Ioannis G. Ntagkas

This paper addresses the issue of stipulation in three cases of implicit definitions. It argues that the alleged implicit definitions do not have a purely stipulative status. Stipulation of the vehicles of the implicit definitions in question should end up with true postulates. However, those postulates should not be taken to be true only in virtue of stipulation since they have extra commitments. Horwich’s worry emerges in all three kinds of implicit definitions under consideration, since the existence of meanings so that the alleged postulates are true depends on extra requirements that should be fulfilled. Moreover, if Ramseyfication method is applied to the three kinds of implicit definition, they are split up into two components from which the first one is broadly factual while the second one is purely stipulative. The paper argues that their definitional task in each case should be assigned to their second component i.e. their Carnap-conditional.

Plato's theory of forms is developed and compared to the modern theory of recursion. I show how Plato's theory, as it applies to mathematical objects, is essentially a primitve version of modern recursion theory, which has all the essential elements of the ancient theory. However, Plato himself thought there was more than mathematics to his forms. He believed that form had a noncomposite, unanalyzable component. So, while recursion theory provides an adequate formalization of Plato's theory, it cannot be considered identical to it. I argue--drawing from material in the "Meno," "Phaedo," and "Republic"--that Plato's arguments for noncomposite form are largely fallacious. Plato would, I believe, have taken the computational version developed here seriously, since mathematics was his primary source for clear examples of forms (one could argue that it was his only source short of dipping into mysticism). In fact, there is a long-standing oral tradition that Plato developed a more formal version of his theory in lecture notes for courses he taught at the Academy (the university he founded in Athens). Any such notes, if they existed at all, have been lost. But if such a formal version did exist, it is tantalizing to wonder to what extent Plato may have anticipated modern theoretical computer science and metamathematics.

This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege.ion principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account should be construed as putting emphasis on intentionality of human mind towards certain invariant features of the elements of initial domains of discourse that are involved in equivalence relations. Definition of terms like direction, shape, number etc. is achieved by a kind of transformation of those invariants into ideal objects that is involved in intuition. Then the paper argues that at the period of 1926 Weyl’s writings on implicit definitions, he is inclined to endorse symbolic construction as a way to explicate the objectivity of certain processes as those that are carried out in case of implicit definitions.

One of the most pressing challenges that occupy the Russellian panpsychist’s agenda is to come up with a way to reconcile the traditional argument from categorical properties (Seager, 2006; Alter & Nagasawa, 2015) with H. H. Mørch’s dispositionalism-friendly argument from the experience of causation (2014, 2018, 2020) — on the way to a unitary, all-encompassing case for the view. In this regard, Mørch claims that, via the commitment to the Identity theory of properties, one can consistently hold both panpsychist arguments without contradiction (2020: 281) — I shall refer to such proposal as Reconciliation. In my paper, I shall argue that this is not the case. To this extent, I will first consider H. Taylor’s argument that the Identity theorists have the exact same resources as the dispositionalists (as, after careful enquiry, their views on the metaphysics of properties turn out to coincide (2018: 1438)), and thus contend that Reconciliation fails to obtain. Then, I will suggest that one can avoid the problem and reconcile the arguments by adopting a different version of the powerful qualities view, namely the Compound view — and thus advance a reformulated version of the claim, i.e. Reconciliation*. Finally, even though pursuing my proposed solution might expose Russellian panpsychism to the risk of epiphenomenalism, I shall conclude that such specific form of epiphenomenalism is a rather benign one, and thus that, via Reconciliation*, the constitution of a unitary case for panpsychism as a positive proposal (and not as a mere alternative to dualism and physicalism) can be achieved.

