Abstract
Transparent Intensional Logic is a logical theory developed with a view to logical analysis of sizeable fragments of primarily natural language.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The idea of linguistic sense as a calculation will be familiar not least from Moschovakis’ work on constructive semantics. See Section 1.5 for discussion.
- 2.
Muskens, in (2005, p. 474, n. 2), interprets constructions as ‘procedures that can be used to compute [Fregean] references]’ (ibid., p. 474), which is basically on the right track. We agree, with one proviso, with Muskens’ characterisation of a computational, or procedural, interpretation of Fregean sense: ‘If senses are a certain kind of algorithms, then two senses are identical if the corresponding algorithms are. While identity of algorithms itself is a non-trivial problem, this at least gives something to start with’ (Ibid.). The proviso is that constructions are allowed to be non-finitary. With this proviso in mind, we subscribe to the general ‘propositions-as-algorithms picture’ that Muskens sketches in (ibid., pp. 487ff). For an introduction to how reference-fixing along Fregean lines works in Martin-Löf’s type theory, see Primiero (2004) and (2008).
- 3.
We have avoided the term ‘determiner’ in this book, because it is already in use in linguistics where it has a somewhat different meaning; e.g., articles are determiners.
- 4.
For functions-in-intension as rules or ‘codes’ for rules, see Mitchell (1990, p. 371) or Church (1941).
- 5.
Saarinen (1982, p. 131) offers the same list of trouble-makers, adding logical omniscience. As an aside, it is interesting to note that whereas epistemology has been preoccupied with skepticism (the spectre of knowing too little or nothing at all), epistemic logic has been preoccupied with omniscience (the spectre of knowing too much).
- 6.
See Ranta (1994) for an application of Martin-Löf’s type theory to natural-language discourse.
- 7.
Three cases in point would be Fregean Sinn and Russellian propositions, and also Bolzanian Sätze an sich; see Materna (1998, 2004a).
- 8.
See also Simons (2007, §8): ‘A complex whole is an object with more than one proper part, such that the parts are related together in the whole in a determinate way. This way of their being together in the whole is the structure of the whole.’ Hence, ‘a musket is not a sum of parts: it is a structured whole of parts put together in a certain way’ (ibid., §7).
- 9.
It turns out, however, that we occasionally also need a fifth and a sixth construction, called Execution and Double Execution. Furthermore, the application of Transparent Intensional Logic to database theory has prompted two more constructions; one for constructing ordered n-tuples and another for constructing projections; see Duží (1992).
- 10.
See Section 2.6.
- 11.
For further comparison of TIL and Montague’s IL, see Section 2.4.3.
- 12.
We are neglecting Mill’s actual psychologistic semantic theory here.
- 13.
See Davidson (1968).
- 14.
As Muskens says, ‘Why does [Montague’s] IL show such exotic behaviour; why do Leibniz’s Law, Universal Instantiation and Lambda Conversion not hold under the normal conditions? Because the logic was explicitly designed to reflect certain opacity phenomena in natural language’ (1989, p. 10).
- 15.
In a recent comparison of Tichý and Zalta, Sierszulska says correctly that, ‘[K]nowing all the values of the [intensions] … would be the same as knowing all the facts … The proper analysis of a proposition cannot assume such [empirical, as opposed to logical] omniscience, and it stops at the point where all the possibilities are taken into account, but none is specified’ (2006, p. 491).
- 16.
Tichý puts the point succinctly in a 1966 paper; ‘We assume, of course, a normal linguistic situation, in which communication proceeds between two people, both of whom understand the language. Logical semantics does not deal with other linguistic situations’ (2004, p. 55, n. 1). Likewise, C.A. Anderson says about Church’s Alternative (0): ‘Sense is what is known when the language is understood. In accordance with this, the intensional semantical rules should state essential facts about the semantics, the mastery of which constitutes (ideal) competence with the language. These may include the rules of synonymy [.]’ (1998, p. 163).
- 17.
