Intensional Notions Research Articles

The Fate of the Act of Synthesis

I investigate the role of the subject in judgment in Kant, Frege, and Husserl, situating it in the broader and less-often-considered context of their accounts of presentation (Vorstellung) as well as judgment. Contemporary philosophical usage of “representation” tends to elide the question of what Kant called the constitution of content, because of a reluctance, traced to Frege’s anti-psychologism, to attend to subjectivity. But for Kant and Husserl, anti-psychologism allows for synthesis as the subjective act necessary for both “mere presentation” and judgment. In Begriffshrift, Frege alludes to a significant logical role for the subjective act of judgment, and in later work, traces of this logical role remain in the intensional notions of grasping a thought and judging as acknowledging its truth. But Frege’s anti-psychologism blocks interpreting these subjective notions in term of synthesis. Although similar in certain ways to Frege and equally anti-psychologistic, Husserl’s theory of judgment in the Logical Investigations maintains a role for subjective syntheses for presentations and judgments, and goes beyond Kant in allowing for a kind of objectivity at the level of non-judgment presentations. These two great anti-psychologists at the dawn of the parallel heydays of linguistic and phenomenological analysis are thus differentiated by the fates they assign to the act of synthesis.

Intensional Composition as Identity

Composition as Identity claims that a composite object is identical to its parts taken collectively. This is often understood as reducing the identity of composite objects to the identity of their parts. The author argues that Composition as Identity is not such a reduction. His central claim is that an intensional notion of composition, which is sensitive to the arrangement of the composing objects, avoids criticisms based on an extensional understanding of composition. The key is to understand composition as an intensional kind of identity relation, many-one identity. Eventually, the author suggests an arrangement condition for many-one identity that allows him to distinguish between composite objects, even if they have the same parts.

Fuzzy intensional semantics

The study of weighted structures is one of the important trends in recent computer science. The aim of the article is to provide a weighted, many-valued version of classical intensional semantics formalised in the framework of higher-order fuzzy logics. We illustrate the apparatus on several variants of fuzzy S5-style modalities. The formalism is applicable to a broad array of weighted intensional notions, including alethic, epistemic, or probabilistic modalities, generalised quantifiers, counterfactual conditionals, dynamic and non-monotonic logics, and some more.

The Dead End of Radical Interpretation

Resumo: O projeto semântico de Davidson toma a forma de reducionismo que visa explicar as noções intencionais com base em noções puramente extensionais. O objetivo desse trabalho consiste na investigação do fracasso do projeto de Davidson como um argumento indireto contra sua suposição segundo a qual a chamada interpretação radical seria o fundamento do significado linguístico e do pensamento. Abstract: Davidson's semantic program is a form of semantic reductionism that aims to account for intensional notions on a purely extensional basis. My aim in this paper is not to show that Davidsons fails in addressing the so-called extensionality problem. That is no novelty. Even Davidsonians recognize Davidson's failure. My main goal is to explore Davidson's failure as an indirect argument against his key assumption that the radical interpretation is the basis of sense and hence the possibility of thought. There is no priority of language over thought. This is a remnant of the so-called linguistic turn that Davidson inherited from the analytical tradition. The moral is the following: we must come back to Lockean common sense that to learn a natural language and to translate an alien tongue into our own is merely to learn a vehicle for communicating and expressing thoughts we have already had.

Ideology in a Desert Landscape*

AbstractOn one influential view, metaphysical fundamentality can be understood in terms of joint‐carving. Ted Sider has recently argued that (i) some first order quantifier is joint‐carving, and (ii) modal notions are not joint‐carving. After vindicating the theoretical indispensability of quantification against recent criticism, I will defend a logical result due to Arnold Koslow which implies that (i) and (ii) are incompatible. I will therefore consider an alternative understanding of Sider's metaphysics to the effect that (i) some first order quantifier is joint‐carving, and (iii) intensional notions are not joint‐carving. Another result due to Koslow entails that (i) and (iii) are also incompatible. I will argue that this second result is inconclusive. Nevertheless, (iii) is incompatible with another tenet of Sider's metaphysics, namely that (iv) ‘being joint‐carving’ is itself joint‐carving. In order to resolve the inconsistency, I will tentatively argue that condition (iv) should be renounced.

Nonstandardness and the bounded functional interpretation

The bounded functional interpretation of arithmetic in all finite types is able to interpret principles like weak König's lemma without the need of any form of bar recursion. This interpretation requires the use of intensional (rule-governed) majorizability relations. This is a somewhat unusual feature. The main purpose of this paper is to show that if the base domain of the natural numbers is extended with nonstandard elements, then the bounded functional interpretation can be seen as falling out from a functional interpretation of nonstandard number theory without intensional notions. The original bounded functional interpretation can be seen as the trace left behind by the new interpretation when one sees it restricted to the standard number theoretical setting.We also answer an open question regarding the conservativity of the transfer principle vis-à-vis functional interpretations of nonstandard arithmetic.