A prominent objection to supervenience physicalism is that a definition of physicalism in terms of supervenience allows for physicalism to be compatible with nonphysicalist outlooks, such as certain forms of emergentism. I take as my starting point a recent defense of supervenience physicalism from this objection. According to this line of thought, the subvenient base for emergent properties cannot be said to be purely physical; rather, it is “polluted” with emergent features in virtue of necessarily giving rise to them. Thus, if emergentism is true, it is false that everything supervenes on physical properties. I argue that this gives way to a new challenge for supervenience physicalism. The challenge, roughly, is to distinguish the emergentist’s “polluted” base from a physical supervenience base; that is, to give conditions under which the subvenient base is not “polluted” by supervenient properties. The problem, I argue, is that it is hard to see how this can be done without collapsing supervenience physicalism into alternative approaches to physicalism. I thus argue that if the present defense of supervenience physicalism succeeds in defending the adequacy of a supervenience-based definition of physicalism, it does so by compromising its uniqueness

We provide a formulation of physicalism, and show that this is to be favoured over alternative formulations. Much of the literature on physicalism assumes without argument that there is a fundamental level to reality, and we show that a consideration of the levels problem and its implications for physicalism tells in favour of the form of physicalism proposed here. Its hey elements are, fast, that the empirical and substantive part of physicalism amounts to a prediction that physics will not posit new entities solely for the purpose of accounting for mental phenomena, nor new entities with essentially mental characteristics such as propositioned attitudes or intentions; secondly, that physicalism can safely make do with no more than a weak global formulation of supervenience.

This correction reflects that I forgot to cite Stephan Leuenberger's unpublished work in the paragraph beginning "More promising, perhaps, is the orthodox view ..." in Section 5. The overall argument of Section 5 is a development of an argument I gave in footnote 27 of 'No Work for a Theory of Grounding' (Inquiry, 2014). At issue in the relevant sections of 'No Work...' and 'Grounding-based Formulations...' is whether a proponent of Grounding has resources to accommodate strongly emergent phenomena, where strong emergence is understood as contrasting with physicalism. In 'No Work...', after arguing in the text that an account of strong emergence as involving a failure of full Grounding would not accommodate the live possibility that strongly emergent goings-on might be partially but not completely metaphysically dependent on physical goings on, I considered in note 27 whether strong emergence, again understood as contrasting with physicalism, could be characterized by appeal to a Finean notion of partial Grounding, as the view that strongly emergent goings-on are partially but not fully Grounded in physical goings-on, and I argued that assuming that the notion of partial Grounding was taken to be primitive, then (since there were no prospects of defining full Grounding in terms of primitive partial Grounding along lines of defining a general notion of parthood in terms of primitive proper parthood or identity), such an approach would require that full Grounding also be taken as primitive, with possibly yet another primitive connecting partial and full Grounding. I heard Leuenberger's talk 'Emergence and Failures of Supplementation' in May 2015; for purposes of developing my previous argument (as per Section 5 in 'Grounding-based Formulations...') this talk was helpful since Leuenberger correctly argued that there were also no prospects for implementing the partial Grounding-based strategy by taking full Grounding to be primitive and defining partial Grounding in terms of full Grounding, since that would import a weak supplementation structure that might not be present in cases of strong emergence. I wrote to Leuenberger asking for his slides so that I could reference him and his work (which again is presented in the paragraph beginning "More promising, perhaps, is the orthodox view..."), but somehow forgot to include a citation to his talk, for which I sincerely apologize. One last thing: the erratum is a bit misleading about my use of Leuenberger's work. My discussion of whether a primitivist (i.e., 'non-orthodox') understanding of Finean partial Ground serves as a suitable basis for a partial Grounding-based approach to strong emergence stems from footnote 27 of my 2014, not Leuenberger's 2015 talk, and in both 'No Work...' and 'Grounding-based Formulations...' I argue that such an approach would be problematic, not "suitable", since involving two or three primitives. Also worth noting is that I do not claim or argue that the orthodox conception of partial Grounding as defined in supplementary fashion in terms of full Grounding is *incompatible* with strong emergence. Again, at issue in both 'No Work...' and in 'Grounding-based Formulations...' is strong emergence understood as contrasting with physicalism, so the relevant application of a partial Grounding-based strategy, whether or not involving an 'orthodox' account of partial Grounding as definable in terms of full Grounding, is in my papers one according to which strongly emergent goings-on are partially but not fully Grounded in *physical* goings-on. So far as I can tell, there might be cases of strong emergence that *do* obey supplementation, and which would be compatible with a partial Grounding-based account of strong emergence, where the operative notion of partial Grounding is 'orthodox' (non-primitive). For my purposes, what is important is that cases of strong emergence might not obey supplementation.

