I. Introductio ad totam philosophiam. Philosophia instrumentalis seu logica.--II. Philosophia naturalis.--III. Metaphysics. 2 v.

Human beings inhabit a symbolic reality that articulates meaning. This is culture understood as a web of meanings that actually builds our identity by providing guidance in the complexity of our environment. It is the complex interplay between identity and alterity, between interiority and exteriority, between familiarity and strangeness. Worldviews set up borders that delimit one's own world and others' ground by establishing stereotypes and prejudices. This article presents the results of a research project on prejudices towards the other in (...) students majoring in Education and Psychology with the aim of offering some reflections on what is at stake in social exclusion policies. (shrink)

Vietnam’s money and capital markets continue to see dramatic stages in the remaining months of 2011 due to high bank rates and also increasing foreign-exchange exposure faced by domestic enterprises.

Newtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh+tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oplus \beta _2=\tanh \big +\tanh ^{-1}\big )$$\end{document}, although multiplication β1⊙β2=tanh·tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\odot \beta _2=\tanh \big \cdot \tanh ^{-1}\big )$$\end{document}, and division β1⊘β2=tanh/tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oslash \beta _2=\tanh \big /\tanh ^{-1}\big )$$\end{document} do not seem to appear in the literature. The map fX=tanh-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}=\tanh ^{-1}$$\end{document} defines an isomorphism of the arithmetic in X=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}=$$\end{document} with the standard one in R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. The new arithmetic is projective and non-Diophantine in the sense of Burgin, 1977), while ultrarelativistic velocities are super-large in the sense of Kolmogorov, 1961). Velocity of light plays a role of non-Diophantine infinity. The new arithmetic allows us to define the corresponding derivative and integral, and thus a new calculus which is non-Newtonian in the sense of Grossman and Katz. Treating the above example as a paradigm, we ask what can be said about the set X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} of ‘real numbers’, and the isomorphism fX:X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathbb{X}}}:{\mathbb{X}}\rightarrow {\mathbb{R}}$$\end{document}, if we assume the standard form of Newtonian mechanics and general relativity but demand agreement with astrophysical observations. It turns out that the observable accelerated expansion of the Universe can be reconstructed with zero cosmological constant if fX≈0.8sinh/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}\approx 0.8\sinh /$$\end{document}. The resulting non-Newtonian model is exactly equivalent to the standard Newtonian one with ΩΛ=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _\Lambda =0.7$$\end{document}, ΩM=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _M=0.3$$\end{document}. Asymptotically flat rotation curves are obtained if ‘zero’, the neutral element 0X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0_{{\mathbb{X}}}$$\end{document} of addition, is nonzero from the point of view of the standard arithmetic of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. This implies fX-1=0X>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^{-1}_{{\mathbb{X}}}=0_{{\mathbb{X}}}>0$$\end{document}. The opposition Diophantine versus non-Diophantine, or Newtonian versus non-Newtonian, is an arithmetic analogue of Euclidean versus non-Euclidean in geometry. We do not yet know if the proposed generalization ultimately removes any need of dark matter, but it will certainly change estimates of its parameters. Physics of the dark universe seems to be both geometry and arithmetic. (shrink)

Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both.

The pace of change and, indeed, the sheer number of clinical ethics committees has accelerated during the COVID-19 pandemic. Committees were formed to support healthcare professionals and to operationalise, interpret and compensate for gaps in national and professional guidance. But as the role of clinical ethics support becomes more prominent and visible, it becomes ever more important to address gaps in the support structure and misconceptions as to role and remit. The recent case of Great Ormond Street Hospital for Children (...) NHS Foundation Trust v MX, FX and X, [21]–[23] and [58]) has highlighted the importance of patient/family representation at clinical ethics committee meetings. The court viewed these meetings as making decisions about such treatment. We argue that this misunderstands the role of ethics support, with treatment decisions remaining with the clinical team and those providing their consent. The considered review by clinical ethics committees of the moral issues surrounding complex treatment decisions is not a matter of determining a single ethical course of action. In this article, we consider current legal understandings of clinical ethics committees, explore current concepts of ethics support and suggest how they may evolve, considering the various mechanisms of the inclusion of patients and their representatives in ethics meetings which is not standard in the UK. (shrink)