We know we are cutting corners here by paraphrasing ‘Bedeutung’ as ‘entity’. We are doing so in order not to get bogged down in the ongoing discussion of how best to render ‘Bedeutung’. The standard translation has been ‘reference’, but this does not do justice to Frege’s idiosyncratic distinction between ‘Sinn’ and ‘Bedeutung’, which are more or less synonymous nouns in ordinary German, barring idiomatic usage; e.g., ‘sinnlos’ and ‘bedeutungslos’ are certainly not synonymous adjectives. The best verbatim translation would have been ‘meaning’, to be contrasted with ‘sense’. But the idea of Frege being the meaning of ‘Frege’ sits very poorly indeed on the ears. Besides, ‘Bedeutung’ comes with a suggestion of pointing at an entity―‘deuten auf’―that ‘meaning’ lacks. Fortunately, we can afford to be offhand about ‘Bedeutung’, since we are so strongly biased toward Sinn.
- 18.
See also Carnap (1947) .
- 19.
Church (1956) has ‘denotation’.
- 20.
Originally, Tichý also held to the view that Fregean sense may be explicated as a possible-world intension; cf. (1986a, p. 253, 2004, p. 651).
- 21.
See Section 3.3.
- 22.
See Section 2.1.2 for another aspect of this problem, and Section 2.2.1 for the definitions of synonymy and equivalence.
- 23.
This is not to say that it would have empirical information to offer; see Section 5.4.
- 24.
Note that the first place in Frege (1892a) where he introduces the notion of sense is not the famous one involving ‘The Morning Star’ and ‘The Evening Star’, but one involving the medians of a triangle. Here we chose a still simpler example.
- 25.
They express empty concepts, the former identifying an empty class of geometrical figures, the latter identifying no number at all. See Section 2.2.
- 26.
The general idea that concepts are procedures was, however, advanced by Tichý already in 1968 and 1969. We will deal with concepts (i.e. closed constructions in normal form) as procedural meanings in Section 2.2.
- 27.
See Section 2.4.2.
- 28.
Moreover, intensional* supposition is dominant with respect to the extensional* one. For details, see Section 2.6.
- 29.
This marks an advance over Tichý’s stance as expounded in 1986a and 1988 (§41).
- 30.
See Hintikka and Sandu (1989).
- 31.
See Section 5.1.2.
- 32.
See Section 3.4. Though incomplete is, strictly speaking, a privative modifier, such that an incomplete meaning would not be a meaning, by ‘pragmatically incomplete meaning’ we intend, stipulatively, a meaning that is an open construction with free variables.
- 33.
We are making a simplification here to get the top-down picture clear. As a matter of fact, there are several floors of hyperintensions, intensions and extensions to get off at. In particular, while you always start out at the top, at a level of hyperintensions, there are going to be floors of hyperintensions above the floor you are on. Furthermore, the floor you get off at may itself be one of hyperintensions (though a floor one level down from where you started out). On the other hand, the vast bulk of empirical cases that we analyse in this book conform to the picture of starting out with a hyperintension, descending to the intension it presents and then descending from intension to extension. ‘Charles is happy’ would be a case in point.
- 34.
Also Montague (1974a), together with other semanticists, has opted for the functional approach and adopted a typed λ-calculus for his logical analysis of natural language.
- 35.
We will deal with partiality in detail in Sections 2.6 and 2.7, where the need for partial functions is demonstrated together with a specification of inference rules for working with them.
- 36.
See Section 2.1.2 and also Tichý (1988, p. 287).
- 37.
―which is to say that we adhere to ‘the Fregean doctrine that predicates name functions’, as Bealer says (1982, p. 89).
- 38.
In particular, we are not going to draw distinctions that reflect notational differences that are not backed up by abstract procedural differences. So Mates’ puzzle is not a puzzle for us; see Section 5.1.
- 39.
Tichý (1988) devotes an entire chapter to variables, explaining their objectual role as constructions; for details see (1988, pp. 47–62).
- 40.
The degree of a first-order entity corresponds roughly to an order in predicate logics. For instance, in order to ascribe properties to individual properties in predicate logic, we need to work within second-order logic. However, in TIL, properties of individuals are 1st-order objects of degree 1. Properties of properties of individuals are 1st-order objects of degree 2; and so on.
- 41.
See Montague (1974a).
- 42.
For a more detailed comparison of Tichý’s TIL with Montague’s IL, see Section 2.4.3.
- 43.
For further background, see Tichý (1988, pp. 177–200).
- 44.
