Abstract
In this chapter I bring hyperintensionality in to the picture. In the previous chapter I introduced classical ands non-classical semantics for deontic modals, and suggested some of the problems they have to face are due to their coarseness of grain. Hyperintensionality is one way to get finer-grained tools.
The first Project was to shorten Discourse by cutting Polysyllables into one, and leaving out Verbs and Participles, because in reality all things imaginable are but Nouns. The other, was a Scheme for entirely abolishing all Words whatsoever; and this was urged as a great Advantage in Point of Health as well as Brevity. For it is plain, that every Word we speak is in some Degree a Diminution of our Lungs by Corrosion, and consequently contributes to the shortening of our Lives. An Expedient was therefore offered, that since Words are only Names for Things, it would be more convenient for all Men to carry about them, such Things as were necessary to express the particular Business they are to discourse on.
Jonathan Swift, Gulliver’s Travels
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- 1.
While these definitions are problematic, their formulation is standard. Cf. for instance Forbes (2006), pp. 6–7. The fact that this thesis is more or less endorsed by the academicians of Lagado, Laputa (as quoted at the beginning of the present chapter), and that their language, Balnibarbian, sounded to Gulliver close to Italian, should be taken as a mere coincidence and no consequence about the present author’s philosophical inclinations should be drawn.
- 2.
Cf. Williamson (2006) . We can also define extensionality as an inference rule, rather than an implication: If \(\vdash \alpha \leftrightarrow \beta \) then \(\vdash \mathbf {C}(\alpha ) \leftrightarrow \mathbf {C}(\beta )\), as Olivier Roy (p.c.) suggests, which is obviously weaker.
- 3.
Of course we are considering numbers (as mathematical entities), not arithmonyms (number names: e.g.: ‘three’, ‘tre’, ‘trzy’) or arithmograms (number signs: e.g.: ‘9’, ‘IX’) under a fairly standard view of mathematical entities.
- 4.
Cf. Williamson (2006).
- 5.
This example may well be a false positive: in fact, (54) may be more plausible than (55) because the protasis and the apodosis of (54) are relevantly related; whereas the protasis and the apodosis of (55) are not. But this false positive may be caused by the perennial problem of how to model natural language conditionals in logic. This question would lead us too far from the scope of this work.
- 6.
One of the very first attempts to consider a similar issue, about the identity of thoughts, was obviously by Frege, who had several (unsatisfying, by contemporary standards) proposals (Frege 1918–1919, 1979). See Bernini (2007) for an interesting discussion. Bernini, in particular, proposes to limit the “logical equivalents have the same denotation” principle to “explicit” sentences (i.e. those where substitution of identicals does not cause loss of information) which are also “fundamental” (i.e. there are as many names as individuals).
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- 8.
Other definitions are of course possible: \( \vdash \diamond (\alpha \equiv \beta ) \rightarrow \square (\mathbf {C}(\alpha ) \not \equiv \mathbf {C}(\beta ))\), where ‘\(\rightarrow \)’ is a strict conditional (Tommaso Piazza, (p.c.)) We could weaken HYPERINTENSIONAL and consider it an inference rule rather than an implication: If \(\vdash \square (\alpha \equiv \beta )\) then \(\nvdash \square (\mathbf {C}(\alpha ) \equiv \mathbf {C}(\beta ))\). David Chalmers (p.c.) would define hyperintensionality negatively, saying that it is non intensionality, but he would distinguish between weak hyperintensionality, using metaphysical necessity, and strong hyperintensionality, using apriority. See the next chapter for a discussion of this idea.
- 9.
This is the simplest picture. Of course propositions can be taken as functions from a set of indices (worlds, times, contexts) to truth-values, or as complex functions from context to contents à la Kaplan. The point I make does not change.
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- 11.
Within this approach we can list (i) Fox and Lappin’s Property Theory with Curry Typing (PTCT) (Fox and Lappin 2005) and Pollard’s hyperintensionalism in two versions, i.e. in Pollard (2008b) he proposed to take propositions as primitive, against the standard pictures assuming worlds as primitive; whereas in Pollard (2015) he has built an “agnostic” hyperintensional semantics, working both under the standard assumption that propositions are sets of worlds, and on the rival account where worlds are maximally consistent sets of propositions.
- 12.
Within this approach we can list Pollard’s Category-theoretic Semantics (Pollard 2004) , Tichý et al. Transparent Intensional Logic (TIL) (Tichý 1988 and more recently Duží et al. 2010; Duží and Jespersen forthcoming; Duží 2014; Duží and Materna 2016) and Muskens’s Intensional Type Theory (see especially Muskens 2007a, b).
- 13.
In the last few years there has been an explosion of new proposals involving partial situations, among which which the “possibility semantics” of Holliday et al., HYPE by Leitgeb, and the whole truthmaker approach proposed by Kit Fine in a rather large series of paper. See Chap. 5 for more details.
