This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework within which his technical contributions were conceived and developed has been so deep that he has a strong case (...) to be regarded as the inventor of much of the agenda of modern analytical philosophy itself. The continuing importance of the Grundgesetze lies not only in its bearing on issues in the foundations of mathematics but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. (shrink)
This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form (...) of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program. (shrink)
It has been proposed that inferring personal authorship for an event gives rise to intentional binding, a perceptual illusion in which one’s action and inferred effect seem closer in time than they otherwise would . Using a novel, naturalistic paradigm, we conducted two experiments to test this hypothesis and examine the relationship between binding and self-reported authorship. In both experiments, an important authorship indicator – consistency between one’s action and a subsequent event – was manipulated, and its effects on binding (...) and self-reported authorship were measured. Results showed that action-event consistency enhanced both binding and self-reported authorship, supporting the hypothesis that binding arises from an inference of authorship. At the same time, evidence for a dissociation emerged, with consistency having a more robust effect on self-reports than on binding. Taken together, these results suggest that binding and self-reports reveal different aspects of the sense of authorship. (shrink)
This is a reply to Vincent Carraud/René Verdon « Remarques circonspectes sur la mort de Descartes » (published in Revue du dix-septième siècle, n° 265, 2014/4, pp. 719-726, online: http://www.cairn.info/revue-dix-septieme-siecle-2014-4-page-719.htm, containing a critique of my "L'énigme de la mort de Descartes" Paris, 2011). I discuss the fatal illness and the death of Descartes, arguing that Descartes was very probably the victim of arsenical poisoning. The suspected murderer is a French priest, François Viogué, living with Descartes in 1650 at the French (...) embassy in Stockholm who may have seen in Descartes an obstacle to the hoped for conversion of queen Christina of Sweden. As against Carraud/Verdon I stress the medical facts, in particular the fact that Descartes himself seems to have suspected poisoning, since he asked for an emetic shortly before his death. (shrink)
A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
In 1885, Georg Cantor published his review of Gottlob Frege's Grundlagen der Arithmetik . In this essay, we provide its first English translation together with an introductory note. We also provide a translation of a note by Ernst Zermelo on Cantor's review, and a new translation of Frege's brief response to Cantor. In recent years, it has become philosophical folklore that Cantor's 1885 review of Frege's Grundlagen already contained a warning to Frege. This warning is said to concern the defectiveness (...) of Frege's notion of extension. The exact scope of such speculations varies and sometimes extends as far as crediting Cantor with an early hunch of the paradoxical nature of Frege's notion of extension. William Tait goes even further and deems Frege 'reckless' for having missed Cantor's explicit warning regarding the notion of extension. As such, Cantor's purported inkling would have predated the discovery of the Russell-Zermelo paradox by almost two decades. In our introductory essay, we discuss this alleged implicit (or even explicit) warning, separating two issues: first, whether the most natural reading of Cantor's criticism provides an indication that the notion of extension is defective; second, whether there are other ways of understanding Cantor that support such an interpretation and can serve as a precisification of Cantor's presumed warning. (shrink)
This paper is a historical, legal and philosophical analysis of the concept of human dignity in German and Kenyan constitutional law. We base our analysis on decisions of the Federal Constitutional Court of Germany, in particular its take on life imprisonment and its 2006 decision concerning the shooting of hijacked airplanes, and on a close reading of the Constitution of Kenya. We also present a dialogue between us in which we offer some critical remarks on the concept of human dignity (...) in the two constitutions, each one of us from his own philosophical perspective. (shrink)