This holds no less for communication between solitary language-users and themselves in the form of inner soliloquies, as ought to be uncontroversial as far as philosophical theses go. We also tend to think that unverbalized thinking is impossible without the use of (a non-private) language; but we are not broaching this issue here.
- 45.
Cmorej calls such a string a ‘semi-expression’ in his 2005 discussing the thesis that semantics is a priori.
- 46.
In a wider philosophical context, the notion of epistemic framework might be of use to hermeneutics; e.g., with respect to Gadamer-like melting-together (Verschmelzung) of two or more different epistemic frameworks. We have not attempted to take the notion into this direction, though.
- 47.
To be sure, in mathematics we can model them as zero-arity functions. But this hardly makes them functions.
- 48.
See below; it is the type of a function (ω → (τ → ξ)) for a type ξ.
- 49.
As of early 2010.
- 50.
Also Hintikka seems to accept this conception, but his possible worlds are epistemic, dependent on particular language-users (See, e.g., Hintikka and Hintikka, 1989).
- 51.
Remember that collections, sets, classes of α-objects are members of type (οα); TIL handles classes (subsets of a type) as characteristic functions. Similarly, relations (-in-extension) are of type(s) (οβ1…β m ).
- 52.
For the theory of concepts, see Section 2.2.
- 53.
See Section 3.1 dealing with definite descriptions.
- 54.
See Section 5.1 dealing with propositional attitudes.
- 55.
We are presupposing―naïvely, as it happens―the existence of a definition of the property of planethood that will decide unequivocally for any celestial body in our solar system whether it is a planet.
- 56.
Now we are using ‘trivial’ and ‘non-trivial’ intuitively. By ‘trivial’ we do not mean epistemically trivial. Once we explain what is meant by ‘trivial’, we will use rigorous terms instead.
- 57.
See Definition 1.6.
- 58.
The term ‘essential core’ was coined by Pavel Cmorej (1996). See also Cmorej (1988, 2006).
- 59.
The distinction between ‘primary’ vs. ‘secondary’ intensions is not to be confused with some other distinctions like, e.g. Evans’ ‘deep’ vs. ‘superficial’ intensions or what also goes under the name ‘primary and secondary intensions’ in two-dimensional semantics. See Evans (1977).
- 60.
We do not consider here subatomic particles of quantum physics, of course. After all, Heisenberg’s uncertainty principle has a negligible effect on objects of macroscopic scale.
- 61.
The claim that there are no dependencies between primary properties of the intensional base requires qualification, however. Consider being red and being blue. Neither is parasitic upon the other, but at the same time they are dependent, by being defined in terms of their respective positions in a spectrum.
- 62.
Cmorej (2006) calls these properties partly essential.
- 63.
Cmorej (2006) calls these properties essential.
- 64.
We add this category just for completeness. Purely partial properties are bizarre properties like the one defined as follows: \({{\uplambda }}w{{\uplambda }}t\,\iota c\,[[c = \emptyset ] \wedge \neg [c = \emptyset ]]\), where \(c/^* _1 \to _v ({{\textrm{o}\upiota }})\).
- 65.
The idea of modest anti-essentialism owes much to Pavel Cmorej.
- 66.
This example is due to Pavel Cmorej.
- 67.
However, as Cmorej points out in 1988, it is an open question whether there are properties that are partly constant in a less obvious way, for which the respective essential core would be decidable only a posteriori. The thoughts on how to categorize properties arose from a discussion with Cmorej in 2005.
- 68.
As Tichý argues in 1987, where he uses the example of a watch being ‘repaired’ by a watchmaker in such a way as to become a key.
- 69.
The full logic of requisites is set out in Chapter 4.
- 70.
See Duží (2007) for a discussion of wharrots. A wharrot is an individual consisting of a carrot and a whale. Unless further restrictions are laid down, wharrots exist as soon as whales and carrots do. (We are indebted to Maarten Franssen for the example of wharrots.)
- 71.
This problem is connected with the analysis of property modification, including being a malfunctioning P, dealt with in Section 4.4.
- 72.
See also Geach (1972, pp. 215–16) for the related problem of ‘the cat on the mat’.
- 73.
A proper part of X is an individual Y such that Y is a part of X and Y ≠ X.
- 74.
