Anselm's argument for the existence of God in Proslogion Chap.II starts from the contention that `lq when a Fool hears `something-than-which-nothing-greater-can-be-thought', he understands what he hears, and what he understands is in his mind. This is a special feature of the Pros.II argument which distinguishes the argument from other ontological arguments set up by, for example, Descartes and Leibniz. This is also the context which makes semantics necessary for evaluation of the argument. It is quite natural to ask `lq What (...) is understood by the Fool, and what is in his mind? It is essential for a proper consideration of the argument to identify the object which is understood by the Fool, and so, is in his mind. A semantics gives answers to the questions of `lq What the Fool understands? and `lq What is in the Fool's mind? If we choose a semantics as a meta-theory to interpret the Pros.II argument, it makes an effective guide to identify the object. It is a necessary condition for a proper evaluation of the Pros.II argument to fix our universe of discourse, especially since, in the argument, we are involved in such talk about existing objects as Anselm's contention that `when a Fool hears `something-than-which-nothing-greater-can-be-thought', he understands what he hears, and what he understands is in his mind. The ontology to which a semantic theory commits us will be accepted as our scope of objects when we introduce our semantic theory to interpret the Pros.II argument, and this ontological boundary constrains us to identify the object in a certain way. Consistent application of an ontology, most of all, is needed for the evaluation of the logical validity of an argument. If we take Frege's three-level semantics, we are ontologically committed to intensional entities, like meaning, as well as extensional entities. Sluga contends that Frege's anti-psychologism for meanings should not be interpreted as vindicating reification of intensional entities in relation to Frege's contextualism, that Frege's anti-psychologism with his contextualism is nothing but a linguistic version of Kantian philosophy for the transcendental unity of a judgement. There is, however, another possible interpretation of Frege's contextualism. According to Dummett, the significance of Frege's contextualism must be understood as a way of explanation for a word's having meaning. If Dummett's view is cogent, we could say that Frege's contextualism does not prevent our interpreting his semantics as being committed to intensional entities. We need not worry that Frege's over all semantics, especially with his contextualism, would internally deny the ontological interpretation of his theory. We see Anselm's argument for the existence of God in Pros.II is an invalid argument if we introduce Frege's three-level semantics, i.e. if we acknowledge meanings of words as entities in our universe of discourse. We can also employ extensional semantics for the interpretation of the Pros.II argument. According to extensionalists, like Quine and Kripke, we need not assume intensional entities, like meaning, to be part of our ontological domain. They argue that we can employ our language well enough without assuming intensional entities. If we choose extensional semantics as a meta-theory to interpret the Pros.II argument, it commits us only to extensional entities as objects in the Universe of our interpretation. In Sections 1.4 and 1.5, I show that extensional semantics makes the Pros.II argument a valid argument for the existence of God. `lq Necessary existence is the central concept of Anselm's argument for the existence of God in Proslogion Chap.III. It has been said that, even if the argument is formally valid, it cannot stand as a valid argument for the existence of God, since `lq necessary existence is an absurd concept like `lq round square. And further that even if there is a meaningful combination of concepts for `lq necessary existence, it cannot quality as a subject of an a priori argument. As objections to the interpretations which make the Pros.III argument valid, it has been argued that even if there is a concept of `lq necessary existence which is meaningful and there is another concept of `lq necessary existence which is suitable as a subject of an a priori argument, there is no concept of `lq necessary existence which is meaningful and at the same time suitable as a subject of an a priori argument. In Chap.2 and Chap.3, I try to show that there can be concepts of `lq necessary existence which are proof against these objections. Anselm's arguments for the existence of God in Proslogian Chap.II and Chap.III are logically valid arguments on some logical principles. Some fideists, K. Barth, for example, argue that Anselm's arguments for the existence of God in Proslogion are not proofs for the existence of God even if they are logically valid arguments. I raise the question how this attitude could be possible, in Chap.4 and Chap.5. Barth's fideistic interpretation of Anselm's Proslogion arguments does not find any flaw in the validity of the arguments, and it accepts the meaningfulness and truth of the premises even to the fool in Proslogion. If this is the case, i.e. if Barth's interpretation accepts the validity of the arguments and the truth of the premises, I raise the question, how can the arguments not be interpreted as proofs for the existence of God? How is it possible that the function of the arguments is not that of proving the existence of God? According to Wittgensteinian fideism, premises in the arguments should not be intelligible to those who do not believe in God's existence already, and so the real function of the arguments is the elucidation, the understanding of believer's belief, rather than proving articles of belief to unbelievers. Barth's fideistic interpretation of the arguments, however, fully recognizes the meaningfulness and truth of the premises in the arguments as well as the validity of the arguments. I argue that there could be a justification for the Barthian fideism. As Malcolm notices, there are still atheists who understand Anselm's arguments as valid, but the only possibility for the people who recognize the validity of Anselm's arguments still to remain atheists has been thought to be to challenge the truth of premises employed in the arguments. Now, of the atheistic possibility, we can change the direction of our attention, that is, to the question about the function of a logically valid argument itself. What has not been thought of in relation to Anselm's arguments is the significance of logical truth or the logical validity of an argument. We have not asked such questions as `lq What does a logical truth say? and `lq What does a logically valid argument guarantee with true premises? Let us assume that even the premises are accepted by atheists. Do they all convert to theism? If that were so, the disagreement between atheist and believer over the ontological arguments should turn only on the truth of premises. If that is not so, there is some point in raising this other question. If there are people who, recognizing the premises and validity of an argument, are still reluctant to accept the conclusion, we have reason to question the function of a valid argument. I argue that there is a way of being consistently reasonable while accepting the premises and the validity of the ontological arguments and yet remaining an atheist or an agnostic. (shrink)

