Dummett Realism
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What is it?
Dummett trying to give a general account of what is going on in the realism debate (as well as arguing for anti-realist positions with regard to a few different areas).
Where can it be found?
Dummett, M.; ‘Realism’ in Truth and Other Enigmas, pp. 145 - 165.
How does it fit in?
It’s the fundamental source for Dummett’s anti-realist position.
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Summary
The realism debate in general - there exists a disputed class of statements (D) - debate is with regard to whether or not the statements in D have an objective truth-value — realist: elements of D have fixed truth-value — anti-realist: elements of D are neither T or F — denies law of the excluded middle - can also be seen as a debate over the notion of meaning: — realist: meaning is what it is for a statement to be true — anti-realist: meaning is knowing what counts as evidence for a statement — hence the anti-realist can still give an account of how we know what statements in D mean - the different attitudes towards truth-values in the debate lead to different conceptions regarding valid deductive inference - note that Dummett does not believe that adopting the anti-realist position commits one to three-valued logic — possibly because statements in D just do not have a truth-value
Evidence - a distinction needs to be made between direct and indirect evidence — but what does indirect evidence mean for the anti-realist? — something like: if then X — can D statements be used in the antecedent? - yes => X a D statement - no => X and antecedent must be given in terms of R statements (see ‘Reduction’ below) - so anti-realist is okay with truth-values being asserted in cases where there is evidence in principle (i.e. we have an indirect justificastion) but not when we are incapable of obtaining evidence - context changes what is considered to be conclusive evidence — e.g. the acceptability of inductive reasoning as conclusive proof in science
Reduction - anti-realist accounts are often reductive: — identify some reductive class of statements R — element of D is T only if some corresponding element of R is T — the reductive class is what provides evidence necessary for meaning on the anti-realist account — hence it is essential that statements in R can be understood independently of statements in D - reductive account is neither necessary nor sufficient for anti-realism however
Particular applications - covered pretty well in Garrett Dummett so I’ll just cover a few points of interest here - only direct evidence available in the case of mathematics - anti-realism as constructivism in mathematics
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What do I think? - the context-dependent stuff needs to be worked through a little more — exactly how does a context come about? is it socially constructed? — if so, then realism (or at the very least the existence of truth-values) becomes a social construction too and many on both sides would be unhappy with this characteristion — how does Carnap fit in here? - overall two stratgies for criticism: - 1. Descriptive inaccuracy (doesn’t adequately capture the realism debate) - 2. Internal problems with Dummett’s position
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