Classicalmereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classicalmereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. We examine the relations between the main definitions of fusion and correct some (...) technical errors in prominent discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classicalmereology, using three different notions of fusion. We also clarify the connection between classicalmereology and complete Boolean algebra by giving two "neutral" axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of "strong complement" that helps explicate the connections between the theories. (shrink)
Abstract Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language Hm is maximally acceptable for nominalistic mereology. In an extension Hgem of Hm, a modal analog for the classical systems of Leonard and Goodman (J Symb Log 5:45–55, 1940) and Lesniewski (1916) is introduced and shown to be complete with respect to 0- deleted Boolean algebras. (...) We characterize the formulas of first-order logic invariant for Hgem-bisimulations. (shrink)
Do mereological fusions have their parts necessarily? None of the axioms of non-modal formulations of classicalmereology appear to speak directly to this question. And yet a great many philosophers who take the part-whole relation to be governed by classicalmereology seem to assume that they do. In addition to this, many philosophers who make allowance for the part-whole relation to obtain merely contingently between a part and a mereological fusion tend to depart from non-modal formulations (...) of classicalmereology at least when it comes to the axiom of Unique Fusion, which states that no two different mereological fusions ever fuse exactly the same objects. This is no coincidence. There are reasons of principle why one’s adherence to classicalmereology should exert some pull towards the view that mereological fusions have their parts necessarily. There is, however, no direct route from the combination of classicalmereology and propositional modal logic to the hypothesis that the part-whole relation obtains necessarily between a part and a mereological fusion. In order to bridge between a modal formulation of classicalmereology and the hypothesis that fusions have their parts necessarily, one needs to strengthen the axiom of Unrestricted Fusion in a way that is agreeable to many philosophers on both sides of the debate. (shrink)
Classicalmereology (CM) is usually taken to be formulated in a tenseless language, and is therefore associated with a four-dimensionalist metaphysics. This paper presents three ways one might integrate the core idea of flat plenitude, i.e., that every suitable condition or property has exactly one mereological fusion, with a tensed logical setting. All require a revised notion of mereological fusion. The candidates differ over how they conceive parthood to interact with existence in time, which connects to the distinction (...) between endurance and perdurance. Similar issues arise for the integration of mereology with modality, and much of our discussion applies to this project as well. (shrink)
This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are (...) compared to classicalmereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)
This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean (and Gentzenian) rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination (...) of mereology with class theory. The Division Thesis plays a crucial role in Lewis’s informal argument for his Second Thesis in his book Parts of Classes. In order to present Lewis’s argument in rigorous detail, an elegant new principle is offered for the theory that combines class theory and mereology. The new principle is called the Canonical Decomposition Thesis. It secures Lewis’s Division Thesis on the strong construal required in order for his argument to go through. The exercise illustrates how careful one has to be when setting up the details of an adequate foundational theory of parts and classes. The main aim behind this investigation is to determine whether an anti-realist, inferentialist theorist of meaning has the resources to exhibit Lewis’s argument for his Second Thesis—which is central to his marriage of class theory with mereology—as a purely conceptual one. The formal analysis shows that Lewis’s argument, despite its striking appearance to the contrary, can be given in the constructive, relevant logic IR. This is the logic that the author has argued, elsewhere, to be the correct logic from an anti-realist point of view. The anti-realist is therefore in a position to regard Lewis’s argument as purely conceptual. (shrink)
I examine the link between extensionality principles of classicalmereology and the anti-symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti-symmetry. I examine the notions of proper parthood, weak supplementation and non-well-foundedness. By rejecting anti-symmetry, the anti-extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non-extensional mereology in which anti-symmetry fails. If the notion of 'mereological equivalence' is made explicit, this non-anti-symmetric mereology recaptures (...) all of the structure of classicalmereology. (shrink)
Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper (...) has done (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classicalmereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”. (shrink)
Given Quine's views on philosophical methodology, he should not have taken the axioms of classicalmereology to be "self-evident", or "analytic"; but rather, he should have set out to justify them by what might be broadly called an "inference to the best explanation". He does very little to this end. In particular, he does little to examine alternative theories, to see if there might be anything they could explain better than classicalmereology can. I argue that (...) there is something important that needs to be explained, namely, the way that properties "travel around in clusters" (eg. we often know that "when and where there is something with such-and-such property, there is also something with so-and-so other property", and so on). I argue that these clusterings of properties can be given various subtle (broadly "commonsense") explanations using a version of mereology that denies the classical axiom of "extensionality" (that is, denying that two distinct things must have distinct parts). I offer a challenge to the Quinean metaphysics: to show that these "non-extensional" explanations can be replaced by better explanations that use only classical, extensional mereology and set theory. (shrink)
David Lewis insists that restrictivist composition must be motivated by and occur due to some intuitive desiderata for a relation R among parts that compose wholes, and insists that a restrictivist’s relation R must be vague. Peter van Inwagen agrees. In this paper, I argue that restrictivists need not use such examples of relation R as a criterion for composition, and any restrictivist should reject a number of related mereological theses. This paper critiques Lewis and van Inwagen (and others) on (...) their respective mereological metaphysics, and offers a Golden Mean between their two opposite extremes. I argue for a novel account of mereology I call Modal Mereology that is an alternative to ClassicalMereology. A modal mereologist can be a universalist about the possible composition of wholes from parts and a restrictivist about the actual composition of wholes from parts. I argue that puzzles facing Modal Mereology (e.g., puzzles concerning Cambridge changes and the Problem of the Many, and how to demarcate the actual from the possible) are also faced in similar forms by classical universalists. On my account, restricted composition is rather motivated by and occurs due to a possible whole’s instantiating an actual type. Universalists commonly believe in such types and defend their existence from objections and puzzles. The Modal Mereological restrictivist can similarly defend the existence of such types (adding that such types are the only wholes) from similar objections and puzzles. (shrink)
We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, (...) thereby demonstrating the independence of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)
When do several objects compose a further object? The last twenty years have seen a great deal of discussion of this question. According to the most popular view on the market, there is a physical object composed of your brain and Jeremy Bentham’s body. According to the second-most popular view on the market, there are no such objects as human brains or human bodies, and there are also no atoms, rocks, tables, or stars. And according to the third-ranked view, there (...) are human bodies, but still no brains, atoms, rocks, tables, or stars. Although it’s pleasant to have so many crazy-sounding views around, I think it would also be nice to have a commonsense option available. The aim of this paper is to offer such an option. The approach I offer begins by considering a mereological question other than the standard one that has been the focus of most discussions in the literature. I try to show that the road to mereological sanity begins with giving the most straightforward and commonsensical answer to this other question, and then extending that answer to further questions about the mereology of physical objects. On the approach I am recommending, it turns out that all of the mereological properties and relations of physical objects are determined by their spatial properties and relations. (shrink)
In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of (...) a problem first noted by Gideon Rosen and requires an additional assumption about the mereological structure of certain beliefs. That assumption is that an omniscient being’s beliefs are mereological simples. However, this assumption is dropped when I present my second argument. Thus, I hope to show that if Classical Extensional Mereology is true of the part-whole relation, there cannot be an omniscient being. (shrink)
In “Compassionate Phenomenal Conservatism” (2007), “Phenomenal Conservatism and the Internalist Intuition” (2006), and Skepticism and the Veil of Perception (2001), Michael Huemer endorses the principle of phenomenal conservatism, according to which appearances or seemings constitute a fundamental source of (defeasible) justification for belief. He claims that those who deny phenomenal conservatism, including classical foundationalists, are in a self-defeating position, for their views cannot be both true and justified; that classical foundationalists have difficulty accommodating false introspective beliefs; and that (...) phenomenal conservatism is most faithful to the central internalist intuition. I argue that Huemer’s self-defeat argument fails, that classical foundationalism is able to accommodate fallible introspective beliefs, and that classical foundationalism captures a relatively clear internalist intuition. I also show that the motivation for phenomenal conservatism is less than clear. (shrink)
A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of (...) this paper is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)
In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept (...) of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator. (shrink)
In Justification without Awareness (2006), Michael Bergmann presents a dilemma for internalism from which he claims there is “no escape”: The awareness allegedly required for justification is either strong awareness, which involves conceiving of some justification-contributor as relevant to the truth of a belief, or weak awareness, which does not. Bergmann argues that the former leads to an infinite regress of justifiers, while the latter conflicts with the “clearest and most compelling” motivation for endorsing internalism, namely, that for a belief (...) to be justified its truth must not be an accident from the subject’s perspective. Bergmann’s dilemma might initially seem to have the force of a knock-down argument against the classical foundationalist accounts he considers, if not against all forms of internalism. I argue, however, that the weak-awareness horn of Bergmann’s dilemma is unsuccessful. Classical foundationalists can hold on to the main motivation for internalism and avoid a vicious regress of justifiers. (shrink)
Mereology is the logic of part—whole concepts as they are used in many different contexts. The old chemical metaphysics of atoms and molecules seems to fit classicalmereology very well. However, when functional attributes are added to part specifications and quantum mechanical considerations are also added, the rules of classicalmereology are breached in chemical discourses. A set theoretical alternative mereology is also found wanting. Molecular orbital theory requires a metaphysics of affordances that also (...) stands outside classicalmereology. (shrink)
Multilocation and Minimal Mereology do not mix well. It has been pointed out that Three-Dimensionalism, which can be construed as multilocation-friendly, runs into trouble with Weak Supplementation. But in fact, regardless of one’s theory of persistence, if someone posits the possibility of any one of several kinds of multilocation, he or she will not be able to maintain the necessity of any of the three axioms of Minimal Mereology: the Transitivity of Proper Parthood, the Asymmetry of Proper Parthood, (...) and Weak Supplementation. In fact, positing even the mere conceivability of cases involving multilocation will require the denial of the analyticity of Minimal Mereology. In response to this, some have claimed that we ought to relativise parthood, either to one region or to two. Unfortunately, if we replace the axioms of Minimal Mereology with region-relativised counterparts, we will not be able to capture the intuitions that supported the original axioms. The only adequate solution, I maintain, is to restrict multilocation to a domain outside the scope of the rules we intuitively take to govern the parthood relation. For those who take Minimal Mereology to be necessary and universal, that will mean relinquishing the possibility of multilocation. (shrink)
This paper provides a brief overview of the relationship between libertarian political theory and the Universal Basic Income (UBI). It distinguishes between different forms of libertarianism and argues that a one form, classical liberalism, is compatible with and provides some grounds of support for UBI. A classical liberal UBI, however, is likely to be much smaller than the sort of UBI defended by those on the political left. And there are both contingent empirical reasons and principled moral reasons (...) for doubting that the classical liberal case for UBI will be ultimately successful at all. (shrink)
Could we plausibly believe in the fundamental tenets of classical liberalism and, at the same time, support the state’s raising of immigration barriers? The thesis of this paper is that if we accept the main tenets of classical liberalism as essentially correct, we should regard immigration barriers as essentially illegitimate. Considered under ideal conditions, immigration barriers constitute an unjustified infringement on individuals’ ownership rights, since it is difficult to identify a purpose that such an infringement could have that (...) would outweigh the disadvantages created by eliminating important competitive pressures on governments. Considered under nonideal conditions, the problem is, roughly, that immigration barriers cannot be seen as the choice of a lesser evil in the face of either an expected extension of the redistributive state or an expected threat on liberal institutions. On the contrary, since they relax the constraints faced by governments, immigration barriers should be seen as a major contributor in creating the conditions for the perpetuation of the sort of political arrangements that classical liberals resist. If individual sovereignty is to be protected, the sovereignty of the state over a particular territory should not include a prerogative to determine who is to inhabit it. (shrink)
Contrary to Bell’s theorem it is demonstrated that with the use of classical probability theory the quantum correlation can be approximated. Hence, one may not conclude from experiment that all local hidden variable theories are ruled out by a violation of inequality result.
How do we figure out the fundamental nature of the world from a mathematically formulated physical theory? To figure out the nature of a world’s spacetime, we follow this rule: posit the least spacetime structure to the world that’s required by the fundamental dynamical laws. Applied to special relativity, for example, this rule tells us to not posit an absolute simultaneity structure. I suggest that we use this rule for more than just spacetime structure. We should also posit the least (...) statespace structure required by the fundamental dynamical laws. This rule yields surprising conclusions. Applied to classical mechanics, it suggests that a world governed by the theory has less fundamental structure than we ordinarily think. For the theory’s statespace imparts less structure to a world’s physical space than we ordinarily think. (shrink)
In “Mathematics is megethology,” Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate (...) that mereology and plural quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, if—as Lewis maintains—MPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)
Panentheism seems to be an attractive alternative to classical theism. It is not clear, though, what exactly panentheism asserts and how it relates to classical theism. By way of clarifying the thesis of panentheism, I argue that panentheism and classical theism differ only as regards the modal status of the world. According to panentheism, the world is an intrinsic property of God – necessarily there is a world – and according to classical theism the world is (...) an extrinsic property of God – it is only contingently true that there is a world. Therefore, as long as we do not have an argument showing that necessarily there is a world, panentheism is not an attractive alternative to classical theism. (shrink)
This article focuses on the following three novel and original philosophical approaches to classical liberalism: Den Uyl and Rasmussen’s perfectionist argument from meta-norms, Gaus’s justificatory model, and Kukathas’s conscience-based theory of authority. None of these three approaches are utilitarian or consequentialist in character. Neither do they appeal to the notion of a rational bargain as it is typical within contractarianism. Furthermore, each of these theory rejects the idea that classical liberalism should be grounded on considerations of interpersonal justice (...) such as those that are central to the Lockean tradition. It is argued that these three theories, despite their many attractive features, fail to articulate in a convincing manner some central classical liberal concerns. (shrink)
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the (...) possibility of describing real objects in an observer-independent way. (shrink)
Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several (...) hypotheses: the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity. (shrink)
Mereology is the logic of partâ€”whole concepts as they are used in many different contexts. The old chemical metaphysics of atoms and molecules seems to fit classicalmereology very well. However, when functional attributes are added to part specifications and quantum mechanical considerations are also added, the rules of classicalmereology are breached in chemical discourses. A set theoretical alternative mereology is also found wanting. Molecular orbital theory requires a metaphysics of affordances that also (...) stands outside classicalmereology. (shrink)
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem (...) of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian? (shrink)
We show that a standard axiomatization of mereology is equivalent to the condition that a topological space is discrete, and consequently, any model of general extensional mereology is indistinguishable from a model of set theory. We generalize these results to the Cartesian closed category of convergence spaces.
Quantum logic is only applicable to microscopic phenomena while classical logic is exclusively used for everyday reasoning, including mathematics. It is shown that both logics are unified in the framework of modal interpretation. This proposed method deals with classical propositions as latently modalized propositions in the sense that they exhibit manifest modalities to form quantum logic only when interacting with other classical subsystems.
The question as to whether the Vedas have an author is the topic of vivid polemics in Indian philosophy. The aim of this paper is to reconstruct the classical Sāṁkhya view on the authorship of the Vedas. The research is based chiefly on the commentaries to the Sāṁkhyakārikā definition of authoritative verbal testimony given by the classical Sāṁkhya writers, for these fragments provide the main evidence (both direct and indirect) for the reconstruction of this view. The textual analysis (...) presented in this paper leads to the following conclusion. According to most classical Sāṁkhya commentaries, the Vedas have no author. Two commentators state directly that the Vedas have no author, and four commentators allude to the authorlessness of the Vedas. Only one commentator seems to hold the opposite view, stating that all the authoritative utterances are based on perception or inference of imperceptible objects by authoritative persons, from which it follows that the Vedas too have an author or authors. (shrink)
We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
This paper develops co-ordinated multiple-domain supervenience relations to model determination and dependence relations between complex entities and their constituents by appealing to R-related pairs and by making use of associated isomorphisms. Supervenience relations are devised for order-sensitive and repetition-sensitive mereologies, for mereological systems that make room for many-many composition relations, as well as for hierarchical mereologies that incorporate compositional and hylomorphic structure. Finally, mappings are provided for theories that consider wholes to be prior to their parts.
