What Can Our Best Scientific Theories Tell Us About The Modal Status of Mathematical Objects?

Erkenntnis ◽  
2021 ◽  
Author(s):  
Joe Morrison
Keyword(s):  
Scientific Theories ◽  
Mathematical Objects

scholarly journals IMAGINE THERE'S NO (PLATONIC) HEAVEN

Think ◽  
2014 ◽  
Vol 14 (39) ◽  
pp. 73-75
Author(s):  
Matteo Plebani
Keyword(s):  
Scientific Theories ◽  
Mathematical Objects

Some people think that numbers and other mathematical entities exist. They believe in a platonic heaven of ideal mathematical objects, as some (other) people like to put it. This may seem a very strange thing to believe in: after all, we cannot see numbers, nor touch them, nor smell them. So why should one believe that they exist? Because, as Putnam and Quine used to say, numbers are indispensable to science: it seems almost impossible to state our best scientific theories without mentioning numbers or other mathematical objects.

scholarly journals The Honest Weasel A Guide for Successful Weaseling

Disputatio ◽  
2020 ◽  
Vol 12 (56) ◽  
pp. 41-69
Author(s):  
Patrick Dieveney
Keyword(s):  
Good News ◽  
Scientific Theories ◽  
Mathematical Realism ◽  
Mathematical Objects ◽  
Indispensability Arguments ◽  
Take Back ◽  
Controversial Nature

AbstractIndispensability arguments are among the strongest arguments in support of mathematical realism. Given the controversial nature of their conclusions, it is not surprising that critics have supplied a number of rejoinders to these arguments. In this paper, I focus on one such rejoinder, Melia’s ‘Weasel Response’. The weasel is someone who accepts that scientific theories imply that there are mathematical objects, but then proceeds to ‘take back’ this commitment. While weaseling seems improper, accounts supplied in the literature have failed to explain why. Drawing on examples of weaseling in more mundane contexts, I develop an account of the presumption against weaseling as grounded in a misalignment between two types of commitments. This is good news to the weasel’s opponents. It reinforces that they were right to question the legitimacy of weaseling. This account is also beneficial to the weasel. Uncovering the source of the presumption against weaseling also serves to draw out the challenge that the weasel must meet to override this presumption—what is required to be an ‘honest weasel’.

INDISPENSABILITY ARGUMENTS AND INSTRUMENTAL NOMINALISM

2012 ◽  
Vol 5 (4) ◽  
pp. 687-709 ◽  
Author(s):  
RICHARD PETTIGREW
Keyword(s):  
Possible Worlds ◽  
Philosophy Of Mathematics ◽  
Scientific Theories ◽  
Mathematical Objects ◽  
Modal Operators ◽  
Indispensability Arguments ◽  
Everyday Reasoning ◽  
Do So

In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that mathematical objects exist on the grounds that we make indispensable reference to such objects in our best scientific theories (Quine, 1981a; Putnam, 1979a) and in our everyday reasoning (Ketland, 2005). I wish to defend a particular objection to such arguments called instrumental nominalism. Existing formulations of this objection are either insufficiently precise or themselves make reference to mathematical objects or possible worlds. I show how to formulate the position precisely without making any such reference. To do so, it is necessary to supplement the standard modal operators with two new operators that allow us to shift the locus of evaluation for a subformula. I motivate this move and give a semantics for the new operators.

Review of The structure of scientific theories. 2nd ed.

1978 ◽  
Vol 23 (6) ◽  
pp. 473-473
Author(s):  
DAVID L. KRANTZ
Keyword(s):  
Scientific Theories

Science and Dialectics in the Philosophies of Deleuze, Bachelard and DeLanda

Paragraph ◽  
2006 ◽  
Vol 29 (2) ◽  
pp. 98-114 ◽  
Author(s):  
James Williams
Keyword(s):  
Gilles Deleuze ◽  
Explanatory Power ◽  
Scientific Theories ◽  
Gaston Bachelard ◽  
Contemporary Science

This article charts differences between Gilles Deleuze's and Gaston Bachelard's philosophies of science in order to reflect on different readings of the role of science in Deleuze's philosophy, in particular in relation to Manuel DeLanda's interpretation of Deleuze's work. The questions considered are: Why do Gilles Deleuze and Gaston Bachelard develop radically different philosophical dialectics in relation to science? What is the significance of this difference for current approaches to Deleuze and science, most notably as developed by Manuel DeLanda? It is argued that, despite its great explanatory power, DeLanda's association of Deleuze with a particular set of contemporary scientific theories does not allow for the ontological openness and for the metaphysical sources of Deleuze's work. The argument turns on whether terms such as ‘intensity’ can be given predominantly scientific definitions or whether metaphysical definitions are more consistent with a sceptical relation of philosophy to contemporary science.

Laws of Nature

2018 ◽  
Keyword(s):  
Philosophy Of Science ◽  
Laws Of Nature ◽  
Current Debate ◽  
Scientific Theories ◽  
Law Of Nature ◽  
First Time ◽  
The Universe

The concept of a law of nature, while familiar, is deeply puzzling. Theorists such as Descartes think a divine being governs the universe according to the laws which follow from that being’s own nature. Newton detaches the concept from theology and is agnostic about the ontology underlying the laws of nature. Some later philosophers treat laws as summaries of events or tools for understanding and explanation, or identify the laws with principles and equations fundamental to scientific theories. In the first part of this volume, essays from leading historians of philosophy identify central questions: are laws independent of the things they govern, or do they emanate from the powers of bodies? Are the laws responsible for the patterns we see in nature, or should they be collapsed into those patterns? In the second part, contributors at the forefront of current debate evaluate the role of laws in contemporary Best System, perspectival, Kantian, and powers- or mechanisms-based approaches. These essays take up pressing questions about whether the laws of nature can be consistent with contingency, whether laws are based on the invariants of scientific theories, and how to deal with exceptions to laws. These twelve essays, published here for the first time, will be required reading for anyone interested in metaphysics, philosophy of science, and the histories of these disciplines.

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