scholarly journals A Metaphysics for Mathematical and Structural Realism

2019 ◽  
Vol 2 (1) ◽  
pp. 75-89
Author(s):  
Adam InTae Gerard
Keyword(s):  
Scientific Realism ◽  
Philosophy Of Mathematics ◽  
Structural Realism ◽  
Ontic Structural Realism ◽  
Mathematical Realism ◽  
Ante Rem Structuralism ◽  
And Mathematics ◽  
Mathematics And Science

The goal of this paper is to preserve realism in both ontology and truth for the philosophy of mathematics and science. It begins by arguing that scientific realism can only be attained given mathematical realism due to the indispensable nature of the latter to the prior. Ultimately, the paper argues for a position combining both Ontic Structural Realism and Ante Rem Structuralism, or what the author refers to as Strong Ontic Structural Realism, which has the potential to reconcile realism for both science and mathematics. The paper goes on to claims that this theory does not succumb to the same traditional epistemological problems, which have damaged the credibility of its predecessors.

Imre Lakatos

Philosophy ◽  
2014 ◽  
Author(s):  
Brendan Larvor ◽  
Colin Jakob Rittberg
Keyword(s):  
Philosophy Of Science ◽  
Philosophy Of Mathematics ◽  
London School ◽  
Mathematical Concepts ◽  
Imre Lakatos ◽  
Gregory Currie ◽  
And Mathematics ◽  
London School Of Economics ◽  
Modern Mathematics ◽  
Mathematics And Science

Imre Lakatos (b. 1922–d. 1974) was a philosopher of mathematics and science. Having left Hungary in 1956, he made his first appearance on the international stage with a series of four papers during 1963 and 1964 in the British Journal for the Philosophy of Science, later published together posthumously in Proofs and Refutations (1976), in which he discusses the formation of mathematical concepts by proof-analysis. This radical break with classical approaches to the philosophy of mathematics attracted sufficient interest that Kitcher and Aspray deem Lakatos to have started a new and “maverick” tradition in the field (“An Opinionated Introduction,” in History and Philosophy of Modern Mathematics, 1988). By 1959, Lakatos had become an assistant lecturer in the Department of Philosophy, Logic and Scientific Method at the London School of Economics and Political Science. This department was still under the direction of its founder, Karl Popper, and Lakatos’s evolving and ultimately antagonistic relations with Popper and the Popperians conditioned much of his work. The chief part of this work was a series of influential papers on the philosophy of science. These are included in the two books of his work that two of his former students, John Worrall and Gregory Currie, published after his death (Lakatos 1978a and Lakatos 1978b, cited under Posthumously Published). In 1974, Lakatos died of a heart attack, leaving his projects in philosophy of science and mathematics incomplete.

The Benacerraf Problem as a Challenge for Ontic Structural Realism†

2019 ◽  
Vol 28 (1) ◽  
pp. 35-59
Author(s):  
Majid Davoody Beni
Keyword(s):  
Philosophy Of Mathematics ◽  
Structural Realism ◽  
Ontic Structural Realism ◽  
Mathematical Structures ◽  
Scientific Representations

ABSTRACT Benacerraf has presented two problems for the philosophy of mathematics. These are the problem of identification and the problem of representation. This paper aims to reconstruct the latter problem and to unpack its undermining bearing on the version of Ontic Structural Realism that frames scientific representations in terms of abstract structures. I argue that the dichotomy between mathematical structures and physical ones cannot be used to address the Benacerraf problem but strengthens it. I conclude by arguing that versions of OSR that do not rely on mathematical frameworks for representational purposes need not be vulnerable to Benacerraf’s second problem.