In this paper I will argue that Boghossian's explanation of how we can acquire a priori knowledge of logical principles through implicit definitions commits a transmission of warrant-failure. To this end, I will briefly outline Boghossian's account, followed by an explanation of what a transmission of warrant-failure consists in. I will also show that this charge is independent of the worry of rule-circularity which has been raised concerning the justification of logical principles and of which Boghossian is fully aware. My (...) argument comes in two steps: firstly, I will argue for the insufficiency of Boghossian's template which is meant to explain how a subject can acquire a warrant for logical principles. I will show however that this insufficiency of his template can be remedied by adopting what I call the Disquotational Step. Secondly, I will argue that incorporating this further step makes his template subject to a transmission of warrant-failure, assuming that certain rather basic and individually motivated principles hold. Thus, Boghossian's account faces a dilemma: either he adopts the Disquotational Step and subjects his account to the charge of a transmission of warrant-failure, or he drops this additional step leaving the account confronted with explaining the gap that has previously been highlighted. I will then suggest various rejoinders that Boghossian might adopt but none of which - I will argue - can resolve the dilemma. Lastly, I will raise and briefly discuss the question whether this worry generalizes to other accounts, such as Hale and Wright's that aim to explain our knowledge of logic and/or mathematics in virtue of implicit definitions. (shrink)
The existence of predatory animals is a problem in animal ethics that is often not taken as seriously as it should be. We show that it reveals a weakness in Tom Regan's theory of animal rights that also becomes apparent in his treatment of innocent human threats. We show that there are cases in which Regan's justice-prevails-approach to morality implies a duty not to assist the jeopardized, contrary to his own moral beliefs. While a modified account of animal rights that (...) recognizes the moral patient as a kind of entity that can violate moral rights avoids this counterintuitive conclusion, it makes non-human predation a rights issue that morally ought to be subjected to human regulation. Jennifer Everett, Lori Gruen and other animal advocates base their treatment of predation in part on Regan's theory and run into similar problems, demonstrating the need to radically rethink the foundations of the animal rights movement. We suggest to those who, like us, find it less plausible to introduce morality to the wild than to reject the concept of rights that makes this move necessary to read our criticism either as a modus tollens argument and reject non-human animal rights altogether or as motivating a libertarian-ish theory of animal rights. (shrink)
The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status over the (...) other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)
In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and (...) explain how it differs from the role played by extensions in his earlier book “Die Grundlagen der Arithmetik”. Lastly, we will demonstrate that this hitherto neglected yet foundational aspect of Frege’s use of Basic Law V helps to resolve a number of important interpretative challenges in recent Frege scholarship, while also shedding light on some important differences between Frege’s logicism and recent neo-logicist approaches to the foundations of mathematics. (shrink)
Belief in free will is widespread. The present research considered one reason why people may believe that actions are freely chosen rather than determined: they attribute randomness in behavior to free will. Experiment 1 found that participants who were prompted to perform a random sequence of actions experienced their behavior as more freely chosen than those who were prompted to perform a deterministic sequence. Likewise, Experiment 2 found that, all else equal, the behavior of animated agents was perceived to be (...) more freely chosen if it consisted of a random sequence of actions than if it consisted of a deterministic sequence; this was true even when the degree of randomness in agents’ behavior was largely a product of their environments. Together, these findings suggest that randomness in behavior—one’s own or another’s—can be mistaken for free will. (shrink)
In this paper, we present the results of two surveys that investigate subjects’ judgments about what can be known or justifiably believed about lottery outcomes on the basis of statistical evidence, testimonial evidence, and “mixed” evidence, while considering possible anchoring and priming effects. We discuss these results in light of seven distinct hypotheses that capture various claims made by philosophers about lay people’s lottery judgments. We conclude by summarizing the main findings, pointing to future research, and comparing our findings to (...) recent studies by Turri and Friedman. (shrink)
The paper discusses the active part in the process of perceiving, usually expressed by the Greek word krinein. It is argued that krinein in one of its uses means "to judge" in the sense of judging a case, i. e. deciding it. It is not used for making statements. A second meaning of the Greek word is that of discerning or discriminating, and it is this meaning that plays a central part in Aristotle's theory of perception.
The paper discusses Habermas` contribution to a debate between him and Joseph Ratzinger, at the time the prefect of the Congregation for the Catholic faith. Habermas is criticized for his tendency to adopt openly anti-enlightenment positions.