It may appear that in order to be any way at all, a thing must exist. A possible – worlds version of this claim goes as follows: (E) For every x, for every possible world w, Fx at w only if x exists at w. Here and later in (R), the letter ‘F’ is used as a schematic letter to be replaced with a one – place predicate. There are two arguments against (E). The first is by analogy. Socrates is (...) widely admired now but he does not exist now. So, it is not the case that for every x, for every time t, Fx at t only if x exists at t. Possible worlds are analogous to times. Therefore, (E) is false (cf., Kaplan 1973: 503 – 05 and Salmon 1981: 36 – 40). For the second argument, replace ‘F’ with ‘does not exist’. (E) then says that for every x, for every possible world w, x does not exist at w only if x exists at w. This is obviously false. Therefore (E) is false (cf., Kaplan 1977: 498). Despite their considerable appeal, these arguments are not unassailable. The first argument suffers from the weakness inherent in any argument from analogy; the analogy it rests on may not.. (shrink)

Standard sorites paradoxes can always be put into a simple canonical form, employing the sole inference modus ponens. For example, consider the following paradox. Take a continuum of colours going from red to blue, and let a1,..., am be a sequence of segments of this continuum such that each segment is phenomenologically indistinguishable in colour from its immediate neighbours. Let Fx be the predicate ‘x is red’. Then the untrue conclusion Fam can be inferred from the premises Fa0 and Fan (...) → Fan + 1. (shrink)

Many philosophers of science think that most laws of nature (even those of fundamental physics) are so called ceteris paribus laws, i.e., roughly speaking, laws with exceptions. Yet, the ceteris paribus clause of these laws is problematic. Amongst the more infamous difficulties is the danger that 'For all x: Fx ⊃ Gx, ceteris paribus' may state no more than a tautology: 'For all x: Fx ⊃ Gx, unless not'. One of the major attempts to avoid this problem (and others concerning (...) ceteris paribus laws) is to claim that the subject matter of laws are ascriptions of dispositions, powers, capacities etc., and not the regular behaviour we find in nature. That we do not know whether the cetera are paria in a specific situation does not matter to the dispositionalist because the objects have the disposition regardless of the circumstances. The defence of the latter claim is that dispositions can be instantiated without being manifested. Hence, the laws that ascribe dispositions are strict and it looks as if they do not face the above mentioned problems of ceteris paribus laws. In this essay I attempt to show that these assumptions are wrong. I hope to illustrate that not only does the ceteris paribus clause reoccur inside the dispositions, moreover, there are laws—laws about non-fundamental entities with instable dispositions—which bear a ceteris paribus clause that cannot be hidden in a disposition. (shrink)

This paper outlines an account of numbers based on the numerical equivalence schema (NES), which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, which strongly (...) parallels the minimalist (deflationary) account of truth. One may be tempted to develop the minimalist account in a fictionalist direction, according to which arithmetic is useful but untrue, if taken at face value. In the second part, I argue that this suggestion is not as attractive as it may first appear. The NES suffers from a similar problem to the T-schema: it is deductively weak and does not enable the derivation of any non-trivial generalizations. In the third part of the paper, I explore some strategies to deal with the generalization problem, again drawing inspiration from the literature on truth. In closing this paper, I briefly compare the minimalist to some other accounts of numbers. (shrink)

Climate change is an existential risk reinforced by ordinary actions in afuent societies—often silently present in comfortable and enjoyable habits. This silence is sometimes broken, presenting itself as a nagging reminder of how our habits fuel a catastrophe. As a case in point, global warming has created a state of urgency among wine makers in Spain, as the alcohol level has risen to a point where it jeopardises wine quality and thereby Spanish viticulture. Eforts are currently being made to solve (...) this problem technologically by developing (non-GMO) strains of yeast that produce less alcohol. If successful, this could help save Spanish viticulture. This kind of technological solution is routinely criticised for ofering simplistic “techno-fx” solutions to solve complex societal problems. However, it is not clear what features are criticised by the notion of techno-fx and hence how to avoid this criticism. In our interpretation, the techno-fx notion is not exclusively used as a dismissive term. The notion points to a general virtue of engineering: to create technological solutions that work silently in the background. This asset of technological solutions might sometimes be problematic and sometimes not. Hence, it needs to be analysed case-by-case by paying attention to the moral relevance of the hidden implications of the technology and of the unrefective actions and habits that they facilitate. Such moral analysis will in turn inform strategies for foregrounding this technology to counteract silencing. We discuss what this means in the case of modifying yeast as a viticultural climate resilience strategy. (shrink)