Thomist vs. Scotist Perspectives on Ontic Structural Realism

2020 ◽  
Vol 60 (3) ◽  
pp. 323-337
Author(s):  
Travis Dumsday ◽  
Keyword(s):  
Scientific Realism ◽  
Structural Realism ◽  
Science Literature ◽  
Ontic Structural Realism ◽  
Metaphysics Of Science ◽  
Important Player ◽  
Epistemic Structural Realism

Structural realism has re-emerged as part of the debate between scientific realism and antirealism. Since then it has branched into several different versions, notably epistemic structural realism and ontic structural realism. The latter theory (which itself has now divided into competing formulations) is still an important perspective in the realism/antirealism dialectic; however, its significance has expanded well beyond that debate. Today ontic structural realism is also an important player in the metaphysics of science literature, engaging with a variety of ontological questions. One of these pertains to the basic categories of ontology, with the proponents of ontic structural realism typically advocating a radical rethinking of how to view substance and relation while calling into question the (allegedly) traditional privileging of the former over and against the latter. In this paper I assess ontic structural realism from the perspective of two major systems: Thomism and Scotism. I argue that the basic commitments of Thomism allow for some surprising convergences with ontic structural realism, while Scotism does not.

The Definition of Religion, Super-empirical Realities and Mathematics

2016 ◽  
Vol 58 (1) ◽  
Author(s):  
Andrea Sauchelli
Keyword(s):  
Necessary Conditions ◽  
Philosophy Of Mathematics ◽  
Precise Definition ◽  
Mathematical Realism ◽  
Sufficient And Necessary Conditions ◽  
Definition Of Religion ◽  
And Mathematics ◽  
Definition Of

SummaryProviding a precise definition of “religion” – or an analysis in terms of sufficient and necessary conditions of the concept of religion – has proven to be a difficult task, more so in light of the diverse types of practices considered religious by scholars. Here, I discuss Kevin Schilbrack’s recent definition of “religion”, elaborate it and raise several objections, one of which is based on a specific theory in philosophy of mathematics: mathematical realism.

scholarly journals Invariance as a basis for necessity and laws

2021 ◽  
Author(s):  
Gila Sher
Keyword(s):  
Scientific Realism ◽  
Laws Of Nature ◽  
Main Idea ◽  
Mathematical Realism ◽  
Biological Laws ◽  
The Difference ◽  
And Mathematics ◽  
Invariant Properties ◽  
Apparent Conflict

AbstractMany philosophers are baffled by necessity. Humeans, in particular, are deeply disturbed by the idea of necessary laws of nature. In this paper I offer a systematic yet down to earth explanation of necessity and laws in terms of invariance. The type of invariance I employ for this purpose generalizes an invariance used in meta-logic. The main idea is that properties and relations in general have certain degrees of invariance, and some properties/relations have a stronger degree of invariance than others. The degrees of invariance of highly-invariant properties are associated with high degrees of necessity of laws governing/describing these properties, and this explains the necessity of such laws both in logic and in science. This non-mysterious explanation has rich ramifications for both fields, including the formality of logic and mathematics, the apparent conflict between the contingency of science and the necessity of its laws, the difference between logical-mathematical, physical, and biological laws/principles, the abstract character of laws, the applicability of logic and mathematics to science, scientific realism, and logical-mathematical realism.

scholarly journals Scientific Realism Again

2018 ◽  
Vol 9 (1) ◽  
pp. 99 ◽  
Author(s):  
James Ladyman
Keyword(s):  
Scientific Realism ◽  
Common Sense ◽  
Structural Realism ◽  
Van Fraassen ◽  
Ontic Structural Realism ◽  
Fundamental Physics ◽  
The Real ◽  
Special Sciences ◽  
Do So

The present paper concerns how scientific realism is formulated and defended. It is argued that van Fraassen is fundamentally right that scientific realism requires metaphysics in general, and modality in particular. This is because of several relationships that raise problems for the ontology of scientific realism, namely those between: scientific realism and common sense realism; past and current theories; the sciences of different scales; and the ontologies of the special sciences and fundamental physics. These problems are related. It is argued that ontic structural realism, in the form of the real-patterns account of ontology, offers a unified solution to them all (or at least that it is required to do so, if it is to make good on the promise of naturalised metaphysics).

