Can the new indispensability argument be saved from Euclidean rescues?

The traditional formulation of the indispensability argument for the existence of mathematical entities (IA) has been criticised due to its reliance on confirmational holism. Recently a formulation of IA that works without appeal to confirmational holism has been defended. This recent formulation is meant to be superior to the traditional formulation in virtue of it not being subject to the kind of criticism that pertains to confirmational holism. I shall argue that a proponent of the version of IA that works without appeal to confirmational holism will struggle to answer a challenge readily answered by proponents of a version of IA that does appeal to confirmational holism. This challenge is to explain why mathematics applied in falsified scientific theories is not considered to be falsified along with the rest of the theory. In cases where mathematics seemingly ought to be falsified it is saved from falsification, by a so called ??Euclidean rescue??. I consider a range of possible answers to this challenge and conclude that each answer fails.     

The Indispensability Argument for Mathematical Realism and Scientific Realism

Confirmational holism is central to a traditional formulation of the indispensability argument for mathematical realism (IA). I argue that recent strategies for defending scientific realism are incompatible with confirmational holism. Thus a traditional formulation of IA is incompatible with recent strategies for defending scientific realism. As a consequence a traditional formulation of IA will only have limited appeal.     

Dispensability in the Indispensability Argument

One of the most influential arguments for realism about mathematical objects is the indispensability argument. Simply put, this is the argument that insofar as we are committed to the existence of the physical objects existentially quantified over in our best scientific theories, we are also committed to the mathematical objects existentially quantified over in these theories. Following the Quine–Putnam formulation of the indispensability argument, some proponents of the indispensability argument have made the mistake of taking confirmational holism to be an essential premise of the argument. In this paper, I consider the reasons philosophers have taken confirmational holism to be essential to the argument and argue that, contrary to the traditional view, confirmational holism is dispensable.     

Underdetermination, Holism and the Theory/Data Distinction

I examine the argument that scientific theories are typically 'underdetermined' by the data, an argument which has often been used to combat scientific realism. I deal with two objections to the underdetermination argument: (i) that the argument conflicts with the holistic nature of confirmation, and (ii) that the argument rests on an untenable theory/data dualism. I discuss possible responses to both objections, and argue that in both cases the proponent of underdetermination can respond in ways which are individually plausible, but that the best response to the first objection conflicts with the best response to the second. Consequently underdetermination poses less of a problem for scientific realism than has often been thought.     

Evidential Holism and Indispensability Arguments

The indispensability argument is a method for showing that abstract mathematical objects exist (call this mathematical Platonism). Various versions of this argument have been proposed (§1). Lately, commentators seem to have agreed that a holistic indispensability argument (§2) will not work, and that an explanatory indispensability argument is the best candidate. In this paper I argue that the dominant reasons for rejecting the holistic indispensability argument are mistaken. This is largely due to an overestimation of the consequences that follow from evidential holism. Nevertheless, the holistic indispensability argument should be rejected, but for a different reason (§3)—in order that an indispensability argument relying on holism can work, it must invoke an unmotivated version of evidential holism. Such an argument will be unsound. Correcting the argument with a proper construal of evidential holism means that it can no longer deliver mathematical Platonism as a conclusion: such an argument for Platonism will be invalid. I then show how the reasons for rejecting the holistic indispensability argument importantly constrain what kind of account of explanation will be permissible in explanatory versions (§4).     

Confirmation Theory and Indispensability

In this paper I examine Quine's indispensability argument, with particular emphasis on what is meant by 'indispensable'. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine's argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.     

Data Fabrication and Falsification and Empiricist Philosophy of Science

Scientists have rules pertaining to data fabrication and falsification that are enforced with significant punishments, such as loss of funding, termination of employment, or imprisonment. These rules pertain to data that describe observable and unobservable entities. In this commentary I argue that scientists would not adopt rules that impose harsh penalties on researchers for data fabrication or falsification unless they believed that an aim of scientific research is to develop true theories and hypotheses about entities that exist, including unobservable ones. This argument presents a challenge for constructive empiricists, such as van Fraassen. Constructive empiricists need to be able to explain why rules pertaining to data fabrication and falsification do not threaten their philosophy of science.     

