I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

In a definition (∀ x )(( x є r )↔D[ x ]) of the set r, the definiens D[ x ] must not depend on the definiendum r . This implies that all quantifiers in D[ x ] are independent of r and of (∀ x ). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious (...) Circle Principle was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if ( b є a ) or ( b ⊆ a ). Likewise, the truth of an ordinary first-order sentence with the Gödel number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r. (shrink)

particular alternative logic could be relevant to another one? The most important part of a response to this question is to remind the reader of the fact that independence friendly (IF) logic is not an alternative or “nonclassical” logic. (See here especially Hintikka, “There is only one logic”, forthcoming.) It is not calculated to capture some particular kind of reasoning that cannot be handled in the “classical” logic that should rather be called the received or (...) conventional logic. No particular epithet should be applied to it. IF logic is not an alternative to our generally used basic logic, the received first-order logic, aka quantification theory or predicate calculus. It replaces this basic logic in that it is identical with this “classical” first-order logic except that certain important flaws of the received first-order logic have been corrected. But what are those flaws and how can they be corrected? To answer these questions is to explain the basic ideas of IF logic. Since this logic is not as well known as it should be, such explanation is needed in any case. I will provide three different but not unrelated motivations for IF logic. (shrink)

In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman.

In this paper we study connections between game theoretical concepts and results, and features of IF-predicate logic, extending observations from J. van Benthem (2001) for IF-propositional logic. We highlight how both characteristics of perfect recall can fail in the semantic games for IF-formulas, and we discuss the four Thompson transformations in relation with IF-logic. Many (strong) equivalence schemes for IF-logic correspond to one or more of the transformations. However, we also find one equivalence that does not (...) fit in this picture, by the type of imperfect recall involved. We point out that the connection between the transformations and logical equivalence schemes is less direct in IF-first order logic than in the propositional case. The transformations do not generate a reduced normal form for IF-logic, because the IF-language is not flexible enough. (shrink)

We analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of Independence-Friendly (IF) sentences; we give a syntactical criterion to decide whether a sentence beginning with such prefix exists, such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences.

In this paper it is argued that Hintikka's game theoreticalsemantics for Independence Friendly logic does not formalize theintuitions about independent choices; it rather is aformalization of imperfect information. Furthermore it is shownthat the logic has several remarkable properties (e.g.,renaming of bound variables is not allowed). An alternativesemantics is proposed which formalizes intuitions aboutindependence.

We associate the semantic game with chance moves conceived by Blinov with Blamey’s partial logic. We give some equivalent alternatives to the semantic game, some of which are with a third player, borrowing the idea of introducing the pseudo-player called Nature in game theory. We observe that IF propositional logic proposed by Sandu and Pietarinen can be equivalently translated to partial logic, which implies that imperfect information may not be necessary for IF propositional logic. We also (...) indicate that some independent quantifiers can be regarded as dependent quantifiers of indeterminate sequence, using the interjunction connective in partial logic. We conclude our paper by indicating some further research in a more general setting. (shrink)

Let us assume that you are entrusted by UNESCO with an important task. You are asked to devise a universal logical language, a Begriffsschrift in Frege's sense, which is to serve the purposes of science, business and everyday life. What requirements should such a “conceptual notation” satisfy? There are undoubtedly many relevant desiderata, but here I am focusing on one unmistakable one. In order to be a viable lingua universalis, your language must in any case be capable of representing any (...) possible configuration of dependence and independence between different variables. For if such a configuration is possible in principle, there is no guarantee that it might not one day show up among the natural, human or social phenomena we have to study.But how are dependencies and independencies between variables expressed in our familiar logical notation? Every logician worth his or her truth-table knows the answer. Dependencies between two variables are expressed by dependencies between the quantifiers to which they are bound. For instance, inthe variable y depends on x, while inz depends on x but not on y, while u depends on both x and y.But how is the dependence of a quantifier on another one expressed in familiar logical languages? Obviously by occurring in its scope, indicated by the pair of parentheses following it. But the nesting of scopes is a transitive and antisymmetrical relation which allows branching only in one direction. Hence other kinds of structures of dependence and independence between variables are not representable in the received logical notation. Such previously inexpressible structures form the subject matter of what has been referred to as independence-friendly logic. (shrink)

This paper shows that the logic known as Information-friendly logic (IF-logic) introduced by Jaakko Hintikka and Gabriel Sandu defines its own truth-predicate. The result is interesting given that IF logic is a much stronger logic than ordinary first-order logic and has also a well behaved notion of negation which, on its first-order subfragment, behaves like classical, contradictory negation.

