Abstract
Blackburn has outlined a formal account for moral expressivism, and we argued that the moral Frege-Geach problem can be solved formally by appending two rules for the boo-operator which are missing from his account. We then extended Blackburn’s formal account to generate a similar solution to the problem in modal context and showed that the validity of the modal argument can be preserved too in modal expressivism. However, the higher-order element endorsed by Blackburn does not seem necessary for solving the Frege-Geach problem. Nor is his extension from moral expressivism to modal expressivism tenable, since the latter violates its own ontological constraint. A general moral is drawn on the basis on three observations made in evaluating Blackburn’s expressivism.
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Notes
One of the earliest attempts was made by R. M. Hare (1970). His proposal is essentially compositional semantics for expressivist language, which sets the standard for subsequent proposals. In Schroeder (2008), which is among the most recent attempts, the core of solution is still compositional semantics.
Our explanation of Blackburn’s higher-order approach is based mainly on his (1984: 195). The arrow sign ‘⇒’ first appears in Blackburn (1988: 508).
Blackburn writes ‘If H ! p expresses the attitude of endorsing the goal p, ~H ! p then expresses its opposition: tolerating ~p or allowing it to be consistent with an ideal world. So, we can say that T ! A is substitutable for ~H ! A, and H ! A for ~T ! A.’ (1988: 511). Two notes are in order. First, the words ‘goal’ and ‘ideal world’ indicate that Blackburn’s logic is about norms. Second, if ‘~H ! p’ expresses the tolerance of ~p, i.e. ‘T ! ~p’, then what is substitutable for ‘T ! A’ is ‘~H ! ~A’, and what is substitutable for ‘H ! A’ is ‘~T ! ~A’. Schwartz and Hom (Schwartz and Hom 2014: 834) have the same reading as we have.
This rule is based on Blackburn (1988: 508)‘s idea that ‘The contrary attitude B ! p would rule p out of any perfect world.’
See Blackburn (1988: 512) for his reading of conditional in this logic.
Ian G. McFetridge (1990: 145) testifies to the same reading of Blackburn’s account: ‘[Blackburn] is agnostic as to whether modal judgments have truth conditions in any substantive sense: whether in making them we are describing any further aspects of reality.’
If ‘N!’ and ‘I!’ truly mirror ‘□’ and ‘~◇’, then the modal argument can be reformulated as ‘~ ◇ (2 > 3); □(~ ◇ (2 > 3) ⇒ ~ ◇ (2 > 4)); Therefore, ~ ◇ (2 > 4).’ Its validity can be proved easily in a normal modal logic whose accessibility relation is both symmetric and transitive.
This transformation scheme is not fine-grained enough to handle the negation problem, which requires the expressivist logic to distinguish, say, ‘Smith believes that giving to charity is not required’ from ‘Smith does not believe that giving to charity is required’ and ‘Smith believes that not giving to charity is required.’ This problem is formally solvable, as Schroeder (2008), Silk (2015) and Schwartz and Hom (2014) show, though it will demand a substantial amendment to Blackburn’s logic.
Blackburn’s higher-order approach is a customary target of criticism, for example Mark van Roojen (1996) argues that the higher-order account overgenerates valid arguments.
Here we thank the anonymous reviewer for pointing out that being ontologically committed to possible worlds might not be problematic for someone who takes modal concepts to be irreducible.
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Hung, CH., Tse, C.Y.P. The Frege-Geach Problem and Blackburn’s Expressivism. Philosophia 48, 2021–2031 (2020). https://doi.org/10.1007/s11406-020-00194-6
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DOI: https://doi.org/10.1007/s11406-020-00194-6