It is commonly accepted, after Frege, that identity statements like “Tully is Cicero” differ from statements like “Tully is Tully”. For the former, unlike the latter, are informative. One way to deal with the information problem is to postulate that the terms ‘Tully’ and ‘Cicero’ come equipped with different informative values. Another approach is to claim that statements like these are of the subject/predicate form. As such, they should be analyzed along the way we treat “Tully walks”. Since proper names (...) can appear in predicative position we could go as far as to dismiss the sign of identity altogether, some told us. I will try to discuss the advantages and/or disadvantages of this approach and investigate whether Frege’s view that the ‘is’ of identity must be distinguished from the ‘is’ of predication can be reconciled with the fact that names can appear in predicative position. (shrink)

The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.

This book serves as a concise introduction to some main topics in modern formal logic for undergraduates who already have some familiarity with formal languages. There are chapters on sentential and quantificational logic, modal logic, elementary set theory, a brief introduction to the incompleteness theorem, and a modern development of traditional Aristotelian Logic.

There is a clash between some people's positive logical intuitions about traditional or Aristotelian logic and the assessment ofthat logic made by modem logic. In response to the clash, four sorts of reasons that might be given for referring one logic to the other are considered, but it is argued that none of them provides a decisive reason in favor of one rather than the other. A reformist and a radical response to the apparent inability to give reasons to prefer (...) one logic to the other are considered and reasons given for preferring the radical response. (shrink)

I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on (...) these principles, the Quantified Argument Calculus or Quarc. I provide a truth-value assignment semantics and a proof system for the Quarc. I next demonstrate the system’s power by a variety of proofs; I prove its soundness; and I comment on its completeness. I then extend the system to modal logic, again providing a proof system and a truth-value assignment semantics. I proceed to show how the Quarc versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which I argue is an advantage of the modal Quarc over modal Predicate Logic as a system intended to capture the logic of natural language. (shrink)

We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.

There are several innocuous or trivial ways in which to explicate Aristotle’s hylomorphism. For example: objects are characterisable in terms of matter and form; or analysable into matter and form; or understood on the basis of matter and form. Serious problems arise when we seek to specify the sorts of relation holding among the different contributors to the hylomorphic picture. Here are some central general questions: a. What types of relation are most suitable for each n-tuple of contributors? b. What (...) direction and modal profile should each relation have? In addressing such questions we find that the types, directions, or modal character of the relations that we or Aristotle may favour are often in tension with each other, or clearly lead to inconsistencies. The paper focuses on the Modal Question, also known as ‘Ackrill’s problem’: is form essentially or contingently related to matter? I outline a hylomorphic model, what I label the ‘causal-explanatory’ model, and show how it can tackle M. (shrink)

Cet ouvrage de Pascal Engel doit être fortement recommandé pour plusieurs raisons. On est d'abord frappé par l'ampleur du travail accompli et l'étendue du domaine couvert. La documentation est fouillée, l'exposé est clair et un équilibre est toujours maintenu entre les questions générales et les questions de détail. Engel ne perd jamais de vue la perspective d'ensemble qu'il s'est donnée et qui concerne la nature de la logique, y compris lorsqu'il s'emploie à faire certaines nuances ou à proposer une distinction (...) subtile. Il aurait été facile en pareille matière de proposer un mauvais choix de thèmes. Là encore, Engel s'est bien acquitté de sa tâche. On a affaire à un ouvrage dans lequel l'auteur va toujours droit à l'essentiel. Plusieurs sujets sont à peine effleurés, mais cette décision est très souvent heureuse puisqu'elle permet à l'auteur d'établir des liens entre des problématiques qui, de prime abord, semblent très éloignées les unes des autres. L'auteur fait montre d'un étonnant esprit de synthèse et plusieurs thèmes font, à ma connaissance, une première apparition dans la littérature philosophique francophone. Il s'agit donc d'une contribution à la philosophie de la logique qui mérite d'être signalée. On regrettera peut-être la présence d'un assez grand nombre d'erreurs typographiques. Dans la plupart des cas, il ne s'agit que de coquilles mais, dans d'autres cas, elles risquent de nuire à la compréhension du texte surtout lorsqu'elles interviennent dans des formules ou des définitions. (shrink)