The aim is to uncover the foundations of quine's distinction between definite singular terms and general terms in predicative position, And hence of the general schema of predication, 'fx'. While each term in such a predication specifies its own item, The items so specified exhibit a typical difference exemplified in the basic case by the difference between spatio-Temporal particulars and properties of such particulars. A generally consequential difference of role is that while both terms are applied to the item of (...) lower type, Only the definite singular term has the function of identifying it. (shrink)

The aim is to uncover the foundations of quine's distinction between definite singular terms and general terms in predicative position, And hence of the general schema of predication, 'fx'. While each term in such a predication specifies its own item, The items so specified exhibit a typical difference exemplified in the basic case by the difference between spatio-Temporal particulars and properties of such particulars. A generally consequential difference of role is that while both terms are applied to the item of (...) lower type, Only the definite singular term has the function of identifying it. (shrink)

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural (...) language is what determines both its logical properties and its logical relations to other sentences. The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (e.g., quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx ⊃ Gx)’, ‘Fy’, and ‘Gy’, respectively, where ‘F’, ‘G’, and ‘y’ are all free variables. The argument’s intuitive validity is then explained in virtue of the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language. (shrink)

I november 2020 stod statsminister Mette Frederiksen på en gård i Jylland og kneb en tåre foran den forsamlede presse. Hun havde netop besøgt to generationer af minkfarmere, far og søn, hvis levebrød hun selv lige havde besluttet at slå ned. Var det kynisme eller reelle følelser, der var på spil? Tog statsministeren personligt ansvar for sin egen, svære beslutning, eller var hun en hykler? I denne videnskabeligt funderede debatbog sætter Silas F. Harrebye vores allesammens hykleri under lup. Han skelner (...) mellem forskellige former for hykleri og undersøger, hvad det gør ved demokratiet, at vi ofte er mere optagede af at anklage end at forstå hinanden. Bogen viser, hvorfor vi har brug for flere nuancer i debatten, hvis der skal være plads til politiske visioner og personlig udvikling. Bogen indeholder dybdegående interviews med 8 kendte politikere og meningsdannere som selv har været igennem deciderede shitstorms og anklager om hykleri: Lars Løkke Rasmussen, Pelle Dragsted, Carolina Magdalene Maier, Morten Messerschmidt, Tim Whyte, Rasmus Willig, Anders Gadegaard og Lea Korsgaard. De bliver alle udfordret til at reflektere over både eget og andres hykleri. Derudover præsenterer bogen resultaterne fra en omfattende befolkningsundersøgelse lavet i forbindelse med bogen. Ved hjælp af overraskende teoretiske vinkler og fortolkninger formulerer Silas F. Harrebye et forsvar for hykleriet, som han mener er uundgåeligt og ligefrem kan være politisk produktivt. Som han skriver:?hellere hyklerisk idealist end konsekvent kyniker.? Bogen er skrevet til borgere og fagfolk, der interesserer sig for demokrati, politik og samfund. Den rummer en masse inspiration til at reflektere over de svære valg i livet og blive det, forfatteren kalder?den gode hykler?. Bogen kan oplagt bruges som supplerende litteratur på universiteter og højskoler inden for fx samfundsfag, filosofi og medievidenskab. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:CAUSALITY AND GENERALITY IN THE TREATISE AND THE TRACTATUS In the Tractatus Wittgenstein cryptically rejects the existence of a causal connection (or relation or nexus) : 5.135There is no possible way of making an inference from the existence of one situation to the existence of another, entirely different situation. 5.136There is no causal nexus to justify such an inference. 5.1361 We cannot infer the events of the future from (...) those of the present. Belief stition. Belief in the causal nexus is super1 And he later proceeds to add: 6.37 There is no compulsion making one thing happen because another has happened. The only necessity that exists is logical necessity. What he is claiming can be understood in terms of the "Logical Atomism* of the Tractatus. Atomic sentences, composed of a monadic predicate or a relational predicate and a suitable number of subject terms, represent situations or possible facts. The existence of a represented situation is the ground of truth for (or condition for the truth of or explanation of the truth of) the representing atomic sentence. We can consider 2 such atomic situations or atomic facts to be composed of a monadic property or relational property and an appropriate number of particulars. (This is a matter of some debate among interpreters of the Tractatus, but that issue does not really affect the question at issue in this paper. So, I will simply treat the view in the Tractatus along the lines of Russell's more explicit version of logical atomism in his lectures of 1918.) The world, according to Wittgenstein, is made up of such facts. This is the point of: 1.11The world is the totality of facts, not of things. 1.12The facts in logical space are the world. 1.13The world divides into facts. Consider, then, the claim that a's being F is the cause of its being G. This suggests that we construe causality in terms of a relation between the situations represented by 'Fa' and 'Ga'. With 1C representing a relation or nexus of causality, we could express that situation by: (1)C(Fa, Ga). The existence of the situation represented by (1) would then ground or explain the truth of (1). But that would mean that we recognize a relation of causality and causal relations between facts or situations. I cannot here argue, but will simply assert, that Wittgenstein's logical atomism in the Tractatus is incompatible with the recognition of relations between facts. However, one point that will be relevant to the concerns of this paper is easy to see. Logical atomism involves the claim — 1.21 Each item can be the case or not the case while everything else remains the same. This is not compatible with the recognition of the relation C and a fact grounding the truth of (1), for then Fo and Ga would not be items that were "independent" in the sense of 1.21. Hence, one who holds Wittgenstein's views about the independence of atomic facts cannot recognize causal relations between such facts. Thus, no fact is represented by (1) and C cannot relate atomic facts. The same results would hold if one suggested, in place of (1), that there was a fact corresponding to (2)(X)(Fx * Gx), where we read the arrow as the "causal" arrow — anything's being F causes it to be G. For, if there were a fact corresponding to (2), it would guarantee the link between the purported atomic facts Fa and Ga, since (3)Fa + Ga would be a logical consequence of (2), and we are back to a case like (1), with the arrow replacing 'C. (2) would also be problematic in that it would be some sort of "general" fact, which Wittgenstein also rejects. Thus, as Wittgenstein sees it there is no basis in the world for the explanation of causal statements. If the sentence (4)' (x) (Fx O Gx) ' is a statement of causal law is true, it is so simply because the list of atomic facts will contain the atomic sentence 'Ga' if it contains 'Fa'. That is, (4) is true, not because of any special fact corresponding to (5)(X... (shrink)

In the last few years repeated scandals have rocked their worlds of many industries. Stories which have hit the headlines recently have included news of * Deliberate cheating by car makers to evade emissions tests * LIBOR and FX manipulation by bankers * Falsification of drug testing results plus allegations of bribery and corruption in major pharmaceutical corporations * Unlawful tapping of phones of the famous by newspapers * Cover-ups over high death rates in hospitals. While it is not always (...) obvious what has gone wrong, there is no disguising the widespread impact on many stakeholders, and the catastrophic loss of trust and sense of betrayal that results. Matt Nixon has had a privileged insider seat in several of the organizations which came to suffer major crises, crises which inspired deep emotional responses. (shrink)

The proof of correctness and completeness of a logical calculus w.r.t. a given semantics can be read as telling us that the tautologies (or, more gen erally, the relation of consequence) specified in a model theoretic way can be equally well specified in a proof theoretic way, by means of the calculus (as the theorems, resp. the relation of inferability of the calculus). Thus we know that both for the classical propositional calculus and for the clas sical predicate calculus theorems (...) and tautologies represent two sides of the same coin. We also know that the relation of inference as instituted by any of the common axiom systems of the classical propositional calculus coin cides with the relation of consequence defined in terms of the truth tables; whereas the situation is a little bit more complicated w.r.t. the classical predicate calculus (the coincidence occurs if we restrict ourselves to closed ∀xFx is inferable from Fx without being its conse formulas; otherwise.. (shrink)

Although ‘Rxx’ and ‘Rxy’ are both applications of a two-place predicate to a pair of terms, ‘Rxx’ resembles a one-place predicate in that all one needs to evaluate it is an assignment to ‘x’. A similar point applies to the sequences ‘Fx’, ‘Gx’ and ‘Fx’, ‘Gy’ – even though neither is a one-place predicate. Kit Fine’s semantic relationalism aims to extract a common idea uniting these comparisons, and to use it to provide a Millian solution to Frege’s Puzzle.

Many philosophers of science think that most laws of nature (even those of fundamental physics) are so called ceteris paribus laws, i.e. roughly speaking, laws with exceptions. Yet, the ceteris paribus clause of these laws is problematic. Amongst the more infamous difficulties is the danger that ‘For all x: Fx then Gx, ceteris paribus’ may state no more than a tautology: ‘For all x: Fx then Gx, unless not’. One of the major attempts to avoid this problem (and others concerning (...) ceteris paribus laws) is to claim that the subject matter of laws are ascriptions of dispositions, powers, capacities etc., and not the regular behaviour we find in nature. That we do not know whether the cetera are paria in a specific situation does not matter to the dispositionalist because the objects have the disposition regardless of the circumstances. The defence of the latter claim is that dispositions can be instantiated without being manifested. Hence, the laws that ascribe dispositions are strict and it looks as if they do not face the above mentioned problems of ceteris paribus laws. In this chapter I attempt to show that these assumptions are wrong. I hope to illustrate that not only does the ceteris paribus clause reoccur inside the dispositions, moreover, there are laws – laws about non-fundamental entities with instable dispositions – which bear a ceteris paribus clause that cannot be hidden in a disposition. (shrink)

The purpose of this paper is threefold. First, I visit the Fogelin–Geach-dispute, criticizeMiller''s interpretation of the Geachian notationN(x:N(fx)) and conclude that Fogelin''s argumentagainst the expressive completeness of the Tractariansystem of logic is unacceptable and that the adoptionof the Geachian notation N(x:fx) would not violate TLP5.32. Second, I prove that a system of quantificationtheory with finite domains and with N as the solefundamental operation is expressively complete. Lastly, I argue that the Tractarian system is apredicate-eliminated many-sorted theory (withoutidentity) with finite domains (...) and with N as the solefundamental operation, and thus is expressivelycomplete. (shrink)

A closed λ-term E is called an enumerator if M ε /gL/dg /gTn ε N E/drn/dl = β M. Here Λ° is the set of closed λ-terms, N is the set of natural numbers and the /drn/dl are the Church numerals λfx./tfnx. Such an E is called reducing if moreover M ε /gL/dg /gTn ε N E/drn/dl /a/gb M. In 1983 I conjectured that every enumerator is reducing. An ingenious recursion theoretic proof of this conjecture by Statman is presented in (...) Barendregt . The proof is not intuitionistically valid, however. Dirk van Dalen has encouraged me to find intuitionistic proofs whenever possible. In the lambda calculus this is usually not difficult. In this paper an intuitionistic version of Statmans proof will be given. It took me somewhat longer to find it than in other cases. (shrink)