As this point about typing also shows, TIL requires that the objects that are to be logically manipulated be typed and defined before any (possible) axiomatization. Of course, proposing some axioms involves running a risk, for it could be objected that the chosen axioms do not truly describe the nature of the objects. But this risk is only what characterises scientific work when carried out in a realist manner, according to which axioms do not prescribe what the objects of a domain are, but instead try to describe some properties that are ontologically and conceptually prior to the axioms. Analogously, ‘Poincaré, like Kronecker, thought one does not have to define the whole numbers or construct their properties on an axiomatic foundation. Our intuition precedes such a structure’ (Kline, 1980, p. 233).
- 75.
Presupposition will be defined in Definition 1.14
- 76.
See also Duží (2003a).
- 77.
By ‘type-theoretically polymorphous functions’ we mean a set of functions that are defined and thus behave in the same way, independently of their type. For instance, any member of the set of functions Cardinality associates a finite class with the number of its elements. Hence this definition is polymorphous; there are actually infinitely many cardinality functions, one for each type: \(Card_1 /({{\uptau (o\iota )}})\)―the number of a set of individuals, \(Card_2 /({{\uptau (o\uptau )}})\)―the number of a set of numbers, etc., which we indicate by using a type variable α in the type of \(Cardinality/({{\uptau }}({{\textrm{o}\upalpha }}))\).
- 78.
This principle, and its relevance to semantic analysis, is discussed in Section 2.1.
- 79.
We are disregarding here the problem of physical units.
- 80.
Intensional and hyperintensional context were characterized in Section 1.3, and will be formally defined in Section 2.6 together with valid rules for inferring existence. Here just briefly: a hyperintensional context is one in which constructions are mentioned, whereas an intensional context is one in which constituents are used with intensional (or de dicto) supposition.
- 81.
For the propositional attitudes of knowing and believing, see Sections 5.1 and 5.3.
- 82.
For attitudes and anaphoric sentences, see Chapter 5 and Section 3.5, respectively.
- 83.
See Tichý (1988, pp. 74–5).
- 84.
See, e.g., Gamut (1991) or Montague (1974d).
- 85.
The original German text can be found in the Anhang: Kritik der Kantischen Philosophie in the 2nd Book of (1819), and goes,‘[Kant] ist demjenigen zu vergleichen, der die Höhe des Thurmes aus dessen Schatten mißt, ich aber dem, welcher den Maaßstab unmittelbar anlegt.’
- 86.
Cf. Russell, who famously talked about thinking about logical objects for 2 s every 6 months, the rest of the time thinking about notation (1953, p. 185).
- 87.
Tichý suggested construing his λ-formalism as an iconography or pictorial script (see especially 1988, p. 224). This construal is buttressed by a strict enforcement of the principle of subject matter , which in turn might suggest something like a homomorphism between the set of λ-terms and the set of constructions of a given order (though an isomorphism is excluded, since there are more constructions of a given order than there are λ-terms). However, we have not attempted to develop this sketchy idea of iconography into a theory of λ-terms as something like logical pictures of constructions, mainly because the project of logical analysis of language does not need it and because any such theory would have to be embedded within the vast discussion on perfect languages, the expressive power of pictures, etc. For a discussion of the notion of pictorial script (without reference to TIL), see Jespersen and Reintges (2008).
- 88.
—where ‘office’ is used as in normal English and not as in TIL.
- 89.
See Materna (2004b).
- 90.
More precisely, synonymous expressions express a common concept; see Section 2.2.
- 91.
In choosing the term ‘construction’, Tichý was inspired by geometry ‘where we speak of various constructions of, say, the center of a circle, using rule and compass’ (1986b, p. 514, 2004, p. 601).
- 92.
- 93.
The respective hypothesis expresses an ineffective procedure.
- 94.
For example, see Sundholm (1994) on Frege’s epistemological motivations for a fine-grained individuation of Gedanken.
- 95.