I problematize Grounding-based formulations of physicalism. More specifically, I argue, first, that motivations for adopting a Grounding-based formulation of physicalism are unsound; second, that a Grounding-based formulation lacks illuminating content, and that attempts to imbue Grounding with content by taking it to be a strict partial order are unuseful and problematic ; third, that conceptions of Grounding as constitutively connected to metaphysical explanation conflate metaphysics and epistemology, are ultimately either circular or self-undermining, and controversially assume that physical dependence is incompatible with explanatory gaps; fourth, that in order to appropriately distinguish physicalism from strong emergentism, a Grounding-based formulation must introduce one and likely two primitives in addition to Grounding; and fifth, that understanding physical dependence in terms of Grounding gives rise to ‘spandrel’ questions, including, e.g., “What Grounds Grounding?”, which arise only due to the overly abstract nature of Grounding.

The physicalist thesis that all entities are nothing over and above physical entities is often interpreted as appealing to a supervenience-based account of "nothing over and aboveness”, where, schematically, the A-entities are nothing over and above the B-entities if the A-entities supervene on the B-entities. The main approaches to filling in this schema correspond to different ways of characterizing the modal strength, the supervenience base, or the supervenience connection at issue. I consider each approach in turn, and argue that the resulting formulation of physicalism is compatible with physicalism’s best traditional rival: a naturalist emergentism. Others have argued that supervenience-based formulations of physicalism fail. My aim here, besides addressing the full spectrum of supervenience-based approaches, is to show how certain philosophical and scientific theses concerning naturalism, properties, and laws give us new reasons to think that supervenience-based formulations of physicalism are untenable.

Eriksson thinks that moral disagreements are intuitively faulty whereas disagreements about taste are intuitively faultless. He attempts to account for this difference by arguing, first, that moral judgements and taste judgements differ with regard to the presence of a disposition to challenge conflicting judgements and, second, that the intuition that a judgement is mistaken consists in the disposition to challenge it. In this article, I focus on the reasons given to support the first claim and argue that they are not sufficient. First, I assess the thesis that a taste judgement is only contingently connected with a disposition to challenge conflicting judgements. Second, I focus on the claim that a moral judgement is in part a disposition to challenge conflicting judgements. In both cases, I argue that the reasons given fail to disclose any substantial difference between the two domains.

Non-reductive physicalists have made a number of attempts to provide the relation of supervenience between levels of properties with enough bite to analyze interesting cases without at the same time losing the relation's acceptability for the physicalist. I criticize some of these proposals and suggest an alternative supplementation of the supervenience relation by imposing a requirement of robustness which is motivated by the notion of structural stability familiar from dynamical systems theory. Robust supervenience, I argue, captures what the non-reductive physicalist wants from supervenience; most importantly, it provides a natural background for reconstructing the notion of (diachronic) property emergence in a way acceptable to physicalists

The majority of contemporary philosophers of mind are physicalists. The majority of physicalists, however, are non-reductive physicalists. As nonreductive physicalists, these philosophers hold that a system's mental properties are different from a system's physical properties, that is, they hold that the sum total of mental facts about some system is a different set of facts than the sum total of physical facts about the same system. As physicalists, however, these nonreductivists hold that mental facts are nonetheless determined by physical facts, that is, they subscribe to the supervenience thesis, i.e., the thesis that no mental differences can obtain without physical differences obtaining. In this paper I take up the issue of how best to understand the notion of supervenience, especially in the light of recent advances in the neurosciences

David Papineau, Jerry Fodor and many others wonder how the conjunction of the following three positions can be true: 1) Special science laws: There are lawlike generalizations in the special sciences. These sciences trade in kinds that are such that statements about salient, reliable correlations that are projectible and that support counterfactuals apply to the tokens coming under these kinds. 2) Non-reductionism: The laws of some of the special sciences cannot be reduced to physical laws. 3) Physicalism: Everything there is in the world supervenes on the physical, that is, is fixed by the distribution of the physical properties in the world. The obvious problem is that (3) implies that the similarities among tokens in the world, accounting for the kinds in which the special sciences trade, and the correlations among such tokens, accounting for the laws of the special sciences, are fixed by the distribution of the physical properties. By contrast, (2) implies that some of the laws seizing such correlations are not reducible to physical laws. By using the term “token”, I mean a particular instantiating a property. Papineau’s proposal to reconcile these three positions is to account for (2) in terms of selection (pp. 6-9): There can be laws in the special sciences that are not reducible to physical laws if and only if these laws focus on effects that are selected for in a given context independently of the mechanisms by which they are brought about. Thus, the fact of there being such laws and their non-reducibility to physics do not contradict physicalism (3). The drawback is that the kinds that figure in such laws cannot enter into a rich network of laws 199 and that nothing can be causally efficacious insofar as it is a member of such a kind. In these comments, I shall try to push Papineau further in the direction of a reductive physicalism, thus solving the problem by simply abandoning (2)..