I analyze the relations of constituency or ``being in'' that connect different ontological items in the Tractatus logico-philosophicus by Wittgenstein. A state of affairs is constituted by atoms, atoms are in a state of affairs. Atoms are also in an atomic fact. Moreover, the world is the totality of facts, thus it is in some sense made of facts. Many other kinds of Tractarian notions -- such as molecular facts, logical space, reality -- seem to be involved in constituency relations. (...) How should these relations be conceived? And how is it possible to formalize them in a convincing way? I draw a comparison between two ways of conceiving and formalizing these relations: through sets and through mereological sums. The comparison shows that the conceptual machinery of set theory is apter to conceive and formalize Tractarian constituency notions than the mereological one. (shrink)
In his _Treatise on the Golden Lion_, Fazang says that wholes are _in_ each of their parts and that each part of a whole _is_ every other part of the whole. In this paper, I offer an interpretation of these remarks according to which they are not obviously false, and I use this interpretation in order to rigorously reconstruct Fazang's arguments for his claims. On the interpretation I favor, Fazang means that the presence of a whole's part suffices for the (...) presence of the whole and that the presence of any such part is both necessary and sufficient for the presence of any other part. I also argue that this interpretation is more plausible than its extant competitors. (shrink)
A simple method is provided for translating proofs in Grentzen's LK into proofs in Gentzen's LJ with the Peirce rule adjoined. A consequence is a simpler cut elimination operator for LJ + Peirce that is primitive recursive.
That parthood is a transitive relation is among the most basic principles of classicalmereology. Alas, it is also very controversial. In a recent paper, Ingvar Johansson has put forward a novel diagnosis of the problem, along with a corresponding solution. The diagnosis is on the right track, I argue, but the solution is misleading. And once the pieces are properly put together, we end up with a reinforcement of the standard defense of transitivity on behalf of (...) class='Hi'>classicalmereology. (shrink)
In this work I first develop, motivate, and defend the view that mereological composition, the relation between an object and all its parts collectively, is a relation of identity. I argue that this view implies and hence can explain the logical necessity of classicalmereology, the formal study of the part-whole relation. I then critically discuss four contemporary views of the same kind. Finally, I employ my thesis in a recent discussion of whether the world is fundamentally one (...) in number. (shrink)
underpinning of the cognitive sciences. I argue, however, that it often fails to provide adequate explanations, in particular in conjunction with competence theories. This failure originates in the idealizations in competence descriptions, which either ?block? the cascade, or produce a successful cascade which fails to explain cognition.
This study explains how the myths of Greece and Rome were transmitted from antiquity to the Renaissance. Luc Brisson argues that philosophy was ironically responsible for saving myth from historical annihilation. Although philosophy was initially critical of myth because it could not be declared true or false and because it was inferior to argumentation, mythology was progressively reincorporated into philosophy through allegorical exegesis. Brisson shows to what degree allegory was employed among philosophers and how it enabled myth to take on (...) a number of different interpretive systems throughout the centuries: moral, physical, psychological, political, and even metaphysical. How Philosophers Saved Myths also describes how, during the first years of the modern era, allegory followed a more religious path, which was to assume a larger role in Neoplatonism. Ultimately, Brisson explains how this embrace of myth was carried forward by Byzantine thinkers and artists throughout the Middle Ages and Renaissance after the triumph of Chistianity, Brisson argues, myths no longer had to agree with just history and philosophy but the dogmas of the Church as well. (shrink)
We revisit quantum measurement when the apparatus is initially in a mixed state. We find that, in a particular restriction setup, the amount of entanglement between the system and the apparatus is given by the entropy increasing of the system under the measurement transformation. We show that the information gained is equal to the amount of entanglement under performing perfect measurement. Based on the perfect measurement, we give an upper bound of quantum discord.