Can First-Order Logical Truth be Defined in Purely Extensional Terms?

W. V. Quine thinks logical truth can be defined in purely extensional terms, as follows: a logical truth is a true sentence that exemplifies a logical form all of whose instances are true. P. F. Strawson objects that one cannot say what it is for a particular use of a sentence to exemplify a logical form without appealing to intensional notions, and hence that Quine's efforts to define logical truth in purely extensional terms cannot succeed. Quine's reply to this criticism is confused in ways that have not yet been noticed in the literature. This may seem to favour Strawson's side of the debate. In fact, however, a proper analysis of the difficulties that Quine's reply faces suggests a new way to clarify and defend the view that logical truth can be defined in purely extensional terms.

A note on generic quantification and the ontology of twins and bikini

Indefinite plural generic sentences in French have very limited distributions. In particular, in the absence of nominal modifiers, modals or constrastive prosody, the set of nominal predicates that can appear in subject position includes only so-called “inherently plural predicates” like twins. Pluralized sortal predicates like squares are banned unless modified. The paper builds on the assumption that generic indefinite statements are quantificational (contrary to plural definite statements in French) and that quantification requires “individuation”. It strives to explain why twins denotes a plural individual whereas squares does not. It considers various views that have used extensional tools to account for the ontology of the entity denoted by inherently plural predicates, and proposes an explanation based on the intensional notion of coordinated whole. The ontological view that is proposed complements the syntactic view that twins is a reciprocal predicate.

BETWEEN THE OLD METAPHYSICS AND THE NEW EMPIRICISM: COLLINGWOOD'S DEFENCE OF THE AUTONOMY OF PHILOSOPHY

AbstractCollingwood has failed to make a significant impact in the history of twentieth century philosophy either because he has been dismissed as a dusty old idealist committed to the very metaphysics the analytical school was trying to leave behind, or because his later work has been interpreted as advocating the dissolution of philosophy into history. I argue that Collingwood's key philosophical works are a sustained attempt to defend the view that philosophy is an autonomous discipline with a distinctive domain of inquiry and that Collingwood's attempt to defend the autonomy of philosophy is intimately connected to his defence of intensional notions against the kind of meaning scepticism which came to prevail from the 1920s. I defend the philosophical claim that there is a third way between the idealist metaphysics with which Collingwood is often associated and the neo‐empiricist agenda which characterised analytic philosophy in mid‐century by defending the hermeneutic thesis that Collingwood's work is a sustained attempt to articulate a conception of philosophy as an epistemologically first science. Since there is a via media between the old metaphysics and the new empiricism there is no need to choose between a certain kind of armchair metaphysics and a scientifically informed ontology.

Logic and Intensionality DOI:10.5007/1808-1711.2010v14n1p111

There are different ways we use the expressions “extension” and “intension”. I specify in the first part of this paper two basic senses of this distinction, and try to show that the old metaphysical sense, by means of particular instance vs. universal, is more fundamental than the contemporary sense by means of substitutivity. In the second part, I argue that logic in general is essentially intensional, not only because logic is a rule-guided activity, but because even the extensional definition of a logic system presupposes an intensional notion of logical consequence.

Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as ‘There are necessary a posteriori propositions’ or ‘All laws of physics are necessary’ in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate ‘is necessary’ can then be replaced by ‘is necessarily true’. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators.

Re‐Enactment and Radical Interpretation

AbstractThis article discusses R. G. Collingwood's account of re‐enactment and Donald Davidson's account of radical translation. Both Collingwood and Davidson are concerned with the question “how is understanding possible?” and both seek to answer the question transcendentally by asking after the heuristic principles that guide the historian and the radical translator. Further, they both agree that the possibility of understanding rests on the presumption of rationality. But whereas Davidson's principle of charity entails that truth is a presupposition or heuristic principle of understanding, for Collingwood understanding rests on a commitment to internal consistency alone. Collingwood and Davidson diverge over the scope of the principle of charity because they have radically different conceptions of meaning. Davidson endorses an extensional semantics that links meaning with truth in the attempt to extrude intensional notions from a theory of meaning. Since radical translation rests on a truth‐conditional semantics, it rules out the possibility that there may be statements that are intelligible even though based on false beliefs. Collingwood's account of re‐enactment, on the other hand, disconnects meaning from truth, thereby allowing for the possibility of understanding agents who have false beliefs. The paper argues, first, that Davidson's account of radical translation rests on inappropriately naturalistic assumptions about the nature of understanding, and that Davidson commits this error because he develops his account of radical interpretation in response to an epistemological question that is motivated by a skeptical concern: “how can we know whether we have provided the correct interpretation?” Second, that in the twentieth century far too much philosophizing has been driven by epistemological concerns that have obscured attempts to provide adequate answers to the sort of conceptual question with which Collingwood is concerned, namely: “what does it mean to understand?”