The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another (...) standard fact of IFL, that first-order logic can adequately express uniformity concepts in real analysis, whereas IFL cannot. This not only radically contradicts Hintikka’s particular claim in that article, but also undermines his whole enterprise of founding mathematics on his logic system. (shrink)

While logical principles seem timeless, placeless, and eternal, their discovery is a story of personal accidents, political tragedies, and broad social change. If A, Then B begins with logic's emergence twenty-three centuries ago and tracks its expansion as a discipline ever since. -/- The book treats logic as more than a tale of individual abstraction; it sees logic as also being a result of politics, economics, technology, and geography, because all these factors helped to generate an audience (...) for the discipline from the start. The book thus relates developments in logical theory to the social history of different historical periods. -/- The book defends a number of controversial philosophical theses: (1) that rationally persuasive arguments must always proceed from premises that are initially more convincing than the conclusions to be proved (a position derived from Aristotle), (2) that intuitive logical judgments, though sometimes mistaken, can also count as certain knowledge, independent of the techniques used to construct formal logical systems, (3) that Wittgenstein was mistaken in thinking that philosophy was riddled with unintelligible language and that the real problems, instead, have been ambiguity and pretentious diction, and (4) that Nelson Goodman's argument to the effect that deductive logic can be "virtuously circular" is founded on a non sequitur. -/- . (shrink)

The paper proposes grounding the ternary connective “if … then … else” (classically interpreted), thus far not considered in the logical grounding literature. In doing so, a new kind of plural grounding, called collective immediate grounding, is proposed as more adequate than the traditional complete immediate grounding in avoiding redundancy. The approach is proof‐theoretic.

The paper proposes grounding the ternary connective “if … then … else” (classically interpreted), thus far not considered in the logical grounding literature. In doing so, a new kind of plural grounding, called collective immediate grounding, is proposed as more adequate than the traditional complete immediate grounding in avoiding redundancy. The approach is proof‐theoretic.

There is a persistent methodological problem in primate mindreading research, dubbed the 'logical problem,' over how to determine experimentally whether chimpanzees are mindreaders or just clever behavior-readers of a certain sort. The problem has persisted long enough that some researchers have concluded that it is intractable. The logical problem, I argue, is tractable but only with experimental protocols that are fundamentally different from those that have been currently used or suggested. In the first section, I describe what the logical problem (...) is and how it can, in principle, be solved. In the second section, I illustrate how a well-known experimental protocol by Hare et al. fails to solve the logical problem. In the third section, I do the same for a protocol by Heyes . .) In the fourth section, I describe a novel experimental protocol for visual perspective-taking and argue that it succeeds to discriminate between the relevant mindreading and behavior-reading hypotheses. In addition, this new experimental protocol employs procedures that are realistic enough to suppose that chimpanzees might very well succeed in passing them. (shrink)

In this paper I present some of Robert N. McLaughlin's critique of a truth functional approach to conditionals as it appears in his book On the Logic of Ordinary Conditionals. Based on his criticism I argue that the basic principles of logic together amount to epistemological and metaphysical implications that can only be accepted from a logical atomist perspective. Attempts to account for conditional relations within this philosophical framework will necessarily fail. I thus argue that it is not (...) truth functionality as such that is the problem, but the philosophical foundation of modern logic. (shrink)

Can epistemic logic state anything interesting about the epistemology of mathematics? That's one of Jaakko Hintikka’s claims. Hintikka was not only the founder of modal epistemic logic (1962), since he also worked on the foundations of mathematics (1996). Using what he calls "second generation" epistemic logic (2003), i.e. independence-friendly (IF) epistemic logic, Hintikka revisits the epistemology of mathematics, and in particular the debate between classical and intuitionistic mathematics (2001). The aim of the talk is to show (...) that Hintikka is right regarding IF epistemic logic, for such a logic enables us to account for interesting features of mathematical knowledge. However, the path is not as easy as that Hintikka suggests. I will show that the well-known issue of logical omniscience directly threatens the understanding of intuitionism offered by IF epistemic logic. (shrink)

The present paper provides novel results on the model theory of Independence friendly modal logic. We concentrate on its particularly well-behaved fragment that was introduced in Tulenheimo and Sevenster (Advances in Modal Logic, 2006). Here we refer to this fragment as ‘Simple IF modal logic’ (IFML s ). A model-theoretic criterion is presented which serves to tell when a formula of IFML s is not equivalent to any formula of basic modal logic (ML). We generalize the (...) notion of bisimulation familiar from ML; the resulting asymmetric simulation concept is used to prove that IFML s is not closed under complementation. In fact we obtain a much stronger result: the only IFML s formulas admitting their classical negation to be expressed in IFML s itself are those whose truth-condition is in fact expressible in ML. (shrink)

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...) mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (shrink)

Theoria, Volume 87, Issue 5, Page 1175-1192, October 2021.