In ‘Reichenbach's cubical universe and the problem of the external world’, Elliott Sober attempts a refutation of solipsism à la Reichenbach. I here contrast Sober's line of argument with observati...

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...) spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

On a pragmatist view of quantum theory, a quantum state has the role of advising physically situated agents rather than representing the condition of physical systems. The advice concerns the cognitive significance of a magnitude claim S: σ has, locating the value of magnitude Q on system σ in set Δ of real numbers. The quantum state offers advice both on the content of a magnitude claim S and on its credibility, provided it has enough content. The advice is authoritative—anyone (...) who both accepts quantum theory and agrees on the correct quantum state is bound to heed it. On this view, the content of a magnitude claim is a function of its place in a web of material inferences connecting it to other claims, and hence to perception and action. A quantum state offers advice on the content of a magnitude claim by controlling its place in this inferential web. It thereby adds a contextual element to the content even of claims about the properties of familiar objects like gross experimental apparatus and the moon. But by modeling the behavior of quantum states, quantum theory itself reassures us that only for claims about currently unfamiliar objects does the consequent modification of content amount to anything. (shrink)

Contemporary arguments for scientific realism are typically based on some form of inference to the best explanation. Sometimes such arguments concern the methods of science: given the success of scientific methodology, realism offers the best explanation of this success. Sometimes such arguments concern the content of scientific theories: given observed regularities in nature, explanations must be given of those regularities; the best such explanations will be realist. One forceful explanationist argument about the content of science can be based on Hans (...) Reichenbach’s Principle of the Common Cause. Roughly, CC says that whenever an enduring correlation between two events is observed, there must be some preceding event which is the common cause of the two, and is the explanation for the correlation. Rigid adherence to this demand for a common cause, however, supposedly goes beyond the instrumentalist explanatory resources available to the antirealist, and hence CC is taken to be a sufficient condition for realism. Further, one might claim that any argument that realism has greater explanatory power than antirealism depends either explicitly or implicitly on CC, and hence CC is also a necessary condition for realism. (shrink)

Can the axioms of probability theory and the classical patterns of statistical inference ever be falsified by observation? Various possible answers to this question are examined in a set theoretical context and in relation to the findings of microphysics.

I argue that, in at least one important sense, the hypothesis that you are a brain in a vat provides better explanations than the explanations provided by standard ways of interpreting our best scientific theories. This puts pressure on anyone who—like me!—wishes to resist taking this radical hypothesis seriously when doing science and scientifically-informed metaphysics. Insofar as our resistance is justified, it can’t be justified simply by claiming that the brain in a vast hypothesis is explanatorily impoverished.

Translated here into Polish is Tim Maudlin’s “Distilling Metaphysics from Quantum Physics,” which is a chapter of The Oxford Handbook of Metaphysics. The author discusses six important metaphysical issues on which quantum physics sheds new light. He shows how differently each of the three main intepretations of quantum theory (von Neumann’s and GRW collapse theory, Bohm’s hidden variable theory, and Everett’s many-worlds theory) views each of them. The issues discussed are determinism, determinateness, the role of the observer, uncertainty and complementarity, (...) quantum logic, and entanglement and non-locality. (shrink)

The common practice of advancing arguments based on current physics in support of metaphysical conclusions has been criticized on the grounds that current physics may well be wrong. A further criticism is leveled here: current physics itself depends on metaphysical assumptions, so arguing from current physics is in fact arguing from yet more metaphysics. It is shown that the metaphysical assumptions underlying current physics are often deeply embedded in the formalism in which theories are presented, and hence impossible to dismiss (...) as mere motivational or interpretative speculation. It is then shown that such assumptions, when made explicit, can wreck havoc on otherwise-sensible philosophical arguments. It is argued in conclusion that this situation is both unlikely to be reparable just by being more careful, and unlikely to go away as further, presumably more subtle physical theories are developed. (shrink)

Quantum mechanics is usually presented as a challenge to scientific realism, but I will argue that the details of quantum mechanics actually support realism. I will first present some basic quantum mechanical concepts and results, including the Einstein-Podolsky-Rosen (EPR) experiment and Bell's theorem, and do it in a way that everyone can understand. I will then use the physics to inform the philosophy, showing that quantum mechanics provides evidence to support epistemological realism.