The holistic presumptions of the indispensability argument

The indispensability argument is sometimes seen as weakened by its reliance on a controversial premise of confirmation holism. Recently, some philosophers working on the indispensability argument have developed versions of the argument which, they claim, do not rely on holism. Some of these writers even claim to have strengthened the argument by eliminating the controversial premise. I argue that the apparent removal of holism leaves a lacuna in the argument. Without the holistic premise, or some other premise which facilitates the transfer of evidence to mathematical portions of scientific theories, the argument is implausible.     

Agnostic empiricism versus scientific realism: Belief in truth matters

This paper aims to defend scientific realism against two versions of agnostic empiricism: a naive agnostic position, which suggests that the only rational option is to remain agnostic as to the truth of theoretical assertions, and van Fraassen's more sophisticated agnostic empiricism - which may be called "Hypercritical Empiricism". It first argues that given semantic realism, naive agnostic empiricism cannot be maintained: there is no relevant epistemic difference between theoretical assertions and observational ones. It then focuses on van Fraassen's more sophisticated alternative to scientific realism and suggests that an attitude towards science which involves less than aiming at theoretical truth and believing in theories would be, in some concrete respect that empiricists should recognize, worse off than the recommended realist attitude. To this end, the paper develops the so-called conjunction argument into a diachronic argument for scientific realism.     

Why inference to the best explanation doesn’t secure empirical grounds for mathematical platonism

Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends on a false view of how abductive considerations mediate the transfer of empirical support. More specifically, I argue that even if inference to the best explanation is cogent, and claims about mathematical entities play an essential explanatory role in some of our best scientific explanations, it doesn’t follow that the empirical phenomena that license those explanations also provide empirical support for the claim that mathematical entities exist.

     

Platonism and anti‐Platonism: Why worry?

This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti‐Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the ‘no miracles’ argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific ‘realists’ should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism.     

Holism and Emergence: Dynamical Complexity Defeats Laplace’s Demon

Abstract

The paradigm of Laplacean determinism combines three regulative principles: determinism, predictability, and the explanatory adequacy of universal laws together with purely local conditions. Historically, it applied to celestial mechanics, but it has been expanded into an ideal for scientific theories whose cogency is often not questioned. Laplace’s demon is an idealization of mechanistic scientific method. Its principles together imply reducibility, and rule out holism and emergence. I will argue that Laplacean determinism fails even in the realm of planetary dynamics, and that it does not give suitable criteria for explanatory success except within very well defined and rather exceptional domains. Ironically, the very successes of Laplacean method in the Solar System were made possible only by processes that are not themselves tractable to Laplacean methodology. The results of some of these processes were first observed in 1964, and violate the Lapacean requirements of locality and predictability, opening the door to holism and nonreducibility, i.e., emergence. Despite the falsification of Laplacean methodology, the explanatory resources of holism and emergence remain in scientific limbo, though emergence has been used somewhat indiscriminately in recent scientific literature. I make some remarks at the end about the proper use of emergence in its traditional sense going back to C.D. Broad.     

On Reichenbach’s argument for scientific realism

The aim of this paper is to articulate, discuss in detail and criticise Reichenbach’s sophisticated and complex argument for scientific realism. Reichenbach’s argument has two parts. The first part aims to show how there can be reasonable belief in unobservable entities, though the truth of claims about them is not given directly in experience. The second part aims to extent the argument of the first part to the case of realism about the external world, conceived of as a world of independently existing entities distinct from sensations. It is argued that the success of the first part depends on a change of perspective, where unobservable entities are viewed as projective complexes vis-à-vis their observable symptoms, or effects. It is also argued that there is an essential difference between the two parts of the argument, which Reichenbach comes (somewhat reluctantly) to accept.     

Why Anti-Realism Breaks up Relationships

Some theologians are inclined to regard realism with hostility or indifference. I do not present an argument for realism, but for why realism matters, and what is at stake.
First of all, I separate the heart of realism from gratuitous doctrines which are too often associated with it. Religious realism is the claim that truth is independent of our beliefs about truth, and that we can in principle hope to have true beliefs about God. Realism is not intrinsically concerned with the existence of 'objects', with natural theology or rational justification.
I then show that even thinkers who are hostile or indifferent to religious realism so defined, usually make an implicit appeal to a similar realism in the sphere of ethics.
To establish that realism matters in religion as well as ethics I draw an analogy with realism/anti-realism about persons, to show that anti-realism makes mutually risk-taking and courageous relationships impossible. I go on to argue that far from it being a realist who is obsessed with rational certainty, this is one of the worst vices of the anti-realist, who cannot bear there to be a gap between her beliefs and reality.
I conclude that the most vital feature of religious realism is not certainty of belief, but the opposite – the acknowledged risk that all our hope could be in vain. In closing the possibility on this risk, the anti-realist demonstrates an unfaithful and uncourageous movement of thought.     