The Necessity of Sufficiency

2018 ◽  
Author(s):  
Bruce L. Gordon
Keyword(s):  
Recent Work ◽  
Quantum Physics ◽  
Structural Realism ◽  
Sufficient Reason ◽  
Divine Action ◽  
Ontic Structural Realism ◽  
Existence Of God ◽  
Principle Of Sufficient Reason ◽  
Adequate Understanding ◽  
Quantum Phenomena

There is an argument for the existence of God from the incompleteness of nature that is vaguely present in Plantinga’s recent work. This argument, which rests on the metaphysical implications of quantum physics and the philosophical deficiency of necessitarian conceptions of physical law, deserves to be given a clear formulation. The goal is to demonstrate, via a suitably articulated principle of sufficient reason, that divine action in an occasionalist mode is needed (and hence God’s existence is required) to bring causal closure to nature and render it ontologically functional. The best explanation for quantum phenomena and the most adequate understanding of general providence turns out to rest on an ontic structural realism in physics that is grounded in the immaterialist metaphysics of theistic idealism.

Physics, Structure, and Reality

2021 ◽  
Author(s):  
Jill North
Keyword(s):  
Scientific Realism ◽  
Physical Theory ◽  
Scientific Explanation ◽  
Classical Mechanics ◽  
Careful Attention ◽  
Coordinate Systems ◽  
Spacetime Structure ◽  
The World ◽  
Background Assumption ◽  
And Mathematics

How do we figure out the nature of the world from a mathematically formulated physical theory? What do we infer about the world when a physical theory can be mathematically formulated in different ways? Physics, Structure, and Reality addresses these questions, questions that get to the heart of the project of interpreting physics—of figuring out what physics is telling us about the world. North argues that there is a certain notion of structure, implicit in physics and mathematics, that we should pay careful attention to, and that doing so sheds light on these questions concerning what physics is telling us about the nature of reality. Along the way, lessons are drawn for related topics such as the use of coordinate systems in physics, the differences among various formulations of classical mechanics, the nature of spacetime structure, the equivalence of physical theories, and the importance of scientific explanation. Although the book does not explicitly defend scientific realism, instead taking this to be a background assumption, the account provides an indirect case for realism toward our best theories of physics.

Trends in International Mathematics and Science Study and gendered math teaching in Kuwait

2017 ◽  
Vol 15 (3) ◽  
pp. 327-340 ◽  
Author(s):  
Fatimah Ahmad ◽  
Heather Greenhalgh-Spencer
Keyword(s):  
Education Research ◽  
Math Education ◽  
Math Performance ◽  
Science Study ◽  
Science Technology ◽  
Women And Girls ◽  
Math Teaching ◽  
And Mathematics ◽  
Mathematics And Science

This paper argues for a more complex literature around gender and math performance. In order to argue for this complexity, we present a small portion of data from a case study examining the performance of Kuwaiti students on the Trends in International Mathematics and Science Study and on Kuwait national math tests. Westernized discourses suggest that girls have a harder time in math classes; these discourses frame and are reified by prominent literature and practices within the field of math education research that suggest that women and girls need help in order to reach their potential in math. These Westernized discourses stand in contrast to the discourses in Kuwait that normalize women and girls as outperforming boys in all subjects – including all science, technology, engineering and mathematics subjects. As our study shows, the reality is more complex. And, while the reality is more complex, we yet lack the discourses to understand this complexity.

scholarly journals On individuality in quantum theory

2015 ◽  
Vol 13 (1) ◽  
pp. 29-38
Author(s):  
Jasmina Jeknic-Dugic
Keyword(s):  
Quantum Theory ◽  
Structural Realism ◽  
Mechanical Analysis ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Ontic Structural Realism

A quantum mechanical analysis of the decomposability of quantum systems into subsystems provides support for the so-called "attenuated Eliminative Ontic Structural Realism" within Categorical Structuralism studies in physics. Quantum subsystems are recognized as non-individual, relationally defined objects that deflate or relax some standard objections against Eliminative Ontic Structural Realism. Our considerations assume the universally valid quantum theory without tackling interpretational issues.

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