After the discovery of the structure of DNA in 1953, scientists working in molecular biology embraced reductionism—the theory that all complex systems can be understood in terms of their components. Reductionism, however, has been widely resisted by both nonmolecular biologists and scientists working outside the field of biology. Many of these antireductionists, nevertheless, embrace the notion of physicalism—the idea that all biological processes are physical in nature. How, Alexander Rosenberg asks, can these self-proclaimed physicalists also be antireductionists? With clarity and wit, Darwinian Reductionism navigates this difficult and seemingly intractable dualism with convincing analysis and timely evidence. In the spirit of the few distinguished biologists who accept reductionism—E. O. Wilson, Francis Crick, Jacques Monod, James Watson, and Richard Dawkins—Rosenberg provides a philosophically sophisticated defense of reductionism and applies it to molecular developmental biology and the theory of natural selection, ultimately proving that the physicalist must also be a reductionist.

The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: it does not refer to any abstract mathematical objects, it is free from the usual arbitrary conventions, and it explains why the wave function has its gauge degrees of freedom, something that are usually put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to ``wave function realism.''

This chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. To make plain these nonclassical features, quantum games are analyzed in which a ‘no-signaling’ constraint has to be satisfied. It is further shown how the Lüders Rule may be seen as an instruction how to update probabilities following some measurement. As conditionalization following this rule leads to inevitable losses of information, it is argued that quantum theory implies new constraints on information. A parallel is drawn to the Special Theory of Relativity: The geometric structure of Hilbert spaces imposes new, but objective probabilistic constraints on correlations between events, just as the geometric structure of Minkowski space in special relativity imposes new spatio-temporal kinematic constraints on events.

Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze these arguments. The import of the first two is diminished by their dependence on assumptions about the outcomes of counterfactual measurements. But the third argument establishes its intended conclusion. Even if every well-conducted quantum measurement we ever make will have a definite physical outcome, this argument should make us reconsider the objectivity of that outcome.

This is one of the most important books on quantum mechanics to have appeared in recent years. It offers a dramatically new interpretation that resolves puzzles and paradoxes associated with the measurement problem and the behavior of coupled systems. A crucial feature of this interpretation is that a quantum mechanical measurement can be certain to have a particular outcome even when the observed system fails to have the property corresponding to that outcome just prior to the measurement interaction.

The integration of recent work on decoherence into a so-called modal interpretation offers a promising new approach to the measurement problem in quantum mechanics. In this paper I explain and develop this approach in the context of the interactive interpretation presented in Healey (1989). I begin by questioning a number of assumptions which are standardly made in setting up the measurement problem, and I conclude that no satisfactory solution can afford to ignore the influence of the environment. Further, I argue that there are good reasons to believe that on a modal interpretation environmental interactions rapidly ensure that a quantummechanically describable apparatus indeed records a definite result following a measurement interaction.

Determinism is established in quantum mechanics by tracing the probabilities in the Born rules back to the absolute (overall) phase constants of the wave functions and recognizing these phase constants as pseudorandom numbers. The reduction process (collapse) is independent of measurement. It occurs when two wavepackets overlap in ordinary space and satisfy a certain criterion, which depends on the phase constants of both wavepackets. Reduction means contraction of the wavepackets to the place of overlap. The measurement apparatus fans out the incoming wavepacket into spatially separated eigenpackets of the chosen observable. When one of these eigenpackets together with a wavepacket located in the apparatus satisfy the criterion, the reduction associates the place of contraction with an eigenvalue of the observable. The theory is nonlocal and contextual. Keywords:

This proposes a new theory of Quantum measurement; a state reduction theory in which reduction is to the elements of the number operator basis of a system, triggered by the occurrence of annihilation or creation (or lowering or raising) operators in the time evolution of a system. It is from these operator types that the acronym ‘LARC’ is derived. Reduction does not occur immediately after the trigger event; it occurs at some later time with probability P t per unit time, where P t is very small. Localisation of macroscopic objects occurs in the natural way: photons from an illumination field are reflected off a body and later absorbed by another body. Each possible absorption of a photon by a molecule in the second body generates annihilation and raising operators, which in turn trigger a probability per unit time P t of a state reduction into the number operator basis for the photon field and the number operator basis of the electron orbitals of the molecule. Since all photons in the illumination field have come from the location of the first body, wherever that is, a single reduction leads to a reduction of the position state of the first body relative to the second, with a total probability of mP t , where m is the number of photon absorption events. Unusually for a reduction theory, the larc theory is naturally relativistic

A resolution of the quantum measurement problem would require one to explain how it is that we end up with determinate records at the end of our measurements. Metaphysical commitments typically do real work in such an explanation. Indeed, one should not be satisfied with one's metaphysical commitments unless one can provide some account of determinate measurement records. I will explain some of the problems in getting determinate records in relativistic quantum field theory and pay particular attention to the relationship between the measurement problem and a generalized version of Malament's theorem.

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology and to the quantum measurement problem.

The Wigner’s friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner’s friend thought experiment in detail and show that the reasoning process from each agent that leads to the no-go theorem is inconsistent. The inconsistency is with respect to the requirement that an agent should make use of updated information instead of outdated information. We then apply the relational formulation of quantum measurement to resolve the inconsistent descriptions from different agents. In relational formulation of quantum mechanics, a measurement is described relative to an observer. Synchronization of measurement result is a necessary requirement to achieve consistent descriptions of a quantum system from different observers. Thought experiments, including EPR, Wigner’s Friend and it extended version, confirm the necessity of relational formulation of quantum measurement when applying quantum mechanics to composite system with entangled but space-like separated subsystems.

We suggest a new answer to this intriguing question and argue that the answer may have implications for the solutions to the measurement problem. The main basis of our analysis is the doctrine of psychophysical supervenience. First of all, based on this doctrine, we argue that an observer in a quantum superposition or a quantum observer has a definite conscious experience, which is neither disjunctive nor illusive. The inconsistency of this result with the bare theory is further analyzed, and it is shown that an appropriate use of the strategy of analyzing the disposition of an observer to answer a particular question also leads to the same result. Next, we argue that this new result seems to disfavor Everett's and Bohm's approaches to quantum mechanics when considering the doctrine of psychophysical supervenience. This suggests that dynamical collapse theories are in the right direction to solve the measurement problem. Thirdly, we analyze the concrete content of the conscious experience of a quantum observer. It is argued that the mental content of a quantum observer is related to both the amplitude and relative phase of each branch of the superposition she is physically in, and it is composed of the mental content corresponding to every branch of the superposition. In addition, we argue that when assuming the modulus squared of the amplitude of each branch determines the vividness of the mental content corresponding to the branch, the structured tails problem of dynamical collapse theories can be solved.

The book explores several open questions in the philosophy of statistical mechanics. Each chapter is written by a leading expert in the field. Here is a list of some questions that are addressed in the book: 1) Boltzmann showed how the phenomenological gas laws of thermodynamics can be derived from statistical mechanics. Since classical mechanics is a deterministic theory there are no probabilities in it. Since statistical mechanics is based on classical mechanics, all the probabilities statistical mechanics talks about cannot be fundamental. However, if probabilities are epistemic, how can they play a role, as they seem to do, in laws, explanation, and prediction? 2) Many physicists use the notion of typicality instead of the one of probability when discussing statistical mechanics. What is the connection between the two notions? 3) How can one extend Boltzmann’s analysis to the quantum domain, where some theories are indeterministic? 4) Boltzmann’s explanation fundamentally involves cosmology: for the explanation to go through the Big Bang needs to have had extremely low entropy. Does the fact that the Big Bang was a low entropy state imply that it was, in some sense, “highly improbable” and requires an explanation? 5) What exactly is the connection between statistical and classical mechanics? Is the one of theory reduction or there is no such thing? 6) Statistical mechanics has two main formulation: one due to Botzmann and the other due to Gibbs. What is the connection between the two formulations

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem.