The paper deals with the main contribution of the Finnish logician JaakkoHintikka: epistemic logic, in particular the 'static' version of the system based on the formal analysis of the concepts of knowledge and belief. I propose to take a different look at this philosophical logic and to consider it from the opposite point of view of the philosophy of logic. At first, two theories of meaning are described and associated with two competing theories of linguistic competence. In (...) a second step, I draw the conclusion that Hintikka's epistemic logic constitutes a sort of internalisation of meaning, by the introduction of epistemic modal operators into an object language. In this respect, to view meaning as the result of a linguistic competence makes epistemic logic nothing less than a logic of unified meaning and understanding. (shrink)
On JaakkoHintikka’s understanding of Aristotle’s modal thought, Aristotle is committed to a version of the Principle of Plenitude, which is the thesis that no genuine possibility will go unactualized in an infinity of time. If in fact Aristotle endorses the Principle of Plenitude, everything becomes necessary. Despite the strong evidence that Aristotle indeed accepts that Principle of Plenitude, there are key texts in which Aristotle seems to contradict it. On Hintikka’s final word on the matter, Aristotle (...) either endorses the Principle of Plenitude or Aristotle is simply inconsistent. Without challenging Hintikka’s interpretation of the relevant texts, I show how Aristotle may accept a form of the Principle of Plenitude that allows for genuine unactualized possibilities in the world. What allows me to reconcile the seemingly inconsistent data is to show how Aristotle is only committed to a de re version of the Principle of Plenitude. After I lay out my proposal, I show how it opens up new ways in which we might understand Aristotle’s attempt to reject fatalism in his De interpretatione 9. (shrink)
L’article qui suit a pour but de présenter un des aspects centraux de la contribution philosophique de JaakkoHintikka : l’épistémologie formelle. Le thème choisi, le Paradoxe de Moore, permettra d’illustrer le mot d’ordre de la philosophie formelle, celui d’utiliser des outils logiques en vue de la clarification de problèmes philosophiques. Il s’agit également de mettre en évidence la nature pragmatique du discours épistémique, qui transparaît dans les résultats sémantiques de Hintikka et parle en faveur de la (...) logique illocutoire. (shrink)
JaakkoHintikka, in a series of talks in Brazil in 2008, defended that IF logic and paraconsistent logic are, in a sense, very similar. Having sketched the proposal of a new paraconsistent system, he maintains that several achievements of IF logic could be reproducible in paraconsistent logic. One of the major difficulties, left as a challenge, would be to formulate some truth conditions for this new paraconsistent first-order language in order to make IF logic and paraconsistent logic more (...) inter-related. My proposal is that this would demand an innovative game-theoretical semantic approach to paraconsistentism, but also that the syntax of the paraconsistent “Logics of Formal Inconsistency” can model the internal logic of Socratic elenchi. I aim to discuss these, and other points posed by Hintikka, as challenges and opportunities for paraconsistentism, paraconsistent logics and IF logics, as well as to raise some criticisms on Hintikka’s view about paraconsistency. (shrink)
Cet article a pour but d’étudier les perspectives que l’approche performative de la preuve fournit, afin de répondre à deux questions classiques liées à l’interprétation de l’argument cartésien : Cogito ergo sum. La première question est la suivante : quel type de contrainte logique ou non-logique ergo exprime-t-il dans la formulation de cet argument? La seconde question est celle-ci : quel type d’existence est manifesté par l’argument Cogito, ou Cogito ergo quis est ?
