Logical structuralism and benacerrafs problem, synthese. Pdf this paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The locus classicus of the argument, though presented with a different intent, is paul benacerrafs mathematical truth 1973. While fields challenge is more difficult for the platonist to address than benacerrafs, i argue that this is because fields version is a special case of what i call the sociological challenge. Mathematical truth, the journal of philosophy 70, 1973, s. Contrary to what you might expect from its title, this paper is on the concept of mathematical truth. Review of benacerraf, jubien, and kitcher pdf free download. What mathematical truth could not be i paul benacerraf 2. Truth, objects, infinity new perspectives on the philosophy of paul.
However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Wright went on to claim that humes principle can be regarded as a truth of logic. Its no exaggeration to say that paul benacerrafs essay mathematical truth has had more impact on work in the philosophy of mathematics during the past three decades than any other article or book. Mathematical truth, in the journal of philosophy, vol. But benacerrafs version of the view was antiplatonistic. The amazing thing about the little handful of books on mathematical philosophy2 by shapiro, frege, russell and of course benacerraf and putnams classic, is the paucity of literature in this key field. Benacerrafs 1973 epistemic challenge to platonism is the challenge of explaining how we could gain knowledge of platonic entities. Either a uniform semantics for ordinary language is extended to mathematical language, but then one lapses into platonism. Platonism about mathematics or mathematical platonism is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Philosophy of mathematics stanford encyclopedia of. Paul benacerraf needless to say, we would have liked in a way to reissue the first. Crisis in the foundation of mathematics infinite series pbs infinite series. This solution does not come for free,22 however, since there remains an. Crisis in the foundation of mathematics infinite series.
Knowledge, truth, and mathematics that marcus family. On the nature of mathematical truth we are grateful to our many friends and. This volume features essays about and by paul benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and. Mathematical truth by paul benacerraf ontology and mathematical truth by michael jubien the plight of the platonist by philip kitcher w. Prom full blooded platonism really full blooded platonism. Paul benacerraf, what mathematical truth could not be1. Benacerraf problem as a challenge for ontic structural. The first is devoted to an assessment of the improved version of the original dilemma of mathematical truth due to hartry field. Skepticism about numbers and indeterminacy arguments jerrold j. Benacerraf and mathematical truth arizona state university. Platonism in the philosophy of mathematics stanford.
But actually, the criterion of truth in mathematics is the success of its ideas in practice. Hartry fields epistemological challenge to the mathematical platonist is often cast as an improvement on paul benacerrafs original epistemological challenge. Mathematical truth definition of mathematical truth by. Read the coherence theory of truth online, read in mobile or kindle.
This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. Benacerrafs dilemma and informal mathematics gregory lavers department of philosophy, concordia university abstract. I leaned toward ucla since it was practically free, it had a broader curriculum, it was coed, and many of my friends were going there. Philosophy of mathematics benacerraf putnam scribd. Download the coherence theory of truth ebook free in pdf and epub format. Philosophy of mathematics benacerraf putnam free ebook. Benacerraf, field, and the agreement of mathematicians. In his text, benacerraf quickly lays out the groundwork for how current set theory and i think he kind of implies type theory too. Pdf philosophy of mathematics selected readings second. Some will say that mathematical philosophy, or the closely related philosophy of mathematics, only began in the 1980s in earnest. Benacerrafs mathematical antinomy benacerrafs paper entitled mathematical truth 1973 takes on the form of a wellknown dilemma.
The essays presented a variety of viewpoints on each topic, and gave a good sense of the dialogue and debate that was taking place in the field at the time. Benacerrafs dilemma bd, as formulated by paul benacerraf in mathematical truth, is about the apparent impossibility of reconciling a standard i. Izaak walton, the compleat angler, to the reader of this discourse. History, philosophy and religious studies, school of shprs clasns. Historically, the work became a significant catalyst in motivating the development of mathematical structuralism. In his seminal 1973 paper, mathematical truth, paul benacerraf presented a. If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. Just as electrons and planets exist independently of us, so do numbers and sets. Philosophy can be defined as the rational research of the principles and the truth of conduct, knowledge and being. Such a critic is free to deny that mathematical objects exist, despite their utility in. Logical structuralism and benacerrafs problem logical structuralism and benacerrafs problem yap, audrey 20080827 00. If mathematics is regarded as a science, then the philosophy of. The account builds upon georg kreisels work on informal rigour. Benacerrafs article concerns the difficulty of combining a causal theory of knowledge with the fact that, in the case of mathematics at least, the objects of our knowledge are abstract entities without causal powers.