Van Heijenoort attempts to interpret Fregean Sinn in terms of trees. He suggests (1977, pp. 99–100) that the Fregean Sinn of a formula T is to be identified with a tree T', whose semantic structure will be isomorphic to the syntactic structure of T. The suggestion is prima facie appealing, not least because the diagrammatic structure of trees is in the vicinity of the syntactic structure of Frege’s Begriffsschrift notation. However, as Van Heijenoort himself points out, ‘a tree is a mapping… Thus, in Fregean terms, a tree would be the object that is the Werthverlauf of a certain function. This conclusion may seem quite odd.’ Indeed it does. But, worse, if Fregean Sinn is to be sliced in terms of cognitive significance rather than merely logical equivalence, then a mapping won’t do as analysans due to the crude individuation of mappings.
- 96.
- 97.
Moschovakis’ notion of algorithm borders on being too permissive, since algorithms are normally understood to be effective. (See Cleland (2002) for discussion.) Tichý separates algorithms sharply from constructions: ‘The notion of construction is…correlative not with the notion of algorithm itself but with what is known as a particular algorithmic computation, the sequence of steps prescribed by the algorithm when it is applied to a particular input. But not every construction is an algorithmic computation. An algorithmic computation is a sequence of effective steps, steps which consist in subjecting a manageable object…to a feasible operation. A construction, on the other hand, may involve steps which are not of this sort’ (1986b, p. 526 2004, p. 613).
- 98.
This three-step analysis anticipates Section 2.1.1.
- 99.
The other option amounts to conceiving ‘is a bachelor’ as a semantically complex expression. See also Section 2.2.1.
- 100.
See Section 2.1 for the method of semantic analysis.
- 101.
See Section 1.4.3 for the list of logical objects.
- 102.
This problem was tackled as early as in 1837 by Bolzano , who introduced a modern method of variation of (objective) representations (‘Vorstellungen an sich’) and defined generally valid sentences with respect to representations r 1 ,…,r m such that the sentence remains true if these representations are changed or varied (See 1837, §§147–48).
- 103.
Similarly, the formula ‘\(\neg \exists x\,[E(x) \wedge \neg E(x)]\)’ of first-order predicate logic is true on every interpretation assigning a subset of the universe to the symbol ‘E’, whereas there are interpretations of ‘E’ and ‘O’ on which the formula ‘\(\neg \exists x\,[E(x) \wedge O(x)]\)’ is false, viz. those interpretations that assign non-disjoint sets to the symbols ‘E’ and ‘O’.
- 104.
For the sake of simplicity we are now omitting the symbol of Trivialization of logical objects and using the standard notation of quantifiers and infix notation for the truth-functions.
- 105.
See Tichý (1988, p. 235).
- 106.
Note also that due to the ramified hierarchy of types, no inconsistency problems arise when introducing truth predicates like True and True*. In our higher-order typed approach there is no need to use disquotation like True(‘walks(Bill)’) ⇔ walks(Bill) and a hierarchy of meta-languages with their established grounded truths. The sentence ‘Bill walks’ is true in world w at time t if the proposition constructed by \({{\uplambda }}w{{\uplambda }}t[{}^0 Walk_{wt} {}^0 Bill]\) takes value T in w at t.
- 107.
See Tichý (1986a, p. 256, 2004, p. 654).
- 108.
See Section 2.6.
- 109.
To assign the type ι to a novel is a crass philosophical simplification, of course; here it is logically innocuous, since we are not going to draw inferences.
- 110.
‘Propositional’ attitudes divide into relations (-in-intension) to propositions/οτω and propositional constructions/\(*_n \to {\textrm{o}}_{{{\uptau \upomega }}}\). The former are often called implicit attitudes, the latter explicit attitudes. We will deal with propositional attitudes in detail in Section 5.1.
- 111.
See Strawson (1950).
- 112.
More precisely, its meaning occurs always intensionally, see Section 2.6.2, in particular Definition 2.20.
- 113.
See Zouhar (2009), where he deals with the Kripkean distinction between rigid designators de jure and de facto.
- 114.
Now we use this convention: ‘P’ for a construction of a proposition, ‘P’ for the proposition v-constructed by P.
- 115.
- 116.
It is interesting to note that ‘[the] ground zero [of New York City]’ has now been elevated to the status of proper name, which requires capitalizing both words, as in ‘Ground Zero’. Many sites are ground zero, but only one is Ground Zero, relative to the status that current American English has bestowed upon ‘Ground Zero’. In journalese ‘Ground Zero’ refers to one particular ground zero. So if the Pope visits the NYC ground zero then the New York Times et al. are likely to write ‘The Pope to visit Ground Zero’.