Although epistemic possibility figures in several debates, those debates have had relatively little contact with one another. G. E. Moore focused squarely upon analyzing epistemic uses of the phrase, ‘It’s possible that p’, and in doing so he made two fundamental assumptions. First, he assumed that epistemic possibility statements always express the epistemic position of a community, as opposed to that of an individual speaker. Second, he assumed that all epistemic uses of ‘It’s possible that p’ are analyzable in terms (...) of knowledge, not belief. A number of later theorists, including Keith DeRose, provide alternative accounts of epistemic possibility, while retaining Moore’s two assumptions. Neither assumption has been explicitly challenged, but JaakkoHintikka’s analysis provides a basis for doing so. Drawing upon Hintikka’s analysis, I argue that some epistemic possibility statements express only the speaker’s individual epistemic state, and that contra DeRose, they are not degenerate community statements but a class in their own right. I further argue that some linguistic contexts are belief- rather than knowledge-based, and in such contexts, what is possible for a speaker depends not upon what she knows, but upon what she believes. (shrink)
‘Performative’ transcendental arguments exploit the status of a subcategory of self-falsifying propositions in showing that some form of skepticism is unsustainable. The aim of this paper is to examine the relationship between performatively inconsistent propositions and transcendental arguments, and then to compare performative transcendental arguments to modest transcendental arguments that seek only to establish the indispensability of some belief or conceptual framework. Reconceptualizing transcendental arguments as performative helps focus the intended dilemma for the skeptic: performative transcendental arguments directly confront the (...) skeptic with the choice of abandoning either skepticism or some other deep theoretical commitment. Many philosophers, from Aristotle and St. Thomas Aquinas to JaakkoHintikka, C.I. Lewis, and Bernard Lonergan, have claimed that some skeptical propositions regarding knowledge, reason, and/or morality can be shown to be self-defeating; that is to say, they have claimed that the very upholding of some skeptical position is in some way incompatible with the position being upheld, or with the implied, broader dialectical position of the skeptic in question. Statements or propositions alleged to have this characteristic also sometimes are called ‘self-falsifying,’ ‘self-refuting,’ ‘self-stultifying,’ ‘self-destructive,’ or ‘pointless.’ However, proponents of the strategy of showing skepticism to be self-defeating have not in general adequately distinguished between two types of self-defeating proposition: self-falsifying and self-stultifying. In the first part of this paper I distinguish between self-falsifying and self-stultifying propositions, and introduce the notion of performative self-falsification. In the second part I discuss classical transcendental arguments, ‘modest’ transcendental arguments, and objections to each. In the third part I introduce two types of transcendental argument—each labeled “performative”—corresponding to two types of performatively self-falsifying proposition, and I compare them to modest transcendental arguments. (shrink)
Leibniz frequently argued that reasons are to be weighed against each other as in a pair of scales, as Professor Marcelo Dascal has shown in his article "The Balance of Reason." In this kind of weighing it is not necessary to reach demonstrative certainty – one need only judge whether the reasons weigh more on behalf of one or the other option However, a different kind of account about rational decision-making can be found in some of Leibniz's writings. In his (...) article "Was Leibniz's Deity an Akrates?" Professor JaakkoHintikka has argued that Leibniz developed a new vectorial model for rational decisions which is better suited to complicated decisions, where values are complementary to each other. This model, related closely to his work in metaphysics and the philosophy of mind, is a heuristic device which helps in finding rational combinations - and in an ideal case an optimum - between plural inclinations to the good. I shall argue that Leibniz applies more or less implicitly both of these models in his practical rationality. In simple situations he applied the pair of scales model and in more complicated situations he applied the vectorial model. (shrink)
One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...) be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of JaakkoHintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)
In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview (...) of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities – in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, JaakkoHintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality. (shrink)
John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development (...) of algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. -/- It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems). (shrink)
Are transcendental phenomenology and possible worlds semantics, two seemingly disparate, perhaps even incompatible philosophical traditions, actually complementary? Have two well-known representatives of each tradition, J.N. Mohanty and J. Hintikka, misinterpreted the other's philosophical "program" in such a way that they did not recognize the complementarity? Charles Harvey 1 has recently argued that the answer to both questions is "yes." Here I intend to argue that the answer to the first is unclear, whereas the answer to the second is "no." (...) Mohanty (at least) rightly cites fundamental differences between transcendental phenomenology and possible worlds semantics. (shrink)