In Quantifiers and Propositional Attitudes, Quine held (a) that the rule of exportation is always admissible, and (b) that there is a significant distinction between a believes-true (Ex)Fx and (Ex) a believes-true F of x. An argument of Hintikka's, also urged by Sleigh, persuaded him that these two intuitions are incompatible; and he consequently repudiated the rule of exportation. Hintikka and Kaplan propose to restrict exportation and quantifying in to favoured contexts — Hintikka to contexts where the believer knows who (...) or what the person or thing in question is; Kaplan to contexts where the believer possesses a vivid name of the person or thing in question. The bulk of this paper is taken up with criticisms of these proposals. Its ultimate purpose, however, is to motivate an alternative approach, which imposes no restrictions on exportation or quantifying in, but repudiates Quine's other intuition: this is the approach taken in my A Logical Form for the Propositional Attitudes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 448-449 [Access article in PDF] James Van Cleve. Problems from Kant. New York and Oxford: Oxford University Press, 1999. Pp. xii + 340. Cloth, $45.00. The author acknowledges his debt to the "great Kant books of the 1960s, Jonathan Bennett's Kant's Analytic, and P. F. Strawson's The Bounds of Sense."Their analytical spirit lives on in this book, but the analyses are (...) fresh, take surprising turns, and make unexpected connections to current concerns. In seventeen chapters Van Cleve deals with necessity and the a priori, space and geometry, incongruent counterparts, time, the ideality of matter, experience and objects, substance in the First Analogy, the Second Analogy, noumena, problems of the self, rational theology, and Kant and contemporary irrealism. To sustain the flow of argument, the discussion of certain details, often important, is postponed and taken up in fifteen appendices, and there are nearly seventy pages of careful notes.Chapter 10, "Noumena and Things in Themselves," (134 ff.) criticizes in detail the prevailing "one world" or "double aspect" view of objects, namely that Kant allows just one set of objects, but two ways of "considering" them. Things in themselves are the very same objects as appearances, but considered as they are independent of our experience of them, a view developed in Henry Allison's Kant's Transcendental Idealism. Against this Van Cleve maintains (and I concur) that "appearances are intentionalia, and that intentionalia are constructions out of states of perceivers" (150). The distinction is between two separate universes of discourse, "not between two ways of discoursing [End Page 448] about the same objects" (ibid.). There is no space to report the sharply argued detail that led him to hold the double aspect view to be unfathomable and incoherent. He takes Kant to be a phenomenalist but holding to a version far removed from the reductionist phenomenalism of Russell, Broad, Price, and others. Here the basic elements are not made out to be indubitable givens, but are, rather, sensations. The structures built on them are, according to Van Cleve, "virtual objects" in the sense in which Quine speaks about "virtual classes." To say that something is an element of a class {F:Fx} is only to say that it is F. So, likewise, to say that, e.g., a patch of red exists is short for saying that a certain representation occurs. Carnap's Kantian masterpiece, TheLogical Structure of the World (The Aufbau) could have been consulted as a comprehensive guide to the kind of virtuality here envisaged.It is Van Cleve's stated aim never to discuss Kantian arguments without making their premise and conclusion structure clear (viii). Quite a few of them he finds persuasive; in other cases the arguments are valid, but one or the other premise doubtful. Sometimes he sides with Kant against his critics, sometimes the opposite, and occasionally, as in the case of the Second Analogy, it remains unclear what Kant's argument was. He has shown in this and earlier publications that all reconstructions are flawed, so that either Kant had no good argument, or his argument has not yet been discovered.The title Problems from Kant must be taken seriously. The book rarely deals with textual problems, historical context, or translation difficulties. Rather, the focus is on perennial and still compelling problems. Themes from the First Critique are tracked to and connected with current concerns and sometimes recently ventilated issues are traced back to Kant, as in the last chapter, where the question is raised if Kant was an internal realist in the style of Putnam, or perhaps an anti-realist like Dummett. The contrast with Kant shows that like all complex positions, these are shopping baskets with several goods in them, some in Kant's inventory, others not.Logical notation is used sparingly, and only where it clarifies—no attempt here to shoehorn arguments into unneeded symbolism. Deft examples, Kant's weakness, are a strength of this book. To explain the logic of considering Van Cleve asks, "Consider me apart from my shoes, am I barefoot... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:IT AIN'T NECESSITY, SO... (With Apologies to George Gershwin) I shall argue in this paper that what Hume calls the idea of necessary connection is mislabelled, and that what he ought to call the idea of necessary connection is not so labelled. My argument is not that there are, on Hume's view, real necessary connections between causes and their effects but rather that there is an idea of genuine (...) necessary connection — what I call logical necessity — which we all mistakenly believe extends to causal connections. The genesis of this mistake is given a psychological explanation in the Treatise. Precisely how does Hume account for the origin of what he calls our idea of necessary connection? I have argued elsewhere that, whatever the answer, it has little philosophical importance. My reason was that, given Hume's view that causal connections are not necessary, the question must be viewed as one within psychology. Recent work on Hume, however, has convinced me that my former opinion was much too quick. Imlay, for example, has challenged Hume's distinction between demonstrative and probable inference on the grounds that Hume gives only one account of necessity for both 2 mathematical and lawlike truths. As I now see much more clearly, there are important philosophical distinctions that must be made in any full explication of Hume's view of the origin of our idea of causal necessity. I shall attempt an answer to the lead question of the second paragraph. My strategy is as follows. I shall first present a synopsis of Hume's account of our belief in causal necessity. Next, I shall develop 87. 88. a view of logical necessity. Finally, I shall briefly examine the exact genesis of the confusion between logical and causal necessity. Consider the following three propositions: (1)Hume does not believe that there are necessary causal connections. (2)All statements of laws of nature are on Hume's view descriptions of constant conjunctions, the logical form of which is captured by the Russellian " (x) [fx => gx]." (3)This logical form captures Hume's first definition of "cause." On these three propositions I and many other philosophers agree. I and an ever-shrinking number of philosophers also believe that Hume is right. But everyone, according to Hume, in some sense believes that causal connections are necessary; the Humean philosopher knows they are not but acts otherwise, while the ordinary person simply acts without the knowledge. Since everyone believes what is false, only a psychological explanation can be given for why we believe it anyway. Thus, Hume's second definition of "cause", and the view that the idea of necessity arises from the determination of the mind to pass from the impression of a cause to an idea of 3 its effect. The three most salient passages from the Treatise on the production of the idea of necessary connection follow. As we shall see, these passages cannot be understood without considering a number of others. For after a frequent repetition, I find, that upon the appearance of one of the objecte, the mind is determin 'd by custom to consider its usual attendant, and to consider it in a stronger light upon account of 89. its relation to the first object. 'Tis this impression, then, or determination, which affords me the idea of necessity. (T 156) Tho ' the several resembling instances, which give rise to the idea of power, have no influence on each other, and can never produce any new quality in the object, which can be the model of that idea, yet the observation of this resemblance produces a new impression in the mind, which is its real model. For after we have observ 'd the resemblance in a sufficient number of instances, we immediately feel a determination of the mind to pass from one object to its usual attendant, and to conceive it in a stronger light upon account of that relation. This determination is the only effect of the resemblance; and therefore must be the same with power or efficacy, whose idea is deriv 'd from the resemblance. The several instances of resembling conjunctions leads us into the notion of power and necessity.... Necessity, then... (shrink)