Weinberg on QFT: Demonstrative Induction and Underdetermination

In this essay I examine a recent argument by Steven Weinberg that seeks to establish local quantum field theory as the only type of quantum theory in accord with the relevent evidence and satisfying two basic physical principles. I reconstruct the argument as a demonstrative induction and indicate it's role as a foil to the underdetermination argument in the debate over scientific realism. This revised version was published online in June 2006 with corrections to the Cover Date.     

Informational Realism and World 3

This paper takes up a suggestion made by Floridi that the digital revolution is bringing about a profound change in our metaphysics. The paper aims to bring some older views from philosophy of mathematics to bear on this problem. The older views are concerned principally with mathematical realism—that is the claim that mathematical entities such as numbers exist. The new context for the discussion is informational realism, where the problem shifts to the question of the reality of information. Mathematical realism is perhaps a special case of informational realism. The older views concerned with mathematical realism are the various theories of World 3. The concept of World 3 was introduced by Frege, whose position was close to Plato’s original views. Popper developed the theory of World 3 in a different direction which is characterised as ‘constructive Platonism’. But how is World 3 constructed? This is explored by means of two analogies: the analogy with money, and the analogy with meaning, as explicated by the later Wittgenstein. This leads to the development of an account of informational realism as constructive Aristoteliansim. Finally, this version of informational realism is compared with the informational structural realism which Floridi develops in his 2008 and 2009 papers in Synthese. Similarities and differences between the two positions are noted.     

Two Kinds of Mental Realism

I argue that there is a distinction to be drawn between two kinds of mental realism, and I draw some lessons for the realism-antirealism debate. Although it is already at hand, the distinction has not yet been drawn clearly. The difference to be shown consists in what realism is about: it may be either about the interpretation of folk psychology, or the ontology of mental entities. I specify the commitment to the fact-stating character of the discourse as the central component of realism about folk psychology, and from this I separate realism about mental entities as an ontological commitment towards them. I point out that the two views are mutually independent, which provides the possibility of considering folk psychology as not being in cognitive competition with scientific psychology. At the end I make a tentative suggestion as to how to interpret the former in order to avoid this conflict.     

What is so Magical About a Theory of Intrinsic Intensionality?

Abstract

Curiously missing in the vast literature on Hilary Putnam's so-called model-theoretic argument against semantic realism is any response from would-be proponents of what Putnam would call magical theories of reference. Such silence is surprising in light of the fact that such theories have occupied a significant position in the history of philosophy and the fact that there are still several prominent thinkers who would, no doubt, favor such a theory. This paper develops and examines various responses to Putnam's argument on behalf of the proponent of a magical theory of reference. While Putnam's explicit replies to such responses to his argument seem to involve little more than name calling, I develop arguments that show that there are significant problems facing any would-be proponent of such a view. While magical theories of reference are far from the strawmen Putnam seems to take them to be, there are, I argue, genuine reasons for a semantic realist to prefer a non-magical theory of reference.     

Contact with the Nomic: A Challenge for Deniers of Humean Supervenience about Laws of Nature Part II: the Epistemological Argument for Humean Supervenience

In Part I, we presented and motivated a new formulation of Humean Supervenience about Laws of Nature (HS). Here in Part II, we present an epistemological argument in defense of HS, thus formulated. Our contention is that one can combine a modest realism about laws of nature with a proper recognition of the importance of empirical testability in the epistemology of science only if one accepts HS.     

(Probably) not companions in guilt

In this paper, I will attempt to develop and defend a common form of intuitive resistance to the companions in guilt argument. I will argue that (contra the companions in guilt argument) one can reasonably believe there are promising solutions to the access problem for mathematical realism that don’t translate to moral realism. In particular, I will suggest that the structuralist project of accounting for mathematical knowledge in terms of some form of logical knowledge offers significant hope of success while no analogous approach offers such hope for moral realism.