This paper discusses the reports in Diogenes Laertius and in Sextus Empiricus concerning the classification of propositions. It is argued that the material in Sextus uses a source going back to the Dialectical school whose most prominent members were Diodorus Cronus and Philo of Megara. The material preserved in Diogenes Laertius, on the other hand, goes back to Chrysippus.
This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.
This is a critique of Michael Wolff's ideas on Kant and Aristotle. I criticize in particular his overestimation of Kant as a logician and his claim that Aristotle wants to offer proofs for his perfect syllogisms.
The reason for Aristotle’s treatment of (traditional) fourth figure syllogisms as first figure syllogisms with inverted terms in the conclusion is the following: To disprove the conclusiveness of a premiss pair Aristotle formulates two triplets of true propositions such that two of them correspond to the premiss pair in question and that the third proposition corresponding to a conclusion is an a-proposition in the first case, an e-proposition in the other. Since the truth of an a-proposition grants the falsity of (...) the contrary e- and of the contradictory o-proposition, the first triplet offers two counter-instances for invalid syllogisms with true premisses and false conclusions. Similarly the true e-proposition grants the falsity of an a- and an i-conclusion. Since an a-proposition can be converted to an i-proposition and an e-proposition is equivalent to its converse, these first figure triplets also disprove any first figure syllogism with converted conclusions, with the exception of o-conclusions. The invalidity of the latter ones, however, can be shown by using premiss conversions of (invalid) second and third figure syllogisms. The proposed explanation also makes clear why there are no rejection proofs for invalid syllogisms of (traditional) fourth figure syllogisms in the Analytics. (shrink)
In this paper, we discuss the fact that not only adverbially quantified sentences with singular indefinites or bare plurals but also ones containing plural definites show Quantificational Variability Effects, that is, they receive readings according to which the quantificational force of the respective DP seems to depend on the quantificational force of the Q-adverb. We show that if the Q-adverb is a frequency adverb like usually, there is strong evidence that QVEs come about as indirect effects of a quantification over (...) situations. This conclusion is based on the fact that in such cases the availability of QVEs is constrained in ways that have no parallel in sentences containing adverbs of quantity like for the most part or quantificational DPs instead of frequency adverbs. We show that these constraints can be derived from plausible assumptions about how the situations to be quantified over are constrained: they have to be located in time on the basis of the most specific locally available information, and their running times are not allowed to overlap. (shrink)
This paper (1) criticizes Patzig's explanation of Aristotle's reason for calling his first figure syllogisms perfect syllogisms, i.e. the transitivity relation: it can only be used for Barbara, not for the other three moods. The paper offers (2) an alternative interpretation: It is only in the case of the (perfect) first figure moods that we can move from the subject term of the minor premiss, taken to be a predicate of an individual, to the predicate term of the major premiss. (...) This contention is supported (i) by Aristotle's wording of the dictum de omni et nullo and (ii) by Aristotle's use of a formula which puts the minor term in the first position when he first states Barbara and Celarent. (shrink)
This is a German translation with commentary of Aristotle’s Prior Analytics, Book I. The introduction ('Einleitung', pp. 97–182) contains a concise history of the reception of Aristotle’s syllogistic from Theophrastus to Kant and Hegel. The commentary places special attention to the modal chapters (i. e. I 3 and 8–22). Aristotle’s modal syllogistic is treated with more sympathy than in other modern commentaries and discussions of this part of Aristotle’s logic.
