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2014 | OriginalPaper | Buchkapitel

2. Constructivism

verfasst von : Andreas Kapsner

Erschienen in: Logics and Falsifications

Verlag: Springer International Publishing

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Abstract

In this chapter, I will provide a brief summary of Dummett’s constructivist program. My central topics, the meaning of the logical constants and the admissibility of logical laws, lie at the heart of a grand philosophical system, in which Dummett deftly strings together philosophical insights about language, logic and metaphysics. In some cases, it is quite impossible to understand his arguments about logical consequence without having at least a general idea of the outline of the whole program. This chapter aims to give such an outline.

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Vorheriges Kapitel Introduction

Nächstes Kapitel Intuitionism

For me, the central sources are his essays “TRUTH,” “What Is A Theory Of Meaning (II)” (WTM) and the book “The Logical Basis of Metaphysics” (LBM).

See the introduction of Wright (1993) for detailed discussion on these and other matters that are only skirted here.

“Realists about the area of discourse...” is a bit vague; the reason for this is that it is not always the existence of objects that is at stake, for example in discussions about the reality of the past or the future. In any case, even though Dummett often writes as if the case for or against realism has to be negotiated for each area of discourse separately, the arguments he brings forth are for the most extremely general. Therefore, I’ll drop the relativization to a specific area of discourse until further notice.

cf. Braver (2007) for a comparison between Dummett’s and more liberal and anarchic conceptions of Anti-realism.

The example is adapted from Brouwer, only that he used seven 7s. These have in the meantime been found in the decimal expansion of \(\pi \). As far as I know, seventy 7s have not yet turned up.

There is surely evidence in Dummett’s writings that he sometimes understands “in principle undecidable” in this sense. But on balance, I think he more often uses the phrase “in principle” in the sense outlined above. See for example WTM p. 45, where he talks about “sentences which are, in practice or even in principle, decidable, that is, for which a speaker has some effective procedure which will, in a finite time, put him into a position in which he can recognize whether or not the condition for the truth of the sentence is satisfied.”

I use “disproof” to mean the proof of the negation of a statement.

Ian Rumfitt has suggested such a strategy in Rumfitt (2007).

Like most propositional non-classical logics, intuitionistic logic is strictly weaker than classical logic in that classical logic validates all intuitionistic inferences. Non-classical logics are often described in an impressionistic way by pointing out which kind of classical inferences are not supported, as in this section.

To spell it out, the connection is established by an appeal to the disquotational scheme

“\(A\)” is true iff \(A\),

the principle that a disjunction is true iff at least one of the disjuncts is and the principle that \(\lnot A\) is true iff \(A\) is false, and the semantic demand that no statement may have more than one truth value.

None of these principles is completely uncontroversial, but they surely are intuitively plausible.

TOE, p.XX.

ibid.

The status of LEM and LET will then depend on whether we are dealing with a verificationistic or a falsificationistic theory. In the verificationistic case, both will fail, and in the falsificationistic case, both will hold.

LBM, p.10

There are very important proof theoretic arguments for intuitionistic logic. These arguments, however, are also seen as concerning the meanings of the logical constants. Indeed, the field of study these arguments fall into is now known as proof theoretic semantics. Important as this field is, I will not consider it further.

The talk of “earlier” and “later” is useful, but somewhat problematic. The change from assertibility to truth conditions in Dummett’s thinking is not an abrupt one; rather, one sees a steady increase in the statistical likelihood of his talking about truth conditions, with the tipping point probably somewhere in the late 1970s. More on that in Sect. .

And this is the reason for his earlier view that assertibility conditions suffice for specifying the meaning of a statement.

WTM, p.71

Apart from the sources I cited, Dummett (1975) offers a crisp presentation of the two arguments.

One might start an exploration here: Hale (1999), Miller (2002), Miller (2003), Rosenkranz (2002), Tennant (2002) and Wright (1993).

Cf. Kirkham (1995), p. 248 ff. and Green (2001), p. 24. for further discussion and more sample quotes.

LBM, p.21. Maybe “theory of language use” would have been a better label. Not only easier to discern from “meaning theory,” it would have made the rest of this quote sound less puzzling: “The notion of meaning itself need not, therefore, play an important role in a theory of meaning.” (ibid.) It might not, if there were no tight connection between meaning and use. However, we have seen in Sect. 2.8 that Dummett thinks that such a tight connection does hold.

see Sect. 3.6.

see Sect. 3.7.

Dummett is fully aware that at this point he can’t claim to be following Wittgenstein any more, cf. LBM p. xi.

EOI, p. 250

Carnap (1959)

Beall and Restall (2006)

Beall and Restall offer yet a third way to specify what a case is. A case might be a situation, something which might be incomplete and even inconsistent. This will give them a relevant logic, First Degree Entailment (FDE). I will say more about relevance and FDE in Chap. 3.

If any. In fact, Beall and Restall argue that anti-realists can make use of classical logic (Beall and Restall 2006, p. 46 ff); their argument, however, has nothing much to do with their pluralism.

Titel: Constructivism
verfasst von: Andreas Kapsner
Verlag: Springer International Publishing
Buch: Logics and Falsifications
Print ISBN: 978-3-319-05205-2

Electronic ISBN: 978-3-319-05206-9

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-05206-9_2

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