I argue that sunyata, or something like it, manifested itself in early Western thought. While Plato and Aristotle resisted emptiness or nothingness, they nevertheless felt themselves obliged to venture close to its edge in order to ground their explanations of changing reality to unchanging principles. These principles embody much of the indeterminancy long associated with the Mahayana understanding of sunyata. Although their function was to enable lasting explanations of reality by putting change out of play, they themselves shade off toward (...) a featureless being evocative of non-being. Moving along a somewhat different track, Greek atomists embraced emptiness so as to permit self-existent, fully self-contained atoms to move about. In their system, non-being, a foundational principle of reality, paradoxically coexists with being. Interestingly, modern science has undone the self-containment of atoms—emptied them of properties once thought to be innate—and thereby removed yet another Western safeguard against change. It seems that change cannot be put out of play, though it does slope off toward sunyata-like emptiness. (shrink)

The measurement problem in quantum mechanics is presented in a completely non-technical way by means of the results of some very simple experiments. These experimental results themselves, rather than the formalism of quantum theory, are shown to be extremely hard to incorporate in a sensible state-space picture of the world. A novel twist is then added which makes the problem even harder than it appears to be in other presentations of the measurement problem.

Crystallography has proven a rich source of ideas over several centuries. Among the many ways of looking at space groups, N. David Mermin has pioneered the Fourier-space approach. Recently, we have supplemented this approach with methods borrowed from algebraic topology. We now show what topology, which studies global properties of manifolds, has to do with crystallography. No mathematics is assumed beyond what the typical physics or crystallography student will have seen of group theory; in particular, the reader need not have (...) any prior exposure to topology or to cohomology of groups. (shrink)

The paper introduces mathematical encoding for subjective experience and meaning in natural cognition. The code is based on a quantum-theoretic qubit structure supplementing classical bit with circular dimension, functioning as a process-causal template for representation of contexts relative to the basis decision. The qubit state space is demarcated in categories of emotional experience of animals and humans. Features of the resulting spherical map align with major theoreties in cognitive and emotion science, modeling of natural language, and semiotics, suggesting several generalizations (...) and improvements. The developed model bridges psychological, quantum-theoretic, and semiotic perspectives, allowing for an integrative account of subjectivity, agency, and meaning in living Nature.Graphical abstract. (shrink)

The paper argues for realism in quantum mechanics. Specifically, the formalism of quantum mechanics should be understood as giving a complete description of quantum situations. When it is understood in this way, traditional primary properties of matter can be seen as similar to traditional secondary properties, though at a different level.

Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.

The demand for 'criteria of correctness' to identify recurring particulars in Wittgenstein's private language argument favors an idealist interpretation of quantum phenomena.The indeterminacy principle in quantum physics and the logic of the private language argument share a common concern with the limitations by which microphysical or sensation particulars can be reidentified. Wittgenstein's criteria for reidentifying particular recurrent private sensations are so general as to apply with equal force to quantum particulars, and to support the idealist thesis that quantum phenomena are (...) themselves essentially mental or dependent on mental occurrences. (shrink)

We give a conceptually simple proof of nonlocality using only the perfect correlations between results of measurements on distant systems discussed by Einstein, Podolsky and Rosen—correlations that EPR thought proved the incompleteness of quantum mechanics. Our argument relies on an extension of EPR by Schrödinger. We also briefly discuss nonlocality and “hidden variables” within Bohmian mechanics.

(1994). Bearers of properties in the quantum mechanical description of nature. International Studies in the Philosophy of Science: Vol. 8, No. 3, pp. 179-194.

Mackenzie, this journal, this issue, convincingly shows that in certain dialogue games (commitment games) there are procedural restrictions similar to those that I impose on rationality idealizations. But, whereas my rationality analysis is set in the context of belief games, commitment games do not postulate beliefs. Is this significant? I suggest that mackenzie thinks that it is. There follow discussions of Psychologism and Behaviourism.

Skyrms's formulation of the argument against stochastic hidden variables in quantum mechanics using conditionals with chance consequences suffers from an ambiguity in its "conservation" assumption. The strong version, which Skyrms needs, packs in a "no-rapport" assumption in addition to the weaker statement of the "experimental facts." On the positive side, I argue that Skyrms's proof has two unnoted virtues (not shared by previous proofs): (1) it shows that certain difficulties that arise for deterministic hidden variable theories that exploit a nonclassical (...) probability theory extend to the stochastic case; (2) the use of counterfactual conditionals relates the Bell puzzle to Dummett's (1976) discussion of realism in quantum mechanics. (shrink)

The strength and defects of wave mechanics as a theory of chemistry are critically examined. Without the secondary assumption of wave–particle duality, the seminal equation describes matter waves and leaves the concept of point particles undefined. To bring the formalism into line with the theory of special relativity, it is shown to require reformulation in hypercomplex algebra that imparts a new meaning to electron spin as a holistic spinor, eliminating serious current misconceptions in the process. Reformulation in the curved space–time (...) of general relativity requires the recognition of nonlinear effects that invalidate the practice of linear combination of atomic orbitals, ubiquitous in quantum chemistry, and redefines the electron as a nondispersive wave packet, or soliton. (shrink)