Kant’s Categorical Imperative (CI) is to be taken as a necessary and sufficient condition for any action that is permissible, i. e. not prohibited. The class of permissible actions contains actions which are allowed as well as those which are morally required. If to perform an action and to abstain from this action can be taken to be ‘practical opposites’, then an action that is morally required for, a duty, is an action whose practical opposite is prohibited, and vice versa. (...) The class of actions which are merely allowed (neither prohibited nor morally required for) contains all and only those actions who together with their practical opposites belong to the class of permissible (not prohibited) actions. The paper then adduces passages from Kant’s ethical writings on the CI supporting these distinctions. (shrink)
This paper discusses the question why the first edition of Descartes' Meditations carries a title announcing a proof of the immortality of the soul, whereas Descartes himself (in the Synopsis as well as in his Replies) explicitly denies any intention to deliver such a proof. In the first part of the paper, I refute existing attempts to explain this inconsistency. In the second part, I argue that it was Descartes' intention to announce a proof for the immaterialitas, not for the (...) immortalitas of the soul, and that the first of these two words has been misread, probably by the Paris printer, and turned into immortalitas. I first adduce as evidence a remark by Baillet in his second (abbreviated) version of Descartes' biography, a remark that has hitherto gone unnoticed in the learned literature. (Baillet explicitly states, using French words indeed, that immortalitas/immortalité was put instead of immaterialitas/immaterialité.) I secondly point to three statements by Descartes concerning either the Meditations or the content of metaphysics generally; Descartes mentions the immateriality of the soul on all three occasions. -/- . (shrink)
The paper starts from a distinction between two terms in Aristotle: kategoroumenon and kategoria. It is argued that the job of the first is to pick out 'predicated predicates' (i.e. predicates attached to a specific subject), the job of the second is to designate 'predicable predicates' (terms which can be attached to specific subjects). It is then argued (1) that Aristotle's division of the (erroneously) so-called 'predicables' (i. e. genus, proprium, definiens, accident) is a classification of predicated predicates, (2) that (...) the list of the "genera of kategoriai" in Top. I 9 which starts with ti estin (essence) as its first member contains a classification of predicable predicates, and (3) that the list in Cat. 4 (starting with ousia, 'substance') is a classification not of kategoriai, but of things there are. (shrink)
This paper raises and then discusses a puzzle concerning the ontological commitments of mathematical principles. The main focus here is Hume's Principle—a statement that, embedded in second-order logic, allows for a deduction of the second-order Peano axioms. The puzzle aims to put pressure on so-called epistemic rejectionism, a position that rejects the analytic status of Hume's Principle. The upshot will be to elicit a new and very basic disagreement between epistemic rejectionism and the neo-Fregeans, defenders of the analytic status of (...) Hume's Principle, which will provide a new angle from which properly to assess and re-evaluate the current debate. (shrink)
It is argued that recollection in Plato's "Meno" is used as a metaphor, though not one for a priori knowledge: the point of comparison is the analogy between the processes of learning in the sense of coming to know from an error and recollecting something one has forgotten. Recollecting in this sense as well as correcting an error implies the becoming aware of a lack of knowledge previously unnoticed. It is shown that the geometry lesson (82b9-85b7) is intended to bring (...) out this analogy. It is argued further that the error to be corrected by the staging of the geometry lesson is an error of Meno's concerning the nature of knowledge. It is finally argued that Socrates' speech in 81a5-d5 is a parody of a Gorgian speech and that the learning-is-recollection statement in this passage is an allegorical conceit in the manner of Gorgias and Empedocles. (shrink)
forthcoming in M. McNamee (ed) Philosophy, Risk and Adventure Sports, Routledge The final draft of a co-authored article with Simon Robertson (Leeds). In this paper we examine a recent version of an old controversy within climbing ethics. Our organising topic is the ‘bolting’….
The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)
In this short letter to Ed Zalta we raise a number of issues with regards to his version of Neo-Logicism. The letter is, in parts, based on a longer manuscript entitled “What Neo-Logicism could not be” which is in preparation. A response by Ed Zalta to our letter can be found on his website: http://mally.stanford.edu/publications.html (entry C3).