The relationship between Peircean abduction and the modern notion of Inference to the Best Explanation (IBE) is a matter of dispute. Some philosophers such as Harman and Lipton claim that abduction and IBE are virtually the same. Others, however, hold that they are quite different (e.g., Hintikka and Minnameier) and there is no link between them (Campos). In this paper, I argue that neither of these views is correct. I show that abduction and IBE have important similarities as well (...) as differences. Moreover, by bringing a historical perspective to the study of the relationship between abduction and IBE—a perspective that is lacking in the literature—I show that their differences can be well understood in terms of two historic developments in the history of philosophy of science: first, Reichenbach’s distinction between the context of discovery and the context of justification—and the consequent jettisoning of the context of discovery from philosophy of science—and second, underdetermination of theory by data. (shrink)
The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper concludes (...) with a modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)
The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical (...) language: a dynamic modal logic. Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL). This framework may be seen as an extension of standard Hintikka-style doxastic logic with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about undergoes a change. But then his introspective (higher-order) beliefs have to be adjusted accordingly. In the paper we shall consider various ways of solving this problem. (shrink)
In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but also (...) rationality constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up. (shrink)
The verb ‘to know’ can be used both in ascriptions of propositional knowledge and ascriptions of knowledge of acquaintance. In the formal epistemology literature, the former use of ‘know’ has attracted considerable attention, while the latter is typically regarded as derivative. This attitude may be unsatisfactory for those philosophers who, like Russell, are not willing to think of knowledge of acquaintance as a subsidiary or dependent kind of knowledge. In this paper we outline a logic of knowledge of acquaintance in (...) which ascriptions like ‘Mary knows Smith’ are regarded as formally interesting in their own right, remaining neutral on their relation to ascriptions of propositional knowledge. The resulting logical framework, which is based on Hintikka’s modal approach to epistemic logic, provides a fresh perspective on various issues and notions at play in the philosophical debate on acquaintance. (shrink)
In this paper, I shall consider the challenge that Quine posed in 1947 to the advocates of quantified modal logic to provide an explanation, or interpretation, of modal notions that is intuitively clear, allows “quantifying in”, and does not presuppose, mysterious, intensional entities. The modal concepts that Quine and his contemporaries, e.g. Carnap and Ruth Barcan Marcus, were primarily concerned with in the 1940’s were the notions of (broadly) logical, or analytical, necessity and possibility, rather than the metaphysical modalities that (...) have since become popular, largely due to the influence of Kripke. In the 1950’s modal logicians responded to Quine’s challenge by providing quantified modal logic with model-theoretic semantics of various types. In doing so they also, explicitly or implicitly addressed Quine’s interpretation problem. Here I shall consider the approaches developed by Carnap in the late 1940’s, and by Kanger, Hintikka, Montague, and Kripke in the 1950’s, and discuss to what extent these approaches were successful in meeting Quine’s doubts about the intelligibility of quantified modal logic. (shrink)
In recent decades much literature has been produced on disagreement; the puzzling conclusion being that epistemic disagreement is, for the most part, either impossible (e.g. Aumann (Ann Stat 4(6):1236–1239, 1976)), or at least easily resolvable (e.g. Elga (Noûs 41(3):478–502, 2007)). In this paper I show that, under certain conditions, an equally puzzling result arises: that is, disagreement cannot be rationally resolved by belief updating. I suggest a solution to the puzzle which makes use of some of the principles of (...) class='Hi'>Hintikka’s Socratic epistemology. (shrink)
According to the extended mind thesis, cognitive processes are not confined to the nervous system but can extend beyond skin and skull to notebooks, iPhones, computers and such. The extended mind thesis is a metaphysical thesis about the material basis of our cognition. As such, whether the thesis is true can have implications for epistemological issues. Carter has recently argued that safety-based theories of knowledge are in tension with the extended mind hypothesis, since the safety condition implies that there is (...) an epistemic difference between subjects who form their beliefs via their biological capacities and between subjects who have extended their cognition. Kelp, on the other hand, has argued that a safety-based theory of knowledge can be correct only if the extended mind thesis is true. While these claims are not logically inconsistent, they do leave the safety theorist in an uncomfortable position. I will argue that safety-based theories of knowledge are not hostage to the truth of the extended mind thesis, and that once the safety condition is properly understood it is not in tension with the extended mind thesis. (shrink)