The central part of any cosmological argument for the existence of God is the inference of a conclusion of the form 1(ᴲx)-Fx from a premiss of the form 1 (ᴲx)Fx'. Since the premiss here is known only a posteriori, such an argument would ordinarily be classified as itself a posteriori. But I point out that any argument of this form may by a trivial modifi- cation be turned into an argument which requires no a posteriori premisses, and that the modified (...) version is in fact a less misleading presentation of the reasoning involved. I conclude that cosmological arguments are best viewed as a priori arguments. (shrink)

At samle artikler til en bog om filosofiens anvendelighed signalerer, at det ikke er en selvfølge, at man kan anvende filosofi enten til eller på noget. Fx at anvende den til at opnå ønskelige hensigter. Eller at anvende den på problemstillinger, der dukker op i løbet af et menneskeligt liv, og ikke kan løses på anden eller i hvert fald på en bedre måde. Bogens hensigt er at undersøge, om filosofi kan anvendes på hvilke problemstillinger og til at opnå hvilke (...) ønskelige resultater. Bogens elleve forskellige artikler søger at besvare begge disse spørgsmål fra lige så mange forskellige perspektiver og på lige så mange forskellige måder. Om der er underliggende ligheder mellem disse svar, hvori der måske aftegner sig en fælles grund for filosofiens anvendelighed - skal være overladt til læserens opdagelseslyst. (fra Forlaget). (shrink)

Blandt de værker, der er overleveret under Platons navn, er den forholdsvis ukendte Theages. Det er en ganske kort dialog, som ikke desto mindre behandler et kernespørgsmål i Platons forfatterskab: Hvordan opnår man visdom? Den har tydelige referencer til en række kendte passager i Platons værk, fx iForsvarstalen, Symposion, Staten og Theaitetos. Desuden viser den nogle af de berømteste sider af Platons Sokrates: Hans guddommelige tegn, hans særlige ironi, hans forhold til sofisterne og til de mennesker, der vil følge ham. (...) Dialogen er både filosofisk og litterært vanskelig at fortolke og er ofte blevet anset for uægte. Den platoniske dialog Theages giver en oversættelse af dialogen, gennemgår dens forskningshistorie og fortolker den gennem en omhyggelig læsning og en diskussion af dens vigtigste temaer. Bogen viser, hvordan de sidste århundreders forskning direkte eller indirekte har været afhængig af spørgsmålet om ægthed. I modsætning hertil argumenterer forfatteren for, at den rette forståelse af dialogen bedst findes på baggrund af Platons samlede værk, uafhængigt af forfatterspørgsmålet. Således giver bogen også et overblik over den nyere Platon-forskning og en indføring i en række væsentlige temaer hos Platon. (shrink)