No Future

The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore arises whether the notions that are investigated in tense logic can be consistently formalized as predicates. In this paper it is shown that the answer to this question is negative. The logical treatment of the notions of future and past as predicates gives rise to paradoxes due the specific interplay between both notions. For this reason, the tense paradoxes that will be presented are not identical to the paradoxes referred to above.

An enrichment theorem for an axiomatisation of categories of domains and continuous functions

Domain-theoretic categories are axiomatised by means of categorical non-order-theoretic requirements on a cartesian closed category equipped with a commutative monad. In this paper we prove an enrichment theorem showing that every axiomatic domain-theoretic category can be endowed with an intensional notion of approximation, the path relation, with respect to which the category Cpo-enriches.Our analysis suggests more liberal notions of domains. In particular, we present a category where the path order is not ω-complete, but in which the constructions of domain theory (such as, for example, the existence of uniform fixed-point operators and the solution of domain equations) are available.

Empirical Adequacy

In his book, The Scientific Image, Bas van Fraassen argues for an anti-realist view of science according to which the sole epistemological aim of science is to “save the phenomena”. As originally conceived, his constructive empiricism is strongly extensional, but in his account of the empirical adequacy of probabilistic theories, van Fraassen reluctantly abandons this extensional position, arguing that modal (intensional) notions are unavoidable in interpreting probability. I argue in this paper that van Fraassen has not presented the strongest possible case for a fully extensional account of empirical adequacy. On the present account, a probabilistic theory is empirically adequate just in case there is no theory that has a higher likelihood relative to all the phenomena in the actual world. I prove that a theory is empirically adequate if and only if the probability attributed to each observable event that occurs in the actual world is its limiting relative frequency. Thus, in so far as one is concerned with the empirical adequacy (rather than with the literal truth) of probabilistic theories, strict relative frequencies provide an adequate basis for “interpreting probability”.Probabilistic theories are treated in a genuine measurement context. In this connection I distinguish between worlds that are “strongly infinite” and worlds that are only “weakly infinite”. It is characteristic of the former worlds that there is no limit to the precision of actual measurements. I show by example that in some “strongly infinite” worlds, theories will be empirically adequate only if observables are represented by continuous (rather than discrete) random variables. The range of such examples is clarified by a theorem which states necessary and sufficient conditions under which the “phenomena can be saved” without recourse to continuous random variables and real numbers.

A Problem for Actualism About Possible Worlds

T he notion of a possible has many uses in the formal philosophy of language. Its primary use, of course, is in the interpretation of sentences about necessity and possibility. A proposition is necessary if and only if it is true in all possible worlds; possible if and only if true in some possible world. One advantage of the possible worlds interpretation is its extensionality. The intensional notions of necessity and possibility are replaced by quantifiers over possible worlds. The language in which these quantifiers appear, sometimes called world theory, can be given an ordinary Tarski semantics. A second advantage of the possible worlds interpretation is purely heuristic. It just seems to help our modal thinking to imagine other possible worlds. However, the nature of possible worlds is the subject of a familiar controversy, the dispute between actualism and possibilism. One common position in this controversy, which I shall call atomistic actualism, seems to me the most plausible. Nevertheless, I shall show that it is open to serious objection. It fails to provide an adequate interpretation for certain modal sentences, assuming that we adopt standard rules of interpretation. Thus we must either reject atomistic actualism, even though, as I shall argue in the next section, the alternatives are not attractive, or reject the standard semantics, despite its practical successes.

Quine on Analyticity

Quine's views on analyticity and related intensional notions fall naturally into two parts. First, there is his critical attack on the intelligibility of the intensional terminology. Second, there is his positive articulation of a view of language which dispenses with intensional notions. Whether it finally succeeds or not, each part taken separately has its initial plausibility. What I propose to argue, however, is that if we take both of these parts together, then difficulties emerge. Specifically, I propose to argue that if Quine's positive view of language is correct, then his arguments against the intelligibility of the intensional terminology cannot succeed. Further, that if his arguments against the intelligibility of the intensional terminology succeed, then his positive view of language cannot be correct. The relevant features of the view Quine is arguing against are these.