- 117.
We will deal with temporal de dicto vs. de re cases in Section 2.5.2.3.
- 118.
See Section 1.5.1 for details on the notion of logical form.
- 119.
A valid argument need not be truth-preserving from conclusion back up to its premises, either; namely, if the argument is unsound.
- 120.
See Muskens (1995), Barwise and Perry (1983).
- 121.
See Muskens (1995, pp. 1–3).
- 122.
The semantics of proper names is simplified here, allowing ‘Bill’ to be simply a label of an individual. See, however, Section 3.4. Moreover, on the TIL conception, there are no non-existing individuals: we work with a constant domain of individuals.
- 123.
For the definition of synonymy, see Section 2.2, Definition 2.10.
- 124.
- 125.
It is understood that the temperature is not just any temperature (of something), but a particular temperature, and most likely the temperature at the location of whoever says the temperature is rising.
- 126.
We conceive of believing as a relation-in-intension between an individual and a proposition here, making believing an implicit attitude. See, however, Chapter 5. In order to mark the scope of particular λ-bindings of variables w and t we use numerical subscripts here.
- 127.
For details on arguments, see Sections 1.5.1 and 5.4.
- 128.
For more on requisites and essence, see Chapter 4.
- 129.
See Chapter 5 for details on propositional attitudes.
- 130.
Here we only briefly characterize the three contexts. Precise definitions will be provided in Section 2.6. Note that the notions ‘intensional’ and ‘extensional’ are used here in a broader sense than in possible-world semantics. To distinguish these notions from possible-world intension and extension, we will often add the asterisk ‘*’ when talking about (hyper-) intensional/extensional occurrence of a construction.
References
Cmorej, P. 2006. Holé indivíduá a predikácia (Bare indi-viduals and predication). In Jazyk z pohladu sémantiky, prag-matiky a filozofie vedy (Language from the Point of View of Semantics, Pragmatics, and Philosophy of Science), ed. M. Zouhar, 137–161. Brati-slava: Institute of Philosophy, Slovak Academy of Sciences.
Duží, M. 2007. Properties on the edge. In The World of Language and the World Beyond Language: A Festschrift for Pavel Cmorej, eds. T. Marvan and M. Zouhar, 42–68. Bratislava: Department of Philosophy, Slovak Academy of Sciences.
Geach, P.T. 1972. Logic Matters. Oxford: Blackwell.
Chierchia, G. 1989. Anaphora and attitudes de se. In: Contextual Expressions, eds. J. van Benthem and P. van Emde Boas. Dordrecht: Reidel.
Duží, M. 1992. Semantic information connected with data. In Database Theory ICDT’92, eds. J. Biskup and R. Hull, 376–390. Lecture Notes in Computer Science. Berlin: Springer.
Gamut, L.T.F. 1991. Logic, Language and Meaning, vol. II. Chicago, London: The University of Chicago Press.
Hindley, J.R. and J.P. Seldin. 1986. Introduction to Combinators and λ-Calculus. Cambridge: Cambridge University Press.
Simons, P. 2007. Abstraction, structure, and substitution: lambda calculus and its philosophical significance. Polish Journal of Philosophy 1: 81–100.
Hintikka, J. and M.B. Hintikka. 1989. The Logic of Epistemology and the Epistemology of Logic: Selected Essays, Synthese Library, vol. 200. Dordrecht, Boston, London: Kluwer.
Carnap, R. 1947. Meaning and Necessity. Chicago: Chicago University Press.
Woods, W.A. 1981. Procedural semantics as a theory of meaning. In Elements of Discourse Understanding, eds. A.K. Joshi and B.L. Webber. Cambridge: Cambridge University Press.
Moschovakis, Y.N. 2006. A logical calculus of meaning and synonymy. Linguistics and Philosophy 29: 27–89.
Saarinen, E. 1982. Propositional attitudes are not attitudes towards propositions. In Intensional Logic, Acta Philosophica Fennica, vol. 35, eds. I. Niiniluoto and E. Saarinen, 130–162. Helsinki: Societas Philosphica Fennica.
Jespersen, B. 2003. Why the tuple theory of structured propositions isn’t a theory of structured propositions. Philosophia 31: 171–183.