All metaphors have the logical form “metaphorically, Fx”. “Metaphorically” is a modal operator. If “F” literally denotes the property F and metaphorically denotes the property G, “Metaphorically, Fx” says that x is G in reality because in its home world (Wx) it is F, when (1) x being F is manifest in Wx (2) it is a law of Wx that being F causes being G (3) being G in Wx is essential to x, hence it is G in all (...) possible worlds. For example, Emily Dickinson says that her life is (metaphorically) a loaded gun. This means that the entity x that in the real world is her life, is in its home‐world a loaded gun. A loaded gun is lethal, a trait x manifests in its home world. Therefore in the real world, too, where it is not a loaded gun but a life, x is lethal and, though deceptively (as a life) calm, it is truly dangerous. (shrink)

This paper outlines an account of numbers based on the numerical equivalence schema, which consists of all sentences of the form ‘#x.Fx=n if and only if ∃nx Fx’, where # is the number-of operator and ∃n is defined in standard Russellian fashion. In the first part of the paper, I point out some analogies between the NES and the T-schema for truth. In light of these analogies, I formulate a minimalist account of numbers, based on the NES, which strongly parallels (...) the minimalist account of truth. One may be tempted to develop the minimalist account in a fictionalist direction, according to which arithmetic is useful but untrue, if taken at face value. In the second part, I argue that this suggestion is not as attractive as it may first appear. The NES suffers from a similar problem to the T-schema: it is deductively weak and does not enable the derivation of any non-trivial generalizations. In the third part of the paper, I explore some strategies to deal with the generalization problem, again drawing inspiration from the literature on truth. In closing this paper, I briefly compare the minimalist to some other accounts of numbers. (shrink)

Get the results your camera was meant to deliver With the D700, you've stepped up to a high-performance camera. The possibilities offered by its 12.1-megapixel, FX-format CMOS sensor are exhilarating. This guide helps you take full advantage of every feature you paid for, offering clear and comprehensive directions for setting up the camera, choosing modes, selecting lenses, and much more. With detailed guidance for working with lighting, exposure, and depth of field plus advanced shooting techniques for many different situations, it's (...) your camera's perfect partner. Customize the D700's settings and learn how to use them all Maximize Live View and use single-point and dynamic-area autofocus Explore original, optional, and custom picture controls Investigate wide-angle lenses, VR and DX lenses, filters, and lens accessories Learn secrets for getting great shots of sporting events, concerts, wildlife, products, and people. (shrink)

Paraconsistent logics are logics that can be used to base inconsistent but non-trivial systems. In paraconsistent set theories, we can quan- tify over sets that in standard set theories, if consistent, would lead to contradictions, such as the Russell set, R = fx : x =2 xg. Quasi-set theories are mathematical systems built for dealing with collections of indiscernible elements. The basic motivation for the development of quasi-set theories came from quantum physics, where indiscernible entities need to be considered. Usually, (...) the way of dealing with indiscernible objects within clas- sical logic and mathematics is by restricting them to certain structures, in a way so that the relations and functions of the structure are not sufficient to individuate the objects; in other words, such structures are not rigid. In quantum physics, this idea appears when symmetry conditions are introduced, say by choosing symmetric and anti-symmetric functions in the relevant Hilbert spaces. But in standard mathematics, such as that built in Zermelo-Fraenkel set theory, any structure can be extended to a rigid structure. That means that, although we can deal with certain objects as they were indiscernible, we realize that from out- side of these structures these objects are no more indiscernible, for they can be individualized in the extended rigid structures: ZF is a theory of individuals, distinguishable objects. In quasi-set theory, it seems that there are structures that cannot be extended to rigid ones, so it seems that they provide a natural mathematical framework for expressing quantum facts without certain symmetry suppositions. There may be situations, however, in which we may need to deal with inconsistent bits of infor- mation in a quantum context, even if these informations are concerned with ways of speech. Furthermore, some authors think that superposi- tions may be understood in terms of paraconsistent logics, and even the notion of complementarity was already treated by such a means. This is, apparently, a nice motivation to try to merge these two frameworks. In this work, we develop the technical details, by basing our quasi-set theory in the paraconsistent system C1. We also elaborate a new hierarchy of paraconsistent calculi, the paraconsistent calculi with indiscernibility. For the finalities of this work, some philosophical questions are outlined, but this topic is left to a future work. (shrink)