What is the dilemma presented by benacerraf between an account of truth and an account of knowledge in mathematics. Ebert september 14, 2006 introduction this survey paper will critically discuss four di. The target paper for the conference which was the origin of this collection was benacerrafs mathematical truth 1973. Despite its incoherent presentation, the material of. On what possible worlds could not be robert stalnaker 5. Thus it became a challenge to formulate a philosophical theory of mathematics that was free of. In this connection, it seeks to satisfy simultaneously both horns of benacerrafs dilemma. The mathematical truth enrico bombieri ias, princeton for angling may be said to be so like the mathematics, that it can never be fully learnt. There can be mathematical truth and mathematical knowledge on formal, modeltheoretic grounds despite the fact that mathematical structures cannot enter spatiotemporal relations with the worldly states of affairs. Mathematical truth paul benacerraf the journal of philosophy, vol. And just as statements about electrons and planets are made true or false by the.
I will not present an analysisbut i will try to indicate the direction, or directions, i think analyses should follow. If submitting a hard copy, keep an electronic file or scan. Setting up the benacerraf problem that marcus family. Mathematical truth paul benacerraf that marcus family home.
Mathematics is a science therefore philosophy of mathematics can be referred as a division of the philosophy of science, next to the fields such as the philosophy of biology and the philosophy of physics. Benacerraf s mathematical truth has been deeply in. A major part of the debate in the philosophy of mathematics of the last forty years has been dominated by attempts at escaping the dilemma paul benacerraf suggested in mathematical truth. The theme of the article is that there is a tension between the standard realist interpretation of mathematics and our claim to mathematical knowledge. He was appointed stuart professor of philosophy in 1974, and retired in 2007 as the james s. The oxford handbook of philosophy of mathematics and logic oxford.
Philosophy of mathematics stanford encyclopedia of philosophy. Benacerraf, paul 1973 mathematical truth, the journal of philosophy, 70. Philosophy of mathematics by paul benacerraf and a great selection of related books, art and collectibles available now at. Pdf the coherence theory of truth download ebook for free. In order to explain the benacerraf problem, i will first discuss two moregeneral philosophical topics. Tarski and the correspondence theory marcus, knowledge, truth, and mathematics, slide 18. Philosophy of mathematics fall 2006 winter 2007 our goal over these two quarters is to think through a series of positions on the fundamental metaphysical and epistemological questions about mathematics. Benacerrafs work motivated philosophers to develop both. We cannot reconcile the demands of an account of mathematical truth with the demands of an. In mathematical truth, paul benacerraf presented an epistemological problem for mathematical realism.
Indispensability argument in the philosophy of mathematics. Paul joseph salomon benacerraf is a frenchborn american philosopher working in the field of. Setting up the benacerraf problem benacerraf s paper presents a problem which shaped nearly all discussions of the philosophy of mathematics in the second half of the twentieth century. Paul benacerraf 1973, mathematical truth, the journal of philosophy 70, pp. Mathematical truth synonyms, mathematical truth pronunciation, mathematical truth translation, english dictionary definition of mathematical truth. The proposal attempts to be completely nonrevisionist. This volume features essays about and by paul benacerraf, whose ideas.
Mathematical truth an overview sciencedirect topics. Benacerraf argues that we can devise a successful semantics or a successful epistemology for mathematics, but not both. The twentieth century has witnessed an unprecedented crisis in the foundations of mathematics, featuring a worldfamous paradox russells paradox, a challenge to classical mathematics from a worldfamous mathematician the mathematical intuitionism of brouwer, a new foundational school hilberts formalism, and the profound incompleteness results of. In the philosophy of mathematics, benacerrafs identification problem is a philosophical argument developed by paul benacerraf against settheoretic platonism, and published in 1965 in an article entitled what numbers could not be. Im not sure this is the correct synopsis of the beginning of the paper, and if it is, i dont quite follow how this is so. They define their position against mill, who maintained that mathematical propositions were inductive generalizations based on an extremely large number of instances ayer, p. Clarendon press 1998 abstract this article has no associated abstract. Philosophy of mathematics selected readings second editionedited by paul benacerraf s t u a r t professor o f p h i l. Philosophy of mathematics edited by paul benacerraf. Solomon feferman patrick suppes family professor of humanities and sciences, em. Get your kindle here, or download a free kindle reading app.
1334 243 185 355 697 975 369 1613 939 745 401 1559 1102 901 324 1295 1617 802 417 504 110 23 499 1064 911 710 1308 208 1382 1296 1097 614 1235 1148