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- 15.
- 16.
See Duží and Materna (2016).
- 17.
“\(\alpha \)-conversion expresses the idea of “renaming”, i.e. replacing one k-bound variable x by another k-variable y; \(\beta \)-conversion expresses the ideas of functional application and abstraction, [forming for instance propositions by way of predicating properties—my remark]. \(\eta \)-conversion expresses the idea that two functions are identical if, and only if, they take the same arguments to the same values (Jespersen 2010, p. 103f.).”
- 18.
Marie Duži (p.c.) suggests she agrees with this thesis (which I argue for in the next chapter). See also Duží and Materna (2016).
- 19.
Are procedures normative? TIL considers meanings as procedures , rather than the results of applying these procedures. This is the fundamental distinction between a procedural and a denotational semantics.
But procedures seem instrumentally normative, because a procedure gives a set of ordered instruction with the aim of reaching a result, they require you to do certain things in order to get there.
If procedures are indeed normative, albeit only instrumentally, then it seems the case that under the further TIL assumption that meanings are procedures, meanings are normative.
As far as I know, TIL proponents don’t endorse this thesis explicitly, nor they hint at it.
The thesis that meaning is normative has recently been voiced in Gibbard (2012) . In what sense, if any, this could be used to model normative propositions is still unclear. Conte (2007) , among others, proposed to consider the meaning of deontic expressions as a peculiar kind of propositions, i.e. deontic propositions, as quite different from non-deontic propositions. For one, non-deontic propositions would preserve all the features usually associated with non-deontic language, i.e. truth-beareance, validity, etc, whereas there would be no need to postulate deontic propositions to be capable of being true or false, of validity, etc., for the simple fact of their propositionality (propositional nature).
These remarks can also apply to the specification of intensional identity in terms of operational, rather than denotational, semantics of Lappin (forthcoming). (One must take notice that Fox and Lappin’s specification of intensional identity is equality of \(\lambda \) terms, i.e. \(\alpha -, \beta -, \eta -\) equivalence. Counterexamples are easy to find.)
- 20.
To what extent the algebraic approach of Fox and Lappin, and Pollard is structuralist is disputable.
- 21.
- 22.
While Ripley says explicitly he addresses the question of fine-grained propositions, this can be taken to be equivalent with what I called the hyperintensionality question, as far as propositions are concerned.
References
Barwise, J., and J. Etchemendy. 1990. Information, infons, and inference. In Situation Theory and Its Applications, ed. R. Cooper, K. Mukai, and J. Perry, 33–78. CSLI Lecture Notes.
Barwise, J., and J. Perry. 1981. Situations and Attitudes. The Journal of Philosophy 78: 668–691.
Bealer, George. 1982. Quality and Concept. Oxford: Oxford University Press.
Bernini, Sergio. 2007. Senso, denotazione, verità. Annali del dipartimento di Filosofia (nuova serie) XIII: 75–115.
Bjerring, Jens Christian. forthcoming. Impossible Worlds and Logical Omniscience: An Impossibility Result. Synthese.
Bjerring, Jens Christian. 2010. Non-Ideal Epistemic Spaces. Ph.D. thesis, Australian National University.
Bjerring, Jens Christian. 2015. Stratified Modal Semantics.
Bjerring, Jens Christian, and Wolfgang Schwartz. 2016. Granularity Problems.
Chagrov, Alexander, and Michael Zakharyashchev. 1997. Modal Logic. Oxford: Oxford University Press.
Church, Alonzo. 1954. Intensional Isomorphism and Identity of Belief. Philosophical Studies 5 (5): 65.
Church, Alonzo. 1973. Outline of a Revised Formulation of a Logic of Sense and Denotation (Part I). Noûs 7: 24–33.
Church, Alonzo. 1974. Outline of a Revised Formulation of a Logic of Sense and Denotation (Part II). Noûs 8 (2): 135–156.
Church, Alonzo. 1993. A Revised Formulation of the Logic of Sense and Denotation. Alternative (1). Noûs 27 (2): 141–157.
Conte, Amedeo Giovanni. 2007. Norma: cinque referenti. In Ricerche di filosofia del diritto, ed. Lorenzo Passerini Glazel, 27–35. Turin: Giappichelli.
Cresswell, Max J. 1985. Structured Meanings: The Semantics of Propositional Attitudes. Cambridge (MA): MIT Press.
Duží, Marie. 2014. Structural Isomorphism of Meaning and Synonymy. Computación y Sistemas 18 (3): 439–453.
Duží, Marie, and Bjørn Jespersen. forthcoming. Transparent Quantification into Hyperintensional Objectual Attitudes. Synthese.
Duží, Marie, and Pavel Materna. 2016. Validity and Applicability of Leibniz’s Law of Substitution of Identicals. The Logical Yearbook.