The paper tries to defend the critical rationalism of Popper and Albert against criticisms brought forward by Janich/Kambartel/Mittelstrass in a series of articles entitled: Wissenschaftstheorie als Wissenschaftskritik, Aspekte 1972 - since published as a book. These authors try to overcome the trilemma of infinite regress, circular reasoning and axiomatic foundation which confronts any attempt to base scientific foundations on reasons: they claim that this trilemma is due to an "extremely limited concept of reasoning" which can be overcome by using the (...) notion of the 'defence' of a statement. Against this it is shown that the proposed solution is based on a mere an inadmissible shifting of the burden of proof in scientific reasoning. (shrink)
The paper takes up a proposal made in 1936 by Guido Calogero concerning Parmenides 8.34-41 DK. According to Calogero, these verses should be placed behind 8.52 DK. Calogero's conjecture has gone unnoticed in the bulk of the Parmenides literature. I defend this transposition, partly enlarging Calogero's arguments, and discuss the philosophical implications of moving this text to the beginning of the doxa part of Parmenides' poem.
This monograph discusses the sources for ancient propositional logic, mainly in Sextus Empiricus and Diogenes Laertius bk. VII. It is argued that most of the sources in Sextus which have hitherto been taken to be sources for Stoic logic either do not report Stoic logic at all or report pre-Chrysippean Stoic logic. These texts report (in the first case) a group labelled the Dialecticians whose most prominent members were Diodorus Cronus and Philo or else (in the second case) early Stoic (...) logicians heavily influenced by the Dialecticians. The texts discusssed concern the theory of signs, the theory of proof and the classifications of propositions and of arguments. (shrink)
In this paper I argue that the Stoic theory of signs as reported by Sextus Empiricus in AM and in PH belongs to Stoic logicians which precede Chrysippus. I further argue that the PH-version of this theory presupposes the version in AM and is an attempt to improve the older theory. I tentatively attribute the PH-version to Cleanthes and the AM-version to Zeno. I finally argue that the origin of this Stoic theory is to be found in the Dialectical school (...) (probably Philo of Megara) whose theory of signs has been preserved in Pseudo-Galen, Historia philosopha cap. 9. (shrink)
This paper argues that Plato’s Meno does not offer evidence for a belief, commonly attributed to Plato, that we when learning something recollect what we learn from previous existences. This “theory of recollection” is a construct based on a reading of the relevant passages in the Meno which does not take into account the dialectical aspect of Socrates’ discussion with his interlocutor. And in one passage (81e3) it is based on a variant reading for which a better and better attested (...) reading is available. The reference to recollection is used to make Meno agree to an absurd position. (shrink)
The article demonstrates that the dominance approach—often used for the measurement of welfare in a population in which there are different household types (see e.g., Atkinson and Bourguignon, Arrow and the foundations of the theory of economic policy, 350–370, 1987)—can be based on explicit value judgments on the households’ living standard. We define living standard by equivalent income (functions) and consider classes of inequality averse social welfare functions: Welfare increases if the inequality of living standard is decreased. In this framework, (...) we suggest three new dominance criteria and obtain characterizations of second degree stochastic dominance and of two criteria proposed by Bourguignon (Journal of Econometrics 42:67–80, 1989). (shrink)
This article explores whether the notion of the decent society as a normative concept is applicable under late modern conditions of normative pluralization and individualization. My argument is that the strength of the concept does not primarily lie in its descriptive value. It is rather a ‘utopian horizon’ against which aspects of societies can be analysed. This analytical value can tell us something about the state of various facets of social life. Having to cope with pluralization, individuals are increasingly required (...) to negotiate ambiguous and contradictory norms. It is this negotiation process that defines to a large extent various aspects of contemporary individualization. However, the fact that an individualized negotiation process occurs neither means that this process is characterized by decency nor produces by default a decent society nor a genuine sense of social integration. Thus, I argue that the concept ‘decency’ can make a qualitative addition to normative negotiation processes and thus in terms of social integration. (shrink)
This paper introduces and evaluates two contemporary approaches of neo-logicism. Our aim is to highlight the diﬀerences between these two neo-logicist programmes and clarify what each projects attempts to achieve. To this end, we ﬁrst introduce the programme of the Scottish school – as defended by Bob Hale and Crispin Wright1 which we believe to be a..