There are many forms of utilitarianism, and the development of the theory has continued in recent years. I shall not survey these forms here, nor take account of the numerous refinements found in contemporary discussions. My aim is to work out a theory of justice that represents an alternative to utilitarian thought generally and so to all of these different versions of it. I believe that the contrast between the contract view and utilitarianism remains essentially the same in all these (...) cases. Therefore I shall compare justice as fairness with familiar variants of intuitionism, perfectionism, and utilitarianism in order to bring out the underlying differences in the simplest way. With this end in mind, the kind of utilitarianism I shall describe here is the strict classical doctrine which receives perhaps its clearest and most accessible formulation in Sidgwick. The main idea is that society is rightly ordered, and therefore just, when its major institutions are arranged so as to achieve the greatest net balance of satisfaction summed over all the individuals belonging to it.9.. (shrink)
Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum field theory textbooks this is not so: time reversal does not turn particles into anti-particles. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, in the context (...) of the recent debate between David Albert and David Malament over time reversal in classical electromagnetism. (shrink)
This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)
Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences (...) for our understanding of a host of classical philosophical concepts. (shrink)
In the first part, the paper describes in detail the classical conception of intentionality which was expounded in its most sophisticated form by Edmund Husserl. This conception is today largely eclipsed in the philosophy of mind by the functionalist and by the representationalist account of intentionality, the former adopted by Daniel Dennett and David Chalmers, the latter by John Searle and Fred Dretske. The very considerable differences between the classical and the modern conceptions are pointed out, and it (...) is argued that the classical conception is more satisfactory than the two modern ones, not only regarding phenomenal adequacy, but also on the grounds of epistemological considerations. In the second part, the paper argues that classical intentionality is not naturalizable, that is, physicalizable. Since classical intentionality exists (in the experiences that display it), the non-naturalizability of classical intentionality implies psychophysical dualism. (shrink)
Various fault modes of determinism in classical physics are outlined. It is shown how quantum mechanics can cure some forms of classical indeterminism. †To contact the author, please write to: Department of HPS, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: firstname.lastname@example.org.
Substantivalists claim that spacetime enjoys an existence analogous to that of material bodies, while relationalists seek to reduce spacetime to sets of possible spatiotemporal relations. The resulting debate has been central to the philosophy of space and time since the Scientific Revolution. Recently, many philosophers of physics have turned away from the debate, claiming that it is no longer of any relevance to physics. At the same time, there has been renewed interest in the debate among physicists working on quantum (...) gravity, who claim that the conceptual problems which they face are intimately related to interpretative questions concerning general relativity (GR). My goal is to show that the physicists are correct—there is a close relationship between the interpretative issues of classical and quantum gravity. (shrink)
The central question animating liberal thought is: How can people live together as free and equal? This question is being reinvigorated by the emergence of what we will call neoclassical liberalism. Neoclassical liberals, such as David Schmidtz, Gerald Gaus, Charles Griswold, Jacob Levy, Matt Zwolinski, Will Wilkinson, and we, the authors, share classical liberalism’s commitment to robust economic liberties and property rights as well as modern or “high” liberalism’s commitment to social justice. On the neoclassical liberal view, part of (...) the justification for a society’s basic structure is that it produces conditions where citizens have substantive liberty, and can thus confront each other as free and equal. The basic structure of society is evaluable on the kinds of outcomes produced for citizens. Neoclassical liberals combine a robust commitment to social justice—a commitment as robust as that of high liberals—with a commitment to more extensive set of basic liberties than that advocated by high liberals. Neoclassical liberalism thus stakes out a claim to be the morally ambitious form of liberalism. (shrink)
One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is (...) yes: I state and prove two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument not only clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems. It also provides a decisive counter-example to the semantical view of physical theories, and one, moreover, that shows its crucial deficiency: a theory must be, or at least be founded on, more than its collection of models (in the sense of Tarski), for a complete semantics requires that one take account of global structures defined by relations among the individual models. The example also shows why naively structural accounts of theory cannot work: simple isomorphism of theoretical and empirical structures is not rich enough a relation to ground a semantics. (shrink)
The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be (...) justified from this proof-theoretic perspective. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the standard logical constants cannot all be given by their introduction and/or elimination rules; negation, in particular, comes under close scrutiny. (shrink)
Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), (...) and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic. (shrink)
This paper provides a detailed examination of Kit Fine’s sizeable contribution to the development of a neo-Aristotelian alternative to standard mereology; I focus especially on the theory of ‘rigid’ and ‘variable embodiments’, as defended in Fine 1999. Section 2 briefly describes the system I call ‘standard mereology’. Section 3 lays out some of the main principles and consequences of Aristotle’s own mereology, in order to be able to compare Fine’s system with its historical precursor. Section 4 gives (...) an exposition of Fine’s theory of embodiments and goes on to isolate a number of potential concerns to which this account gives rise. In particular, I argue that (i) Fine’s theory threatens to proliferate primitive sui generis relations of parthood and composition, whose characteristics must be stipulatively imposed on them, relative to particular domains; (ii) given its ‘superabundance’ of objects, Fine’s system far outstrips the (arguably) already inflated ontological commitments of standard mereology; and (iii) there is a legitimate question as to why we should consider Fine’s primitive and sui generis relations of parthood and composition to be genuinely mereological at all, given their formal profile. These three objections lead me to conclude that we ought to explore other avenues that preserve the highly desirable, hylomorphic, features of Fine’s mereology, while avoiding its methodological and ontological excesses. (shrink)
Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their (...) central concepts. The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)
This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide (...) complete (and sound) systems of deduction for supervaluationist consequence in which proofs are completely classical with the exception of a single last step (involving the above mentioned inference). (shrink)
Representation is a central part of models in cognitive science, but recently this idea has come under attack. Researchers advocating perceptual symbol systems, situated action, embodied cognition, and dynamical systems have argued against central assumptions of the classical representational approach to mind. We review the core assumptions of the dominant view of representation and the four suggested alternatives. We argue that representation should remain a core part of cognitive science, but that the insights from these alternative approaches must be (...) incorporated into models of cognitive processing. (shrink)
Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes (...) class='Hi'>mereology look counterintuitive to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)
I argue that the logical difference between classical and quantum mechanics that Stapp (1995) claims shows quantum mechanics is more amenable to an account of consciousness than is classical mechanics is irrelevant to the problem.
The term ‘logical form’ has been called on to serve a wide range of purposes in philosophy, and it would be too ambitious to try to survey all of them in a single essay. Instead, I will focus on just one conception of logical form that has occupied a central place in the philosophy of language, and in particular in the philosophical study of linguistic meaning. This is what I will call the classical conception of logical form. The (...) class='Hi'>classical conception, as I will present it in section 1, has (either explicitly or implicitly) shaped a great deal of important philosophical work in semantic theory. But it has come under fire in recent decades, and in sections 2 and 3 I will discuss two of the recent challenges that I take to be most interesting and significant. (shrink)
1. Pohlers and The Problem. I first met Wolfram Pohlers at a workshop on proof theory organized by Walter Felscher that was held in Tübingen in early April, 1973. Among others at that workshop relevant to the work surveyed here were Kurt Schütte, Wolfram’s teacher in Munich, and Wolfram’s fellow student Wilfried Buchholz. This is not meant to slight in the least the many other fine logicians who participated there.2 In Tübingen I gave a couple of survey lectures on (...) results and problems in proof theory that had been occupying much of my attention during the previous decade. The following was the central problem that I emphasized there: The need for an ordinally informative, conceptually clear, proof-theoretic reduction of classical theories of iterated arithmetical inductive definitions to corresponding constructive systems. As will be explained below, meeting that need would be significant for the then ongoing efforts at establishing the constructive foundation for and proof-theoretic ordinal analysis of certain impredicative subsystems of classical analysis. I also spoke in Tübingen about.. (shrink)
Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we (...) will propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)
It is argued that seemingly “merely technical” issues about the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have interesting implications for foundations problems in classical and quantum physics. For example, pursuing these technical issues reveals a sense in which quantum mechanics can cure some of the forms of indeterminism that crop up in classical mechanics; and at the same time it reveals the possibility of a form of indeterminism in quantum mechanics that is (...) quite distinct from the indeterminism of state vector collapse. More generally, the examples considered indicate that the classical–quantum correspondence is more intricate and delicate than is generally appreciated. The aim of the article is to give a series of examples that reveal why the technical issues about self-adjointness are relevant to the philosophy of science and that help to make the issues accessible to philosophers of science. (shrink)
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of (...) it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)
The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical `or'. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate (...) how application of this analysis to concepts could alleviate some well known problems in cognitive science. (shrink)
Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratic atomists and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium ), and Boethius (especially In Ciceronis Topica (...) ). Mereology has also occupied a prominent role in the writings of medieval ontologists and scholastic philosophers such as Garland the Computist, Peter Abelard, Thomas Aquinas, Raymond Lull, and Albert of Saxony, as well as in Jungius's.. (shrink)
In this paper I present the strategy behind the proof-theoretic justification of logical inference. I then discuss how this strategy leads to the famous requirement that the inference rules for the logical constants should be in harmony. I argue that the proof-theoretic justification of the logical constants can be used to justify classical logic. To substantiate this I present a new normalisation theorem for first order classical logic involving Sheffer Stroke. The proof of this theorem can be modified (...) to yield a normalisation result for classical logic with conjunction, negation and the universal quantifier. (shrink)
After a brief sketch of the history of philosophical pragmatism generally, and of legal pragmatism specifically (section 1), this paper develops a new, neo-classical legal pragmatism: a theory of law drawing in part on Holmes, but also on ideas from the classical pragmatist tradition in philosophy. Main themes are the "pluralistic universe" of law (section 2); the evolution of legal systems (section 3); the place of logic in the law (section 4); and the relation of law and morality (...) (section 5). (shrink)
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic (...) coordinates, is the rectification of vector fields afforded by the local existence and uniqueness of solutions to ordinary differential equations. For the Hamiltonian theorem, the main extra ingredients are the asymmetry of the Poisson bracket, and the fact that a vector field generates canonical transformations iff it is Hamiltonian. (shrink)
This paper deals with the rationalist assumptions behind researches of artificial intelligence (AI) on the basis of Hubert Dreyfus’s critique. Dreyfus is a leading American philosopher known for his rigorous critique on the underlying assumptions of the field of artificial intelligence. Artificial intelligence specialists, especially those whose view is commonly dubbed as “classical AI,” assume that creating a thinking machine like the human brain is not a too far away project because they believe that human intelligence works on the (...) basis of formalized rules of logic. In contradistinction to classical AI specialists, Dreyfus contends that it is impossible to create intelligent computer programs analogous to the human brain because the workings of human intelligence is entirely different from that of computing machines. For Dreyfus, the human mind functions intuitively and not formally. Following Dreyfus, this paper aims to pinpointing the major flaws classical AI suffers from. The author of this paper believes that pinpointing these flaws would inform inquiries on and about artificial intelligence. Over and beyond this, this paper contributes something indisputably original. It strongly argues that classical AI research programs have, though inadvertently, falsified an entire epistemological enterprise of the rationalists not in theory as philosophers do but in practice. When AI workers were trying hard in order to produce a machine that can think like human minds, they have in a way been testing—and testing it up to the last point—the rationalist assumption that the workings of the human mind depend on logical rules. Result: No computers actually function like the human mind. Reason: the human mind does not depend on the formal or logical rules ascribed to computers. Thus, symbolic AI research has falsified the rationalist assumption that ‘the human mind reaches certainty by functioning formally’ by virtue of its failure to create a thinking machine. (shrink)
Naive mereology studies ordinary, common-sense beliefs about part and whole. Some of the speculations in this article on naive mereology do not bear directly on Peter van Inwagen's "Material Beings". The other topics, (1) and (2), both do. (1) Here is an example of Peter Unger's "Problem of the Many". How can a table be a collection of atoms when many collections of atoms have equally strong claims to be that table? Van Inwagen invokes fuzzy sets to solve (...) this problem. I claim that an alternative treatment of vagueness, supervaluations over many-value valuations, provides a better solution. (2) The Special Composition Question asks how parts compose a whole. One who rejects van Inwagen's answer in terms of constituting a life need not provide some alternative answer. Even if all answers to the Special Question fail, there are a multitude of less general composition questions that are not so difficult. (shrink)
In The Mind Doesn’t Work that Way, Jerry Fodor argues that mental representations have context sensitive features relevant to cognition, and that, therefore, the Classical Computational Theory of Mind (CTM) is mistaken. We call this the Globality Argument. This is an in principle argument against CTM. We argue that it is self-defeating. We consider an alternative argument constructed from materials in the discussion, which avoids the pitfalls of the official argument. We argue that it is also unsound and that, (...) while it is an empirical issue whether context sensitive features of mental representations are relevant to cognition, it is empirically implausible. (shrink)
Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use.I argue that Dummett gives a (...) mistaken elaboration of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen"s. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic. (shrink)
This paper describes a long-standing, though little-known, debate between Paul Dirac and Werner Heisenberg over the nature of scientific methodology, theory change, and intertheoretic relations. Following Heisenberg’s terminology, their disagreements can be summarized as a debate over whether the classical and quantum theories are “open” or “closed.” A close examination of this debate sheds new light on the philosophical views of two of the great founders of quantum theory.
Much of the philosophical interest of cognitive science stems from its potential relevance to the mind/body problem. The mind/body problem concerns whether both mental and physical phenomena exist, and if so, whether they are distinct. In this chapter I want to portray the classical and connectionist frameworks in cognitive science as potential sources of evidence for or against a particular strategy for solving the mind/body problem. It is not my aim to offer a full assessment of these two frameworks (...) in this capacity. Instead, in this thesis I will deal with three philosophical issues which are (at best) preliminaries to such an assessment: issues about the syntax, the semantics, and the processing of the mental representations countenanced by classical and connectionist models. I will characterize these three issues in more detail at the end of the chapter. (shrink)
General Process Theory (GPT) is a new (non-Whiteheadian) process ontology. According to GPT the domains of scientific inquiry and everyday practice consist of configurations of ‘goings-on’ or ‘dynamics’ that can be technically defined as concrete, dynamic, non-particular individuals called general processes. The paper offers a brief introduction to GPT in order to provide ontological foundations for research programs such as interactivism that centrally rely on the notions of ‘process,’ ‘interaction,’ and ‘emergence.’ I begin with an analysis of our common sense (...) concept of activities, which plays a crucial heuristic role in the development of the notion of a general process. General processes are not individuated in terms of their location but in terms of ‘what they do,’ i.e., in terms of their dynamic relationships in the basic sense of one process being part of another. The formal framework of GPT is thus an extensional mereology, albeit a non-classical theory with a non-transitive part-relation. After a brief sketch of basic notions and strategies of the GPT-framework I show how the latter may be applied to distinguish between causal, mechanistic, functional, self-maintaining, and recursively self-maintaining interactions, all of which involve ‘emergent phenomena’ in various senses of the term. (shrink)
Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences (...) of a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)
We present a reconstruction of so-called classical, formal or Mendelian genetics using a notation which we believe is more legible than that of earlier accounts, and lends itself easily to computer implementation, for instance in PROLOG. By drawing from, and emending, earlier work of Balzer and Dawe (1986,1997), the present account presents the three most important lines of development of classical genetics: the so-called Mendel's laws, linkage genetics and gene mapping, in the form of a theory-net. This shows (...) that the set theoretic representation format used in the structuralist approach to the philosophy of science also applies to the domain of genetic theories. There construction is intended to lend more clarity to theme thodological, philosophical and didactical discussions of the foundations of genetics, and on the other hand to defend a formally, logically minded view of theories which seems to have become contested through the work of Feyerabend, Kuhn and Kitcher. (shrink)
Fodor and Pylyshyn (1988) argue that any successful model of cognition must use classical architecture; it must depend upon rule-based processing sensitive to constituent structure. This claim is central to their defense of classical AI against the recent enthusiasm for connectionism. Connectionist nets, they contend, may serve as theories of the implementation of cognition, but never as proper theories of psychology. Connectionist models are doomed to describing the brain at the wrong level, leaving the classical view to (...) account for the mind.This paper considers whether recent results in connectionist research weigh against Fodor and Pylyshyn's thesis. The investigation will force us to develop criteria for determining exactly when a net is capable of systematic processing. Fodor and Pylyshyn clearly intend their thesis to affect the course of research in psychology. I will argue that when systematicity is defined in a way that makes the thesis relevant in this way, the thesis is challenged by recent progress in connectionism. (shrink)
: This paper examines the transformation which occurs in Heisenberg's understanding of indeterminacy in quantum mechanics between 1926 and 1928. After his initial but unsuccessful attempt to construct new quantum concepts of space and time, in 1927 Heisenberg presented an operational definition of concepts such as 'position' and 'velocity'. Yet, after discussions with Bohr, he came to the realisation that classical concepts such as position and momentum are indispensable in quantum mechanics in spite of their limited applicability. This transformation (...) in Heisenberg's thought, which centres on his theory of meaning, marks the critical turning point in his interpretation of quantum mechanics. (shrink)
This essay introduces the philosophy of harmony in Classical Confucianism. In the first part of the essay the author summarizes the concept of harmony as it was developed in various Confucian classics. In the second part, the author offers an account of the Confucian program of harmony, ranging from internal harmony in the person, to harmony in the family, the state, the international world, and finally to harmony in the entire universe.
