large part, because of misinterpretations of my view, but also because of Garrison’s systematic reliance on problematic aspects of Dewey’s terminology and philosophy.

Levinas’s analysis of the relationship between ethics, with its uncompromising responsibility, and politics, with its compromises, is difficult. An examination Maimonides’s chapters on charity may help us understand it. According to Maimonides, one is commanded to give the poor person everything he or she lacks, including clothes, furniture, a spouse, as well as a horse and a herald. One is, moreover, required to give “with a friendly face” and to see the face of the poor person. However, it is impossible (...) to fulfill one’s infinite ethical obligation to him or her, since there are many other poor people; one thus compromises and gives a fixed sum to the city’s charity fund. The greatest charity, according to Maimonides, is the ransoming of captives, who are not only destitute but in imminent danger of death. (shrink)

El presente trabajo complemenJa las referencias a la lengua aut6ctona de los día­ guitas chilenos, en la encrucijada histórica de la conquista hispana en el siglo Xlll , cuya primera parte se publicó en WGOS N 2 l.En este número conJrastamos las hipó­ tesis de don Ricardo Latcham con la crftica de don Jorge /ribarren; se ofrece, aderruís, un suscinJo panorama de la situación lingüística en el noroeste argenJino, y las anota­ ciones espedficamenJe lingüísticas sobre el "cacán" de Antonio Tovar, (...) Cestmir Lou­ kotka y RodtJ/fo Schuller, y nuestras propias conclusiones. The following information about the chilean diaguitas'indigenous tongue for the historie period of the spanish conquest complemenJs the previous report published in thefirst issue of the magazine LOCOS. Ricardo Latcham's hypothesis and Jorge lribarren critica/ position are here confronJed in addition to a brief account of the linguistic situation in south-western ArgenJina. There is also a presenJation of sorne specif eally linguistic statemenJs about "cacán" by Antonio Tovar, Cestmir Loukotka and Rodolfo Schuller as well as our own conclusions. (shrink)

The life, works, and philosophy of rabbi Hasdai Crescas.