The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio (...) ad absurdum is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments. (shrink)

Recently, von Fintel (2001) and Gillies (2007) have argued that certain sequences of counterfactuals, namely reverse Sobel sequences, should motivate us to abandon standard truth conditional theories of counterfactuals for dynamic semantic theories. I argue that we can give a pragmatic account of our judgments about counterfactuals without giving up the standard semantics. In particular, I introduce a pragmatic principle governing assertability, and I use this principle to explain a variety of subtle data concerning reverse Sobel sequences.

Nietzsche thought at one point that predication originated through the misapplication of names for particulars to further particulars. I doubt myself that this is where the device came from, although one does occasionally encounter usage – such as ‘another Vietnam’ – that evidently does arise in this manner. However, his account of predication is a useful model for a more sophisticated device which we in fact deploy, namely, the intentional misdescription of one circumstance or another in the interests of expedited (...) inference, often via the misapplication of a predicate. I don’t believe that ‘… is a leaf’ is a systematic reapplication of the name of some ur-leaf, but just the other day, I told my gardener that the leaves were off the tree, and that she could come in and work on my pond. I was triggering an inference rule we both accept: that you schedule fall cleanup once the leaves are off the tree. Rather than describe the actual state of the tree , and then renegotiate the rule to match, it was simpler to work with the misdescriptions. My respondents recall that devices such as predication are flexible anyway; they conclude that there is no need to misapply them. Let me try to get you to think twice about the assumption that flexibility pre-empts misapplication. But as I proceed, bear in mind that my illustrations are not intended as an argument. Any given illustration can be read either as a misapplication of a description, or alternatively as a correct application of a predicate, whose use in context is controlled by, perhaps, the sort of techniques discussed by David Lewis …. (shrink)

I provide a novel semantic analysis of proper names and indexicals, combining insights from the competing traditions of referentialism, championed by Kripke and Kaplan, and descriptivism, introduced by Frege and Russell, and more recently resurrected by Geurts and Elbourne, among others. From the referentialist tradition, I borrow the proof that names and indexicals are not synonymous to any definite description but pick their referent from the context directly. From the descriptivist tradition, I take the observation that names, and to some (...) extent indexicals, have uses that are best understood by analogy with anaphora and definite descriptions, that is, following Geurts, in terms of presupposition projection. The hybrid analysis that I propose is couched in Layered Discourse Representation Theory. Proper names and indexicals trigger presuppositions in a dedicated layer, which is semantically interpreted as providing a contextual anchor for the interpretation of the other layers. For the proper resolution of DRSs with layered presuppositions, I add two constraints to van der Sandt's algorithm. The resulting proposal accounts for both the classic philosophical examples and the new linguistic data, preserving a unified account of the preferred rigid interpretation of both names and indexicals, while leaving room for non-referential readings under contextual pressure. (shrink)

Hard Truths is an important book in its own right. It is also the latest contribution to a complex and impressive project that Elijah Milligram has been developing from his first book onwards. There he characterized practical induction as a type of reasoning that enables agents to learn from experiences of the new and the unfamiliar, agents whose inferences are from beliefs that they have formed either ‘in ways that have a suitable amount to do with [their] truth’, or, when (...) ‘the appeal to truth is unhelpful’, in ways that underwrite such inferences as they are committed to drawing . In his introduction to his anthology on practical reasoning, Millgram catalogued the presently competing theories of practical reasoning, posing the question: what kind of reasoning should we employ in deciding between the claims of rival theories? The subtitle of his third book , ‘Practical Reasoning as a Foundation for Moral Theory’, already suggests its central thesis, that we should first survey the range of theories of practical reasoning , should then identify which moral theory it is with which each theory of practical reasoning is paired , should next decide which theory of practical reasoning is correct , and, finally, should adopt the moral theory paired with that theory of practical reasoning. There are at least three clusters of problems that badly need extended attention, if the claims of these three books are to be sustained: one concerning the account of truth presupposed by Millgram, a second to do with the inferences that we need to employ, and a third concerning the unity of reasoning agents. All three provide Hard Truths with subject-matter, but Millgram’s principal focus is …. (shrink)