Duží, Marie, Bjørn Jespersen, and Pavel Materna. 2010. Procedural Semantics for Hyperintensional Logic: Foundations and Applications of Transparent Intensional Logic. Dordrecht: Springer.
Føllesdal, Dagfinn. 1983. Situations Semantics and the “Slingshot” Argument. Erkenntnis 19: 91–98.
Forbes, Graeme. 2006. Attitude Problems. An Essay on Linguistic Intensionality. Oxford: Oxford University Press.
Fox, Chris, and Shalom Lappin. 2005. Foundations of Intensional Semantics. Oxford: Blackwell.
Fox, Chris, and Shalom Lappin. 2014. Type-Theoretic Logic with an Operational Account of Intensionality. Synthese 192.
Frege, Gottlob [Friedrich Ludwig Gottlob]. 1918–1919. Der Gedanke: Eine logische Untersuchung, Beiträge zur Philosophie des Deutschen Idealismus, I, 58–77.
Frege, Gottlob [Friedrich Ludwig Gottlob]. 1979. Posthumous Writings. Trans. P. Long, and R. White. Oxford: Basil Blackwell
Gibbard, Allan. 2012. Meaning and Normativity. Oxford: Oxford University Press.
Goldblatt, R.I. 1984. Topoi: The Catergorical Analysis of Logic. Amsterdam: Elsevier.
Jago, Mark. forthcoming. Hyperintensional Propositions. Synthese.
Jago, Mark. 2014. The Impossible. An Essay on Hyperintensionality. Oxford: Oxford University Press.
Jespersen, Bjørn. 2010. How Hyper are Hyperpropositions? Language and Linguistic Compass 4 (2): 96–106.
Kratzer, Angelika. 2014. Situations in Natural Language Semantics. In Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta.
Lambek, John, and Dana Scott. 1986. Introduction to Higher Order Categorical Logic. Cambridge: Cambridge University Press.
Lappin, Shalom. forthcoming. Curry Typing, Polymorphism, and Fine-Grained Intensionality. In Handbook of Contemporary Semantics, ed. Shalom Lappin, and Chris Fox. Hoboken: Wiley-Blackwell.
Lewis, David Kellogg. 1983. General Semantics. Philosophical Papers 1: 198–229. Oxford University Press, Oxford.
Moschovakis, Yiannis N. 2006. A Logical Calculus of Meaning and Synonymy. Linguistics and Philosophy 29 (1): 27–89.
Muskens, Reinhard. 1995. Meaning and Partiality. Stanford: Center for the Study of Language and Information.
Muskens, Reinhard. 2007a. Higher Order Modal Logic. In Handbook of Modal Logic, ed. Patrick Blackburn, Johan Van Benthem, and Frank Wolter, 621–653. Amsterdam: Elsevier.
Muskens, Reinhard. 2007b. Intensional Models for the Theory of Types. The Bulletin of Symbolic Logic 72 (1): 98–118.
Pollard, Carl. 2004. Type-logical HPSG. In: Proceedings of the Ninth Annual Conference on Formal Grammar, ed. G. Jäger, P. Monachesi, G. Penn, and S. Wintner, pp. 107–124, Nancy.
Pollard, Carl. 2008a. Hyperintensional Questions. In: Proceedings of the 15th Workshop on Logic, Language, Information, and Computation (WoLLIC ’08), vol. 5110, ed. Wilfrid Hodges, and R. de Queiroz. Springer Lecture Notes in Artificial Intelligence, 261–274. Springer, Dordrecht.
Pollard, Carl. 2008b. Hyperintensions. Journal of Logic and Computation 18 (2): 257–282.
Pollard, Carl. 2015. Agnostic Hyperintensional Semantics. Synthese 192 (3): 535–562.
Ripley, David. 2012. Structures and Circumstances: Two Ways to Fine-Grain Propositions. Synthese 189 (1): 97–118.
Salmon, Nathan U. 1986. Frege’s Puzzle. Ridgeview.
Soames, Scott. 1987. Direct Reference, Propositional Attitudes, and Semantic Content. Philosophical Topics 15 (1): 47–87.
Thomason, Richmond H. 1980. A Model Theory for Propositional Attitudes. Linguistics and Philosophy 4 (1): 47–70.
Tichý, Pavel. 1988. The Foundations of Frege’s Logic. Berlin: de Gruyter.
Von Fintel, Kai, and Irene Heim. 2011. Intensional Semantics, Lecture Notes. Cambridge: MIT.
Williamson, Timothy. 2006. Indicative versus Subjunctive Conditionals, Congruential versus Non-Hyperintensional Contexts. Philosophical Issues 16 (1): 310–333.
Williamson, Timothy. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.
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Faroldi, F.L.G. (2019). A Primer on Hyperintensionality. In: Hyperintensionality and Normativity. Springer, Cham. https://doi.org/10.1007/978-3-030-03487-0_2
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