John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the premises: (...) there must be something deductions can show. Corcoran calls a proposition that follows from given premises a hidden consequence of those premises if it is not obvious that the proposition follows from those premises. By a Euclidean geometry we mean an extended discourse beginning with basic premises—axioms, postulates, definitions—1) treating a universe of geometrical figures and 2) resembling Euclid’s Elements. There were Euclidean geometries before Euclid (fl. 300 BCE), even before Aristotle (384–322 BCE). Bochenski, Lukasiewicz, Patzig and others never new this or if they did they found it inconvenient to mention. Euclid shows no awareness of Aristotle. It is obvious today—as it should have been obvious in Euclid’s time, if anyone knew both—that Aristotle’s logic was insufficient for Euclid’s geometry: few if any geometrical theorems can be deduced from Euclid’s premises by means of Aristotle’s deductions. Aristotle’s writings don’t say whether his logic is sufficient for Euclidean geometry. But, there is not even one fully-presented example. However, Aristotle’s writings do make clear that he endorsed the goal of a sufficient system. Nevertheless, incredible as this is today, many logicians after Aristotle claimed that Aristotelian logics are sufficient for Euclidean geometries. This paper reviews and analyses such claims by Mill, Boole, De Morgan, Russell, Poincaré, and others. It also examines early contrary statements by Hintikka, Mueller, Smith, and others. Special attention is given to the argumentations pro or con and especially to their logical, epistemic, and ontological presuppositions. What methodology is necessary or sufficient to show that a given logic is adequate or inadequate to serve as the underlying logi of a given science. (shrink)
We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi\-agent epistemic logic \CMAELCD\ with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for \CMAELCD\ and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input (...) set of formulae of \CMAELCD\ and closes for every unsatisfiable input set of formulae. (shrink)
Artikkelissaan ”The Balance of Reason” Marcelo Dascal on osoittanut, että metafora syiden punnitsemisesta järjen vaa’assa on yleinen Leibnizin kirjoituksissa ja sitä on pidettävä hänen yleisenä järkeilyn metodinaan tilanteissa, joissa ei voida suorittaa täydellistä loogista analyysiä. Keskustelen tässä esitelmässä tuosta metaforasta ja ehdotan Jaakko Hintikan ja Simo Knuuttilan aiempien esityksien pohjalle rakentaen, että käsityksissään ihmisen praktisesta rationaalisuudesta Leibniz sovelsi myös toista melko tuntemattomaksi jäänyttä heuristista päätöksentekomallia, joka liittyy hänen työhönsä luonnonfilosofiassa ja mielenfilosofiassa, ja jota hän sovelsi tapauksissa joissa päätökseen vaikuttavat (...) arvot ovat toisiaan täydentäviä. Tämä moniarvoisuuden huomioon ottava malli edustaa uudenlaista ja modernia ajattelua moraalifilosofian historiassa. (shrink)
In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the role of presupposition in supervaluations logical systems. (...) At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notions. (shrink)
This essay offers a strategic reinterpretation of Kant’s philosophy of mathematics in Critique of Pure Reason via a broad, empirically based reconception of Kant’s conception of drawing. It begins with a general overview of Kant’s philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant’s constructivism takes up these issues, largely inspired by Hintikka’s unorthodox conception of Kantian intuition. Third, (...) it offers further analyses of three Kantian concepts vitally linked to that of drawing. It concludes with an etymologically based exploration of the seven clusters of meanings of the word drawing to gesture toward new possibilities for interpreting a Kantian philosophy of mathematics. (shrink)
The present essay is a critical study of Barwise and Perry’s book, emphasizing the logical and model-theoretical aspects of their work. I begin by presenting the authors’ criticism of the classical view of logic and semantics within the tradition of Frege, Russell and Tarski. In this connection, I discuss the so-called Frege argument (“the slingshot”). I try to show that the argument appears inconclusive, not only from a situation-theoretic perspective, but also from such alternative perspectives as orthodox Fregean semantics or (...) Russellian semantics. I then discuss the ontology of situation semantics and the way it is modeled within set theory. In particular, I compare the notion of an abstract situation with that of a possible world. The last two sections concern the model-theoretic aspects of the authors’ theory. In Section 7, I discuss how the “partial” perspective of situation semantics differs from that of classical model theory. Finally, in Section 8, different model-theoretic accounts of attitude reports within situation semantics are discussed, in particular the “relations to situations”-approach presented by the authors in Chapter 9 of S & A. The usual problems of “logical omniscience” that appear in standard Hintikka-style epistemic logic are avoided in situation semantics. I argue, however, that situation semantics is faced with analogous counter-intuitive results, unless the expressive power of the language under study is suitably restricted. (shrink)
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