Evans, G. 1977. Reference and contingency. The Monist 62: 161–189.
Tichý, P. 1988. The Foundations of Frege’s Logic. Berlin, New York: De Gruyter.
Ranta, A. 1994. Type-Theoretical Grammar. Oxford: Clarendon Press.
Church, A. 1956. Introduction to Mathematical Logic. Princeton: Princeton University Press.
Kaplan, D. 1975. How to Russell a Frege-Church. Journal of Philosophy 72: 716–729.
Moschovakis, Y.N. 1994. Sense and denotation as algorithm and value. In Lecture Notes in Logic, vol. 2, eds. J. Väänänen and J. Oikkonen, 210–249. Berlin: Springer.
Davidson, D. 1968. On saying that. Synthese 19: 130–46.
Materna, P. 1998. Concepts and Objects, vol. 63. Acta Philosophica Fennica. Helsinki: Philosophical Society of Finland.
Dretske, F. 1977. Laws of nature. Philosophy of Science 44: 248–268.
Yagisawa, T. 2001. Partee verbs. Philosophical Studies 103: 253–270.
Muskens, R. 1995. Meaning and Partiality. CSLI and FOLLI, California: Stanford.
Lambalgen, M. van and F. Hamm. 2004. Moschovakis’ notion of meaning as applied to linguistics. In Logic Colloquium’01, eds. M. Baaz, S. Friedman, and J. Krajicek. Amsterdam: University of Amsterdam. Digital Academic Repository. http://dare.uva.nl/record/123675/. Accessed 7 September 2009.
Sundholm, G. 1994. Proof-theoretical semantics and Fregean identity criteria for propositions. The Monist 77: 294–314.
Primiero, G. 2004. The determination of reference in a constructive setting. Giornale di Metafysica 26: 483–502.
Jespersen, B. and C. Reintges. 2008. Tractarian Sätze, Egyptian hieroglyphs, and the very idea of script as picture. The Philosophical Forum 39: 1–19.
Kline, M. 1980. The Loss of Certainty. Oxford: Oxford University Press.
Johnson-Laird, P.N. 1977. Procedural semantics. Cognition 5: 189–214.
Zouhar, M. 2009. On the notion of rigidity for general terms. Grazer Philosophische Studien 78: 207–229.
Fodor, J.A. 1975. Tom Swift and his procedural grandmother. Cognition 6: 229–247.
Linsky, B. and E.N. Zalta. 1995. Naturalized platonism versus platonized naturalism. Journal of Philosophy 92: 525–555.
Bochvar, D.A. 1939. On a 3-valued logical calculus and its applications to the analysis of contradictions (in Russian). Matematiceskij sbornik 4: 287–308.
Cleland, C.E. 2002. On effective procedures. Minds and Machines 12: 159–179.
Hintikka, J. 1962. Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca: Cornell University Press.
Cocchiarella, N.B. 2003. Conceptual realism and the nexus of predication. Metalogicon 16: 45–70.
Strawson, P.F. 1950. On referring. Mind 59: 320–344.
Cmorej, P. 1996. Empirické esenciálne vlastnosti (Empirical essential properties). Organon F 3: 239–261.
Church, A. 1941. The Calculi of Lambda Conversion. Annals of Mathematical Studies. Princeton: Princeton University Press.
Gaskin, R. 2008. The Unity of the Proposition. Oxford: Oxford University Press.
Priest, G. 1992. What is a non-normal world? Logique et Analyse 139–140: 291–301.
Mitchell, J.C. 1990. Type systems for programming languages. In Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics, ed. J.V. Leeuwen, 365–457. Amsterdam: Elsevier; Cambridge: MIT Press.
Hintikka, J. and G. Sandu. 1989. Informational independence as a semantical phenomenon. In Logic, Methodology and Philosophy of Science, ed. J.E. Fenstad, 571–589. Amsterdam: Elsevier.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Duží, M., Jespersen, B., Materna, P. (2010). A programme of general semantics. In: Procedural Semantics for Hyperintensional Logic. Logic, Epistemology, and the Unity of Science, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8812-3_1
Download citation
DOI: https://doi.org/10.1007/978-90-481-8812-3_1
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8811-6
Online ISBN: 978-90-481-8812-3
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)