According to a Received View, relativistic quantum field theories (RQFTs) do not admit particle interpretations. This view requires that particles be localizable and countable, and that these characteristics be given mathematical expression in the forms of local and unique total number operators. Various results (the Reeh-Schlieder theorem, the Unruh Effect, Haag's theorem) then indicate that formulations of RQFTs do not support such operators. These results, however, do not hold for nonrelativistic QFTs. I argue that this is due to the absolute (...) structure of the classical spacetimes associated with such theories. This suggests that the intuitions that underlie the Received View are non-relativistic. Thus, to the extent that such intuitions are inappropriate in the relativistic context, they should be abandoned when it comes to interpreting RQFTs. (shrink)
We clarify Bohr’s interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.
: The revival of philosophical pragmatism has generated a wealth of intramural debates between neopragmatists like Richard Rorty and contemporary scholars devoted to explicating the classical pragmatism of John Dewey and William James. Of all these internecine conflicts, the most divisive concerns the status of language and experience in pragmatist philosophy. Contemporary scholars of classical pragmatism defend experience as the heart of pragmatism while neopragmatists drop the concept of experience in favor of a thoroughly linguistic pragmatism. I argue (...) that both positions engender formidable risks. After discussing the present impasse, I describe a third version of pragmatism which involves a reconstruction of the classical pragmatist concept of experience in light of the criticisms of foundationalism crucial to the neopragmatist linguistic turn. This third version of pragmatism does justice to both Rorty and Dewey by focusing on experience as a temporal field. (shrink)
This paper aims at answering the simple question, “What is spontaneous symmetry breaking (SSB) in classical systems?” I attempt to do this by analyzing from a philosophical perspective a simple classical model which exhibits some of the main features of SSB. Related questions include: What does it mean to say that a symmetry is spontaneously broken? Is it broken without any causes, or is the symmetry not broken but merely hidden? Is the principle, “no asymmetry in, no asymmetry (...) out,” violated by SSB? What really distinguishes SSB from the usual types of symmetry breaking? (shrink)
The concept of kaivalya (literally, 'aloneness') is of crucial importance to the systems of classical Indian philosophy known as Sākhya and Yoga. Indeed, kaivalya is the supreme soteriological goal to which these systems are directed. Various statements concerning this final goal appear in the classical texts - namely, the Sākhyakārikā and Yogastra - and yet there is no consensus within modern scholarship about how the concept is to be interpreted. More specifically, there appears to be a great deal (...) of confusion over the implications of kaivalya for the existence of the empirical world. In this article I discuss the principal difficulties encountered by existing interpretations of kaivalya, and propose that these difficulties result from an unwarranted assumption that Sākhya and Yoga take a realist view with regard to the empirical world. I further propose that these difficulties can, in large part, be overcome when the assumption of realism is set aside. (shrink)
Original in content and approach, Philosophy in ClassicalIndia focuses on the rational principles of Indian philosophical theory, rather than the mysticism usually associated with it. Ganeri explores the philosophical projects of a number of major Indian philosophers and looks into the methods of rational inquiry deployed within these projects. In so doing, he illuminates a network of mutual reference and criticism, influence and response, in which reason is simultaneously used constructively and to call itself into question.
The Islamic philosophical tradition was the privileged site for the study and continuation of the Classical philosophical tradition in the Middle Ages. An initial chapter on the history of Islamic philosophy sets the stage for sixteen articles on issues across the Islamic, Jewish and Christian traditions. The goal is to see the Islamic tradition in its own richness and complexity as the context of much Jewish intellectual work. Taken together, these two traditions provide the wider context to which Latin (...) Christian intellectuals would turn. The articles are grouped under six topics relevant both to the period and to current philosophical interest: the Islamic philosophical context, the nature of philosophy in the Middle Ages, Neoplatonism and the activity of the soul, creation, virtue, and the Latin reception. Since the nineteenth century Islamic and Jewish philosophy have been neglected in the standard histories of medieval philosophy. The time is right to begin to write a more balanced history of medieval philosophy. In order to begin to write this history, this book focuses on the Islamic, Jewish, and Christian use of - and reaction to - Classical philosophy during the Middle Ages. (shrink)