Reporting on the 7th International Congress of Logic, Methodology, and Philosophy of Science, first the main topics and some organisational aspects of the congress are presented; the main part of the report focuses on recent developments in Philosophical Logic , in particular the theory of so-called generalized quantifiers as presented at the congress. In addition, some background information on logical language analysis, its possible applications and consequences is provided.

Bare conditionals, I argue, exhibit Conditional Duality in that when they appear in downward entailing environments they differ from bare conditionals elsewhere in having existential rather than universal force. Two recalcitrant phenomena are shown to find a new explanation under this thesis: bare conditionals under only, and bare conditionals in the scope of negative nominal quantifiers, or what has come to be known as Higginbotham’s puzzle. I also consider how bare conditionals behave when embedded under negation, arguing that such conditionals (...) often involve denial negation. One important conclusion that emerges from the discussion is that an account of bare conditionals that validates Conditional Excluded Middle is not warranted. By limiting the scope of the strict analysis Conditional Duality is also a way of maintaining such an account. (shrink)

In the late nineteenth century there were two very active lines of research in the field of formal logic. First, logicians (mostly in English-speaking countries) were engaged in formulating a generally traditional logic as an algebra, a part of mathematics; second, logicians (mostly on the continent) were busy building a non-traditional logic that could serve, not as a part of, but as the foundation of, mathematics. By the end of the First World War the former line had been pretty well (...) abandoned while the second continued to expand. However, that old abandoned line, stretching from Aristotle, through the Scholastics and then Leibniz to the nineteenth century algebraists, had not been completely forgotten. One of those logicians who has recently worked on the restoration (and, importantly, the extension) of that line is Fred Sommers. His Term Logic preserves a number of traditional insights (especially involving the theory of logical syntax), while also enjoying a power to account for formal inference at least comparable to that of the standard logic now in place. (shrink)

This paper argues for a version of metalinguistic descriptivism, the Mill-Frege view, comparing it to a currently popular alternative, predicativism. The Mill-Frege view combines tenets of Fregean views with features of the theory of direct reference. According to it, proper names have metalinguistic senses, known by competent speakers on the basis of their competence, which figure in ancillary presuppositions. In support of the view the paper argues that the name-bearing relation—which predicativists cite to account for the properties that they take (...) names to express—depends on acts of naming with a semantic significance. Acts of naming create particular words specifically designed for referential use, which they perform whether or not the language has other words articulated with the same sound or orthography. Like other forms of metalinguistic descriptivism, the Mill-Frege view affords responses to Kripke’s semantic and epistemic arguments against descriptivism. The view is prima facie more complex than predicativism; but the additional complexity is independently attested in natural languages and well-motivated. Finally, the Mill-Frege proposal deals well with Kripke’s modal argument, and accounts for modal intuitions about names, both issues that pose serious trouble to predicativism. (shrink)

Contemporary orthodoxy affirms that singular terms cannot be predicates and that, therefore, ‘is’ is ambiguous as between predication and identity. Recent attempts to treat names as predicates do not challenge this orthodoxy. The orthodoxy was built into the structure of modern formal logic by Frege. It is defended by arguments which I show to be unsound. I provide a semantical account of atomic sentences which draws upon Mill's account of predication, connotation and denotation. I show that singular terms may be (...) predicates, that it is highly implausible that there is an ‘is’ of identity in natural languages, and that modern formal logic is deficient in that it cannot recognize sentences, including singular existentials, in which singular terms are predicates, or inferences which depend upon the logical role rather than the logical category of expressions. (shrink)