Many philosophers claim that understanding a logical constant (e.g. ‘if, then’) fundamentally consists in having dispositions to infer according to the logical rules (e.g. Modus Ponens) that fix its meaning. This paper argues that such dispositionalist accounts give us the wrong picture of what understanding a logical constant consists in. The objection here is that they give an account of understanding a logical constant which is inconsistent with what seem to be adequate manifestations of such understanding. I then outline an (...) alternative account according to which understanding a logical constant is not to be understood dispositionally, but propositionally. I argue that this account is not inconsistent with intuitively correct manifestations of understanding the logical constants. (shrink)
We show that there are denumerably many Post-complete normal modal logics in the language which includes an additional propositional constant. This contrasts with the case when there is no such constant present, for which it is well known that there are only two such logics.
There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these (...) ideas and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory. (shrink)
I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.
The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in (...) particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions. (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)
In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett (...) and his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)
There is as yet no settled consensus as to what makes a term a logical constant or even as to which terms should be recognized as having this status. This essay sets out and defends a rationale for identifying logical constants. I argue for a two-tiered approach to logical theory. First, a secure, core logical theory recognizes only a minimal set of constants needed for deductively systematizing scientific theories. Second, there are extended logical theories whose objectives are to (...) systematize various pre-theoretic, modal intuitions. The latter theories may recognize a variety of additional constants as needed in order to formalize a given set of intuitions. (shrink)
Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and (...) semantic structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)
Donald Dvaidson has claimed that a theory of meaning identifies the logical constants of the object language by treating them in the phrasal axioms of the theory, and that the theory entails a relation of logical consequence among the sentences of the object language. Section 1 offers a preliminary investigation of these claims. In Section 2 the claims are rebutted by appealing to Evans's paradigm of a theory of meaning. Evans's theory is deliberately blind to any relation of logical (...) consequence among the sentences of the object language, and entails only what Evans takes to be a distinct and deeper relation of structural validity among the sentences of the object language. In Section 3 we turn to Evans's motivation in order to compare the two paradigms of a theory of meaning. Evans laid down criteria under which a theory of meaning gives what he called a ‘transcendent’ semantic classification of the lexicon of the object language, in contrast to a mere ‘immanent’ classification. However, when these criteria are applied we find that, pace Evans, they favour Davidson's paradigm over Evans's. In the final section we show that Evans's conception of structural consequence turns out to be a deeper formulation of logical consequence. (shrink)
There is as yet no settled consensus as to what makes a term a logical constant or even as to which terms should be recognized as having this status. This essay sets out and defends a rationale for identifying logical constants. I argue for a two-tiered approach to logical theory. First, a secure, core logical theory recognizes only a minimal set of constants needed for deductively systematizing scientific theories. Second, there are extended logical theories whose objectives are to (...) systematize various pre-theoretic, modal intuitions. The latter theories may recognize a variety of additional constants as needed in order to formalize a given set of intuitions. (shrink)
Bolzano’s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation X . We present this in a precise and abstract form, in particular studying minimal sets of symbols generating X . Then we present a method for going in the other direction: extracting from an arbitrary consequence relation its associated set C of constants. We show that this returns the expected logical constants from familiar consequence relations, and (...) that, restricting attention to sets of symbols satisfying a strong minimality condition, there is an isomorphism between the set of strongly minimal sets of symbols and the set of corresponding consequence relations (both ordered under inclusion). (shrink)
The paper argues that a philosophically informative and mathematically precise characterization is possible by (i) describing a particular proposal for such a characterization, (ii) showing that certain criticisms of this proposal are incorrect, and (iii) discussing the general issue of what a characterization of logical constants aims at achieving.
This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of can be easily and safely ameliorated; (4) the definition of in terms of `proofs from premises" results in a loss of the inductive character of the (...) definitions of and and (5) the same occurs with the definition of in terms of `proofs with free variables". (shrink)
Extending the language of the intuitionistic propositional logic Int with additional logical constants, we construct a wide family of extensions of Int with the following properties: (a) every member of this family is a maximal conservative extension of Int; (b) additional constants are independent in each of them.
The paper deals with the problem of axiomatizing a system 1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 (immediate successor) and -1 (immediate predecessor). 1 is like the Segerberg-Sundholm system W1 in working with so-called infinitary inference rules; on the other hand, it differs from W1 with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a now operator, and, most importantly, with (...) respect to (iii) the presence in of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of 1. (shrink)
The method of Ramsey sentences has been proposed for handling theoretical constructs within a scientific system. Essentially it consists of constructing a certain "monolithic" sentence for an entire theory. In this present paper several improvements are suggested which help to overcome some of the awkward features of the method. In particular we have here many Ramsey sentences rather than just one, each erstwhile primitive theoretical term giving rise to a Ramsey sentence. Such a sentence in effect defines what we call (...) a Ramsey constant. Using Ramsey constants, we attempt to improve the method in important logical and semantical respects. It is suggested also that such constants are of interest for the philosophy of mathematics. (shrink)
We prove ExpTime-membership of the satisfiability problem for loosely ∀-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic.
The following investigation illustrates, by concrete historical examples, some of the basic results, outlined in earlier papers on theory evolution and reference dynamics in science (cf. Balzer, W. et al.: 1989, 'A Static Theory of Reference in Science', Synthese 79, 319-360; Lauth, B.: 1989, 'Reference Problems in Stoichiometry', Erkenntnis 30, 339-362; Lauth, B.: 1990, 'Theory Evolution and Reference Kinematics', Synthese 88, 279-307). All theories considered in this paper are represented within a metatheoretical frame that has become known as the structuralist (...) view in the philosophy of science. The paper focusses on some physical constants, namely the mass and charge of electrons, henceforth denoted by m₀ and e₀, of Boltzmann's constant k, Faraday's constant F and Avogadro's Number ${\rm N}_{{\rm A}}$ , and the evolution of their 'reference spectra' from the beginning of the 19th century until the early days of quantum physics. (shrink)
We present a method to determine the reaction type and kinetic constants for enzyme inhibitors that decreases the number of experimental assays by at least a factor of five. It is based on a new theoretical formalism in terms of concentrations that dismisses the requirement of estimating initial velocities. Expressions for the time evolution of the concentrations of all the reactants are also given.
A model for kinetics of circular substrate cleavage by restriction endonuclease was formulated. The aim of the analysis of the model was to extract kinetic constants for all target sites from time-dependence of fragment concentration in reaction products. That was proved to be possible for molecules with an odd number of fragments only. A symmetry of the molecules with an even number of fragment is the cause. A solution for molecules with an odd number of fragments was found (...) and methods for dealing with the other molecules were suggested. (shrink)
In this paper, we shall confine ourselves to the study of sentential constants in the system R of relevant implication.In dealing with the behaviour of the sentential constants in R, we shall think of R itself as presented in three stages, depending on the level of truth-functional involvement.
An Ackermann constant is a formula of sentential logic built up from the sentential constant t by closing under connectives. It is known that there are only finitely many non-equivalent Ackermann constants in the relevant logic R. In this paper it is shown that the most natural systems close to R but weaker than it-in particular the non-distributive system LR and the modalised system NR-allow infinitely many Ackermann constants to be distinguished. The argument in each case proceeds by (...) construction of an algebraic model, infinite in the case of LR and of arbitrary finite size in the case of NR. The search for these models was aided by the computer program MaGIC (Matrix Generator for Implication Connectives) developed by the author at the Australian National University. (shrink)
We prove ExpTime-membership of the satisfiability problem for loosely ∀-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic.
of a logarithmic time dependence of the fine structure constant is apparently within the limits discussed if there is a corresponding logarithmic time dependence of the strong coupling constant also. Moreover the recent discover> of naturally occurring ' Pu places the Gamow hypothesis of e' r much nearer the allov'able limits than had previously been supposed.
Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...) be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions. (shrink)
What is the relationship between logic and reasoning? How do logical norms guide inferential performance? This paper agrees with Gilbert Harman and most of the psychologists that logic is not directly relevant to reasoning. It argues, however, that the mental model theory of logical reasoning allows us to harmonise the basic principles of deductive reasoning and inferential perfomances, and that there is a strong connexion between our inferential norms and actual reasoning, along the lines of Peacocke’s conception of inferential role.
This paper argues that logical inferentialists should reject multiple-conclusion logics. Logical inferentialism is the position that the meanings of the logical constants are determined by the rules of inference they obey. As such, logical inferentialism requires a proof-theoretic framework within which to operate. However, in order to fulfil its semantic duties, a deductive system has to be suitably connected to our inferential practices. I argue that, contrary to an established tradition, multiple-conclusion systems are ill-suited for this purpose because they (...) fail to provide a 'natural' representation of our ordinary modes of inference. Moreover, the two most plausible attempts at bringing multiple conclusions into line with our ordinary forms of reasoning, the disjunctive reading and the bilateralist denial interpretation, are unacceptable by inferentialist standards. (shrink)
In earlier work we have described how computer algebra may be used to derive composite rate laws for complete systems of equations, using the mathematical technique of Gröbner Bases (Bennett, Davenport and Sauro, 1988). Such composite rate laws may then be fitted to experimental data to yield estimates of kinetic parameters.Recently we have been investigating the practical application of this methodology to the estimation of kinetic parameters for the closed two enzyme system of aspartate aminotransferase (AAT) and malate dehydrogenase (MDH) (...) (Fisher 1990a; Fisher 1990b; Bennett and Fisher, 1990). (shrink)
This year I am on sabbatical at the Max Planck Institute for Physics in Munich, Germany, which by a happy coincidence was also the site of the 17th Texas Symposium on Relativistic Astrophysics held here two weeks ago (December 12-15, 1994). I was able to attend the Symposium, to learn quite a bit about the present state of astrophysics, and to contribute a paper co-authored by SF writers Forward, Benford, and Landis and wormhole theorists Visser and Morris [see my recent (...) AV column on this in the mid-December-94 Analog]. (shrink)
The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\mathbf{t}$ (...) . This calculus, $LT_\to^{\text{\textcircled{$\mathbf{t}$}}}$ , extends the consecution calculus $LT_{\to}^{\mathbf{t}}$ formalizing the implicational fragment of ticket entailment . We introduce two other new calculi as alternative formulations of $R_{\to}^{\mathbf{t}}$ . For each new calculus, we prove the cut theorem as well as the equivalence to the original Hilbert-style axiomatization of $R_{\to}^{\mathbf{t}}$ . These results serve as a basis for our positive solution to the long open problem of the decidability of $T_{\to}$ , which we present in another paper. (shrink)
La pensée fondamentale de Wittgenstein affirme que les constantes logiques ne représentent pas, ne fonctionnent pas sémantiquement comme des noms. En apparence truiviale, cette pensée, nous le montrerons, à des ramifications étonnantes dans la philosophie du premier wittgenstein, en ce qui concerne partmulzer sa conception de la logique. Notre but est d'interpréter l'aphorisme en question (T 4.0312) en montrant comment il se rapporte aux thèses et théories les plus importantes du Tractatus, et comment il permet de les faire tenir ensemble (...) d'une façon cohérente, justifiant par là son caractère "fondamental". Nous tentons également d'apporter une réponse aux questions suivantes: les propositions complexes sont-elles encore — comme les propositions atomiques — des "images" de la réalité? et quelle est cette "logique des faits" dont parle Wittgenstein dans l'aphorisme sous examen? (shrink)
In the first part of the paper it is proved that there exists a one–one mapping between a minimal contingential logic extended with a suitable axiom for a propositional constant τ, named KΔτw, and a logic of necessity ${K\square \tau{w}}$ whose language contains ${\square}$ and τ. The form of the proposed translation aims at giving a solution to a problem which was left open in a preceding paper. It is then shown that the presence of τ in the language of (...) KΔτw allows for the definition, in terms of the non-contingency operator Δ, not only of ${\square}$ but of a second necessity operator O. It is observed that this fact opens the road to an investigation of the τ-free multimodal fragments of KΔτw. (shrink)
The notion of harmony has played a pivotal role in a number of debates in the philosophy of logic. Yet there is little agreement as to how the requirement of harmony should be spelled out in detail or even what purpose it is to serve. Most, if not all, conceptions of harmony can already be found in Michael Dummett's seminal discussion of the matter in The Logical Basis of Metaphysics. Hence, if we wish to gain a better understanding of the (...) notion of harmony, we do well to start here. Unfortunately, however, Dummett's discussion is not always easy to follow. The following is an attempt to disentangle the main strands of Dummett's treatment of harmony. The different variants of harmony as well as their interrelations are clarified and their individual shortcomings qua interpretations of harmony are demonstrated. Though no attempt is made to give a detailed alternative account of harmony here, it is hoped that our discussion will lay the ground for an adequate rigorous treatment of this central notion. (shrink)
This paper considers the question of what knowing a logical rule consists in. I defend the view that knowing a logical rule is having propositional knowledge. Many philosophers reject this view and argue for the alternative view that knowing a logical rule is, at least at the fundamental level, having a disposition to infer according to it. To motivate this dispositionalist view, its defenders often appeal to Carroll’s regress argument in ‘What the Tortoise Said to Achilles’. I show that this (...) dispositionalist view, and the regress that supposedly motivates it, operate with the wrong picture of what is involved in knowing a logical rule. In particular I show that it gives us the wrong picture of the relation between knowing a logical rule and actions of inferring according to it, as well as of the way in which knowing a logical rule might be a priori. (shrink)
The nontechnical ability to identify or match argumentative structure seems to be an important reasoning skill. Instruments that have questions designed to measure this skill include major standardized tests for graduate school admission, for example, the United States-Canadian Law School Admission Test (LSAT), the Graduate Record Examinations (GRE), and the Graduate Management Admission Test (GMAT). Writers and reviewers of such tests need an appropriate foundation for developing such questions--they need a proper representation of phenomenological argumentative structure--for legitimacy, and because these (...) tests affect people's lives. This paper attempts to construct an adequate and appropriate representation of such structure, that is, the logical structure that an argument is perceived to have by mature reasoners, albeit ones who are untrained in logic. (shrink)
This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation (...) for logic. A criterion of logicality is obtained which is based on conjunction, implication and universal quantification as fundamental logical operations. (shrink)
Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...) of S4.3 is radically altered by the addition of a constant: we use it to construct continuum many such normal extensions of S4.3, and continuum many non-normal ones, none of which have the finite model property. But for logics with weakly transitive frames there are only eight maximally normal ones, of which five extend K4 and three extend S4. (shrink)
The requirement of proof-theoretic harmony has played a pivotal role in a number of debates in the philosophy of logic. Different authors have attempted to precisify the notion in different ways. Among these, three proposals have been prominent in the literature: harmony–as–conservative extension, harmony–as–leveling procedure, and Tennant’s harmony–as–deductive equilibrium. In this paper I propose to clarify the logical relationships between these accounts. In particular, I demonstrate that what I call the equivalence conjecture —that these three notions essentially come to the (...) same thing—is erroneous. (shrink)
It is shown that there are exactly six normal DeMorgan monoids generated by the identity element alone. The free DeMorgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the "Ackerman constant problem" of describing the structure of sentential constants in the logic R.
One of the main theorems of the paper states the following. Let R-K-M be finite extensions of a rational one variable function field R over a finite field of constants. Let S be a finite set of valuations of K. Then the ring of elements of K having no poles outside S has a Diophantine definition over its integral closure in M.
Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...) is logic?” drives us to the question “What is a logical constant?” Though what follows contains some argument, limitations of space constrain me in large part to express my Credo on this topic with the broad brush of bold assertion and some promissory gestures. (shrink)
According to rich views of consciousness (e.g., James, Searle), we have a constant, complex flow of experience (or 'phenomenology') in multiple modalities simultaneously. According to thin views (e.g., Dennett, Mack and Rock), conscious experience is limited to one or a few topics, regions, objects, or modalities at a time. Existing introspective and empirical arguments on this issue (including arguments from 'inattentional blindness') generally beg the question. Participants in the present experiment wore beepers during everyday activity. When a beep sounded, they (...) were to take note of the conscious experience, if any, they were having at the last undisturbed moment immediately prior to the beep. Some participants were asked to report any experience they could remember. Others were asked simply to report whether there was visual experience or not (and if so, what it was). Still others were asked about experience in the far right visual field, or tactile experience, or tactile experience in the left foot. A majority of participants in the full experience and the visual conditions reported visual experience in every single sample. Tactile and peripheral visual experience were reported less often. However, the proper interpretation of these results is uncertain. (shrink)
I offer a novel argument for spacetime substantivalism: We should take the spacetime of general relativity to be a substance because of its active role in gravitational causation. As a clear example of this causal behavior I offer the cosmological constant, a term in the most general form of the Einstein field equations which causes free floating objects to accelerate apart. This acceleration cannot, I claim, be causally explained except by reference to spacetime itself.
An interesting case of the complex interaction between theory and experiment can be found in many experiments in quantum physics employing classical reasoning. It is expected that this practice would lead to quantitative inaccuracy, unless the measurements' results were averaged. Whether or not this inaccuracy is significant depends critically on the details of the particular experimental situation. The example of Millikan's photoelectric experiment, in which he obtained a precise value of Planck's constant, provides a good case for illustrating the process (...) of estimating the inaccuracy resulting from the classical-quantum discrepancy. In the case of Millikan's experiment, it seems that a significant inaccuracy was avoided because of fortunate coincidences. In general, in the absence of a careful analysis, it is impossible to say whether the use of classical reasoning interferes with the accuracy of a quantum-physical experiment. (shrink)
In modern physics, the constant “c” plays a twofold role. On the one hand, “c” is the well known velocity of light in an empty Minkowskian space–time, on the other hand “c” is a characteristic number of Special Relativity that governs the Lorentz transformation and its consequences for the measurements of space–time intervals. We ask for the interrelations between these two, at first sight different meanings of “c”. The conjecture that the value of “c” has any influence on the structure (...) of space–time is based on the operational interpretation of Special Relativity, which uses light rays for measurements of space–time intervals. We do not follow this way of reasoning but replace it by a more realistic approach that allows to show that the structure of the Minkowskian space–time can be reconstructed already on the basis of a restricted classical ontology (Mittelstaedt, Philosophie der Physik und der Raum-Zeit, Mannheim: BI-Wissenschaftsverlag, 1988 and Mittelstaedt, Kaltblütig: Philosophie von einem rationalen Standpunkt, Stuttgart: S. Hirzel Verlag, pp. 221–240, 2003 ), and that without any reference to the propagation of light. However, the space–time obtained in this way contains still an unknown constant. We show that this constant agrees numerically with “c” but that it must conceptually clearly be distinguished from the velocity of light. Hence, we argue for a clear distinction between the two faces of “c” and for a dualism of space–time and matter. (shrink)
The cosmological constant problem arises at the intersection between general relativity and quantum field theory, and is regarded as a fundamental problem in modern physics. In this paper, we describe the historical and conceptual origin of the cosmological constant problem which is intimately connected to the vacuum concept in quantum field theory. We critically discuss how the problem rests on the notion of physically real vacuum energy, and which relations between general relativity and quantum field theory are assumed in order (...) to make the problem well-defined. (shrink)
The cosmological constant is back. Several lines of evidence point to the conclusion that either there is a positive cosmological constant or else the universe is filled with a strange form of matter (“quintessence”) that mimics some of the effects of a positive lambda. This paper investigates the implications of the former possibility. Two senses in which the cosmological constant can be a constant are distinguished: the capital Λ sense in which lambda is a universal constant on a par with (...) the charge of the electron, and the lower case λ sense in which lambda is a humble constant of integration. The latter interpretation has been touted as the means to a solution to various problems in physics. These claims are critically examined with an eye to discerning the implications for philosophy of science and foundations of physics. (shrink)
With the discovery that the universe is expanding at an accelerating rate, Einstein’s cosmological constant, which he once supposedly called his biggest blunder, is making a remarkable comeback. Einstein’s introduction of this constant had little to do with cosmology. It was part of yet another failed attempt to eliminate absolute space from physics. It took the Dutch astronomer Willem de Sitter only a few days to blow the idea out of the water. It took Einstein over a year to concede (...) the point. In the process Einstein and De Sitter produced the first two models of relativistic cosmology, the Einstein cylinder universe and the De Sitter hyperboloid universe. (shrink)
The levels that compose biological hierarchies each have their own energetic, spatial and temporal structure. Indeed, it is the discontinuity in energy relationships between levels, as well as the similarity of sub-systems that support them, that permits levels to be defined. In this paper, the temporal structure of living hierarchies, in particular that pertaining to Human society, is examined. Consideration is given to the period defining the lifespan of entities at each level and to a periodic event considered fundamental to (...) the maintenance of that level. The ratio between the duration of these two periods is found to be approximately 2.5 × 104. A similar relationship is found when lower, non-living levels of molecules and atoms are considered. This suggests that there is a constant factor of amplification between analogous periodic events at successive levels of the Human hierarchy. (shrink)
The perpetual music track is a new concept that describes a condition of constant or near-constant musical imagery. This condition appears to be very rare even among composers and musicians. I present here a detailed self-analysis of musical imagery for the purpose of defining the psychological features of a perpetual music track. I have music running through my head almost constantly during waking hours, consisting of a combination of recently-heard pieces and distant pieces that spontaneously pop into the head. (...) Imagery consists mainly of short musical fragments that get looped repeatedly upon themselves. Corporeal manifestations of imagery occur in the form of unconscious finger movements whose patterns correspond to the melodic contour of the imagined piece. Musical dreams occur every week or two, and contain a combination of familiar and originally- composed music. These results are discussed in light of theories of imagery, consciousness, hallucination, obsessive cognition, and most especially the notion that acoustic consciousness can be split into multiple parallel streams. (shrink)
Much of what you thought you knew about the universe and its expansion may be wrong. That expansion appears to be speeding up rather than slowing E = mc 2). down. This column is about recent astronomical evidence for a positive cosmological constant, suggesting that space itself has mass-energy..
In the first years of its existence between 1957 and 1960 the efforts of the radical collective the Situationist International (SI) centred on its program of “unitary urbanism.” This program sought to challenge the functionalist character of hegemonic forms of urban planning through novel practices of urban experimentation and contestation. Situationist urbanism arose largely through the collaboration between Guy Debord and the Dutch avant-garde architect Constant. This article explores the political dimension of situationist urbanism and the tensions that led to (...) Constant’s secession from the group in 1960. Through analysis of the affinities and divergences between urbanism in its modernist and situationist forms a case is made for the crucial contribution situationist practices might make to the restoration of public space as a vital arena of contemporary political contestation and community. (shrink)
The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [ 8 ] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: ( Q - H + D *), ( Q - H + D *&K), ( Q - H + D *& K & J ). Here Q - H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D * (cf. [ 12 ]) is a (...) weakened version of the well-known constant domains principle D . Namely, the formula D states that any individual has ancestors in earlier worlds, and D * states that any individual has $${\neg\neg}$$ -ancestors (i.e., ancestors up to $${\neg\neg}$$ -equality) in earlier worlds. In particular, the logic ( Q - H + D *& K & J ) is the Kripke sheaf completion of ( Q - H + E & K & J ), where E is a version of Markov’s principle (cf. [ 12 ]). On the other hand, we show that the logic ( Q - H + D *& J ) is incomplete w.r.t. Kripke sheaves. (shrink)
The fine structure constant α ≡ e2/ c ≈ 1/137 is one of the fundamental parameters of the standard model of particle physics. There is a long history of attempts to derive the measured value of α from an underlying theory, or exhibit it in the form of a compact mathematical expression [2–4, 6, 8, 14–16]. The most significant advance in this endeavour was made by Dirac, who showed that if magnetic monopoles exist, with magnetic charge μ, then..
Warren Samuels maintains that every society has a constant amount of coercion and order, which vary only in terms of who gains and who loses, because every society has a government that establishes property rights. In making these arguments, Samuels exaggerates the extent to which governmental decisions predetermine the workings of a market society, and he fails to recognize that, with regard to the attainment of specific socioeconomic outcomes, governmental stipulation of private property rights differs fundamentally from governmental (...) command and control. (shrink)
Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.
James L. Anderson analyzed the novelty of Einstein's theory of gravity as its lack of "absolute objects." Michael Friedman's related work has been criticized by Roger Jones and Robert Geroch for implausibly admitting as absolute the timelike 4-velocity field of dust in cosmological models in Einstein's theory. Using the Rosen-Sorkin Lagrange multiplier trick, I complete Anna Maidens's argument that the problem is not solved by prohibiting variation of absolute objects in an action principle. Recalling Anderson's proscription of "irrelevant" variables, I (...) generalize that proscription to locally irrelevant variables that do no work in some places in some models. This move vindicates Friedman's intuitions and removes the Jones-Geroch counterexample: some regions of some models of gravity with dust are dust-free and so naturally lack a timelike 4-velocity, so diffeomorphic equivalence to (1,0,0,0) is spoiled. Torretti's example involving constant curvature spaces is shown to have an absolute object on Anderson's analysis, viz., the conformal spatial metric density. The previously neglected threat of an absolute object from an orthonormal tetrad used for coupling spinors to gravity appears resolvable by eliminating irrelevant fields. However, given Anderson's definition, GTR itself has an absolute object (as Robert Geroch has observed recently): a change of variables to a conformal metric density and a scalar density shows that the latter is absolute. (shrink)
With armed conflict in the Persian Gulf now upon us, Harvard archaeologist Steven LeBlanc takes a long-term view of the nature and roots of war, presenting a controversial thesis: The notion of the "noble savage" living in peace with one another and in harmony with nature is a fantasy. In Constant Battles: The Myth of the Peaceful, Noble Savage , LeBlanc contends that warfare and violent conflict have existed throughout human history, and that humans have never lived in ecological balance (...) with nature. The start of the second major U.S. military action in the Persian Gulf, combined with regular headlines about spiraling environmental destruction, would tempt anyone to conclude that humankind is fast approaching a catastrophic end. But as LeBlanc brilliantly argues, the archaeological record shows that the warfare and ecological destruction we find today fit into patterns of human behavior that have gone on for millions of years. Constant Battles surveys human history in terms of social organization-from hunter gatherers, to tribal agriculturalists, to more complex societies. LeBlanc takes the reader on his own digs around the world -- from New Guinea to the Southwestern U.S. to Turkey -- to show how he has come to discover warfare everywhere at every time. His own fieldwork combined with his archaeological, ethnographic, and historical research, presents a riveting account of how, throughout human history, people always have outgrown the carrying capacity of their environment, which has led to war. Ultimately, though, LeBlanc's point of view is reassuring and optimistic. As he explains the roots of warfare in human history, he also demonstrates that warfare today has far less impact than it did in the past. He also argues that, as awareness of these patterns and the advantages of modern technology increase, so does our ability to avoid war in the future. (shrink)
The aim of this paper is to construct a tableau decision algorithm for the modal description logic K ALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALC-formula with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether is satisfiable in a model with constant domains and arbitrary accessibility relations. Tableau-based algorithms have been shown to be practical even for logics of rather high (...) complexity. This gives us grounds to believe that, although the satisfiability problem for K ALC is known to be NEXPTIME-complete, by providing a tableau decision algorithm we demonstrate that highly expressive description logics with modal operators have a chance to be implementable. The paper gives a solution to an open problem of Baader and Laux [5]. (shrink)
McGavin, PA A constant theme of modern pontificates has been to keep in focus the central generative purpose of human sexuality and its full expression in the marriage relationship. While it is essential to keep this central focus, it nevertheless is necessary to sustain an attitude of 'discovery' in re-examining fundamental issues. This essay proposes such an approach in moving to a more nuanced catechetical reading of human sexuality as this particularly touches on the issue of masturbation.
Professor Rosenblatt presents a study of Benjamin Constant's intellectual development into a founding father of modern liberalism, through a careful analysis of his evolving views on religion. Constant's life spanned the Enlightenment, the French Revolution, Napoleon's rise and rule, and the Bourbon Restoration. Rosenblatt analyses Constant's key role in many of this era's heated debates over the role of religion in politics, and in doing so, exposes and addresses many misconceptions that have long reigned about Constant and his period. In (...) particular, Rosenblatt sheds light on Constant's major, yet much-neglected work, De La Religion. Given that the role of religion is, once again, center-stage in our political, philosophical and historical arenas, Liberal Values constitutes a major and timely revision of our understanding of the origins of modern liberalism. (shrink)
The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ‘blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.
For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)
Abstract The paper presents an outline of a unified answer to five questions concerning logic: (1) Is logic in the mind or in the world? (2) Does logic need a foundation? What is the main obstacle to a foundation for logic? Can it be overcome? (3) How does logic work? What does logical form represent? Are logical constants referential? (4) Is there a criterion of logicality? (5) What is the relation between logic and mathematics?
In this paper, I situate Hans Blumenberg historically and conceptually in relation to a subtheme in the famous debate between Martin Heidegger and Ernst Cassirer at Davos, Switzerland in 1929. The subtheme concerns Heidegger’s and Cassirer’s divergent attitudes toward philosophical anthropology as it relates to the starting points and goals of philosophy. I then reconstruct Blumenberg’s anthropology, which involves reconceptualizing Cassirer’s philosophy of symbolic forms in relation to Heidegger’s objections to the philosophical anthropology of his day (e.g., Max Scheler, Helmuth (...) Plessner, and Arnold Gehlen) as unduly anthropocentric. Blumenberg builds on anthropologist Gehlen’s assumption that human beings are biologically underdetermined and therefore world-open. With this starting point, symbolic forms, such as myth and language, make up a compensatory life-world that supports human existence. Action, or self-assertion, which is necessary given the lack of a seamless fit between human beings and the environment, is thus circumscribed and shaped by the historied, cultural constructs that constitute a life-world. Human beings can thus be characterized as a species that continually renegotiates the shape of its existence through its relation to biological limits on the one hand and cultural constants on the other. Because Blumenberg and philosophical anthropology are relatively unexplored by Anglophone philosophers, and because philosophical anthropology is central to Blumenberg’s methodology generally, this study provides an introduction to both. (shrink)
[Paul Boghossian] The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of 'blind but blameless' reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is (...) possible. /// [Timothy Williamson] The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper 'Blind Reasoning'. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as 'Boche' are examined and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)
I present a novel objection to fine-tuning arguments for God's existence: the metaphysical possibility of different psychophysical laws allows any values of the physical constants to support intelligent life forms, like protons and electrons in love.
The fundamental constants that are involved in the laws of physics which describe our universe are finely tuned for life, in the sense that if some of the constants had slightly different values life could not exist. Some people hold that this provides evidence for the existence of God. I will present a probabilistic version of this fine-tuning argument which is stronger than all other versions in the literature. Nevertheless, I will show that one can have reasonable opinions (...) such that the fine-tuning argument doesn't lead to an increase in one's probability for the existence of God. The fine-tuning argument Objective versus subjective probability Observational selection effects The problem of old evidence Against the fine-tuning argument Many universes. (shrink)
Paul Boghossian advocates a version of the analytic theory of a priori knowledge. His defense of an "epistemic" notion of analyticity is based on an implicit definition account ofthe meaning of the logical constants. Boghossian underestimates the power of the classical Quinean criticisms, however; the challenge to substantiate the distinction between empirical and non-empirical sentences, as forcefully presented in Two Dogmas, still stands, and the regress from Truth by Convention still needs to be avoided. Here, Quine also showed that (...) there are no implicit definers for the logical constants. Moreover, even if they existed, their epistemic analyticity would, on Boghossian's own account, be doubtful. (shrink)
Bertrand Russell (1872-1970) described his philosophy as a kind of “logical atomism”, by which he meant to endorse both a metaphysical view and a certain methodology for doing philosophy. The metaphysical view amounts to the claim that the world consists of a plurality of independently existing things exhibiting qualities and standing in relations. According to logical atomism, all truths are ultimately dependent upon a layer of atomic facts, which consist either of a simple particular exhibiting a quality, or mutliple simple (...) particulars standing in a relation. The methodological view recommends a process of analysis, whereby one attempts to define or reconstruct more complex notions or vocabularies in terms of simpler ones. According to Russell, at least early on during his logical atomist phase, such an analysis could eventually result in a language containing only words representing simple particulars, the simple properties and relations thereof, and logical constants, which, despite this limited vocabulary, could adequately capture all truths. (shrink)
The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that (...) fully understanding a logical constant in turn requires the ability to apply it correctly in particular cases. It is shown, however, that Implicit Definition cannot account for this ability, even if it draws on introduction rules for the logical constants. In particular, Implicit Definition cannot account for our ability to apply negation in particular cases. Owing to constraints relating to the unique characterisation of logical constants, invoking the notion of rejection does not remedy the situation. Given its failure to explain knowledge of logic, the prospects of Implicit Definition to explain other kinds of a priori knowledge are even worse. (shrink)