Putnam and others have argued that an examination of structures arising in quantum mechanics can lead to a non-classical propositional logic, quantum logic. In this paper it is argued that the procedure by which quantum logic is said to be discovered, a process called reading off, is fundamentally flawed. A parody fable shows that reading off leads to absurd consequences. The fable also leads one to cast doubt on the following claims central to the quantum logic (...) program: (i) logic can be reformed locally; (ii) classical logic is read off classical physics; and (iii) reading off is a justifiable process because quantum logic resolves quantum paradoxes. (shrink)

Boehm reasons that human morality began when several heads of households formed a coalition to limit the despotic bullying of an alpha male. The logic is clear and the argument is persuasive. The premises require that: dominant individuals behave like chimpanzees, bullying their subordinates, early humans somehow developed one-male units from a chimpanzee like society and, the power of a despot is limited by group consensus and political activities. Not all alpha males behave like chimpanzees; most primate societies show (...) little evidence of bullying. One-male units are formed by some monkeys but there is little evidence of such tendencies in chimpanzees and bonobos. Hamadryas males do not compete with familiar males for females or possessions regardless of their dominance relationships, but this inhibition is not based on group consensus or coalitions repressing alpha males. Boehm's argument is, nonetheless, possible and plausible but cannot be empirically tested. (shrink)

In late antiquity, logic developed into what Ebbesen calls the LAS, the Late Ancient Standard. This paper discusses the Neoplatonic use of LAS, as informed by epistemological and metaphysical concerns. It demonstrates this through an analysis of the late ancient debate about hypothetical and categorical logic as manifest in the practice of syllogizing Platonic dialogues. After an introduction of the Middle Platonist view on Platonic syllogistic as present in Alcinous, this paper presents an overview of its application in (...) the syllogizing practice of Proclus and others. That overview shows that the two types were considered two sides of the same coin, to be used for the appropriate occasions, and both relying on the methods of dialectic as revealing the structure of knowledge and reality. Pragmatics, dialectic, and didactic choices determine which type or combination is selected in syllogizing Plato. So even though there is no specific Neoplatonic logic, there is a specific Neoplatonic use of LAS. (shrink)

For Derrida, the ‘‘as if’’, as a regulative principle directly appropriated and modified from its Kantian context, becomes the central lynchpin for understanding, not only Derrida's philosophical system as a whole, but also his numerous seemingly enigmatic references to his ‘‘jewishness’’. Through an analysis of the function of the ‘‘as if’’ within the history of thought, from Greek tragedy to the poetry of Wallace Stevens, I hope to show how Derrida can only appropriate his Judaic roots as an act of (...) mourning that seeks to render the lost object as present, ‘‘as if’’ it were incorporated by the subject for whom this act nevertheless remains an impossibility. As Derrida discerns within the poetry of Paul Celan, bringing a sense of presence/presentness to our experiences, and as a confirmation of the subject which the human being struggles to assert, is the poetic task par excellence. It is seemingly also, if Derrida is to be understood on this point, the only option left to a humanity wherein poetry comes to express what religious formulations can no longer justify. (shrink)

If A then B: How the World Discovered Logic is a historically oriented introduction to the basic notions of logic. In particular, and in the words of the authors, it is focused on the idea that ‘lo...

The hybrid logic and the independence friendly modal logic IFML are compared for their expressive powers. We introduce a logic IFML c having a non-standard syntax and a compositional semantics; in terms of this logic a syntactic fragment of IFML is singled out, denoted IFML c . (In the Appendix it is shown that the game-theoretic semantics of IFML c coincides with the compositional semantics of IFML c .) The hybrid logic is proven to be (...) strictly more expressive than IFML c . By contrast, and the full IFML are shown to be incomparable for their expressive powers. Building on earlier research (Tulenheimo and Sevenster 2006), a PSPACE -decidable fragment of the undecidable logic is disclosed. This fragment is not translatable into the hybrid logic and has not been studied previously in connection with hybrid logics. In the Appendix IFML c is shown to lack the property of ‘quasi-positionality’ but proven to enjoy the weaker property of ‘ bounded quasi-positionality’. The latter fact provides from the IFML internal perspective an account of what makes the compositional semantics of IFML c possible. (shrink)

The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these (...) hold without exception. The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g. that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up. (shrink)

The article proposes a formal semantics of happiness and sadness modalities in the imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, (...) and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area. (shrink)