1st FLC Workshop: Report (Crispin Wright)
[Following this post.]
If I had time I would write extensively on all of the contributions to our workshop, but seeing that there is a yet-to-be-written thesis waiting on my desk, I'll keep it short. For this part of the report I want to summarize some interesting points from Crispin Wright's talk. Crispin's paper was a highlight of the workshop, a characteristic confrontation with foundational issues. Nothing could have been more appropriate as an end to the first workshop than these overarching considerations, running from the technical to the speculative. Here I will only briefly address some of Crispin's thoughts on inferentialism, and leave out the very interesting discussion of compatibility and paradox.
Crispin's starting point is a worry about inferentialism that has occupied me quite a lot in the past. (In fact, it was the motivation for a paper I gave at UNILOG'07 in China.) If we assume a, broadly speaking, inferentialist position on the semantic content of logical constants -- that they have their meaning determined by the inferential rules that govern their use, e.g., intro- and elim-rules -- it appears that any revision of the rules threatens to change the meaning of the involved constant. Of course, this is not straightforward. It assumes (i) that all the rules are meaning-determining (if they're not, revising the semantically insignificant set of rules will be ok), and (ii) that any change in the (meaning-conferring) rules is sufficient for a corresponding change in meaning.
Prima facie, then, there is a tension between inferentialism and revision of logic. It appears that the inferentialist idea is somehow wedded to anti-revisionism. A curious result indeed, since many inferentialists are revisionists (e.g. Dummett, Prawitz, Tennant). Crispin: "It the meaning-constitutive anti-revisionist were correct, there would be as little sense in the idea of challenging, say, Modus Ponens as challenging the definition of 'father' as male parent."
Yet, clearly there is more to the revisionism advocated by Dummett and others. In fact, a hesitation to accept a Wittgensteinean line of non-revisionism is precisely one of Dummett's motivations to study the logical constants. Both Dummett and Crispin share the following thought: Even if one accepts inferentialism, one might want to allow that an inferential practice can fail to determine a concept. The practice need not be in good standing, it might be inconsistent or pathological in some other sense. The meaning-determination has misfired. (Think, for example, of the intuitionist's case against classical negation.)
An approach not favoured by either Dummett nor Crispin is pandemic holism. In Crispin's paper this is associated with the plasticity of meaning: Granted, an inferential practice must be consistent (or at least non-explosive) to be in good standing, but nothing else is required. "Provided that a consistent practice is enjoined, both the logical expressions the rules concern, and the statements free of their special vocabulary which they enable us to connect via inference, will simply take on meaning in such a way as to be both intelligible and validly so connected respectively."
However, Crispin denies that consistency is any guarantee of determinacy of content (for logical constants). Tunk (the dual of tonk) is a connective with an elim-rule that is (in some sense) too weak. The point is that tunk is perfectly consistent; it simply does not allow us to infer all that we ought to be able to infer. (An analogous point can be made with quantifiers.) Another example is a consistent rule that requires the domain to be infinite. What is characteristic of these rules: they are consistent but inharmonious. Crispin suggests that for rules like these, it is not merely a matter of them being poor inferential rules, they fail to be meaning-determining. "Commonsense recoils: there are no such meanings to mean."
So why accept that these weird rules come short of content-fixing? This is where Crispin and I part ways, I think. For him a crucial part of the epistemology of logic is "the obviousness of the basic rules". This is a rather intractible phenomenological property a rule-set, and Crispin suggests that it plays a significant rule in meaning-determination. "[T]he virtue of harmony is that it seems to go with the ability of rules of inferential practice to create a concept in such a way that the phenomenology of obviousness kicks in".
Evidence is for this, I take it, is to be found in the phenomenological contrast between, say, disjunction and tunk. Yet, I am not entirely convinced. That the phenomenology of obviousness is connected to harmony rather than, for example, our familiarity with a practice seems to me to be unclear. Logicians are probably familiar with being introduced to new complex rules and axioms, working away almost blindly in the beginning, only to find that after a period of being entrenched we aquire a familiarity that sheds light on the concept behind the formalism. (Compare Gödel on perception and intuition in mathematics.)
If I had time I would write extensively on all of the contributions to our workshop, but seeing that there is a yet-to-be-written thesis waiting on my desk, I'll keep it short. For this part of the report I want to summarize some interesting points from Crispin Wright's talk. Crispin's paper was a highlight of the workshop, a characteristic confrontation with foundational issues. Nothing could have been more appropriate as an end to the first workshop than these overarching considerations, running from the technical to the speculative. Here I will only briefly address some of Crispin's thoughts on inferentialism, and leave out the very interesting discussion of compatibility and paradox.
Crispin's starting point is a worry about inferentialism that has occupied me quite a lot in the past. (In fact, it was the motivation for a paper I gave at UNILOG'07 in China.) If we assume a, broadly speaking, inferentialist position on the semantic content of logical constants -- that they have their meaning determined by the inferential rules that govern their use, e.g., intro- and elim-rules -- it appears that any revision of the rules threatens to change the meaning of the involved constant. Of course, this is not straightforward. It assumes (i) that all the rules are meaning-determining (if they're not, revising the semantically insignificant set of rules will be ok), and (ii) that any change in the (meaning-conferring) rules is sufficient for a corresponding change in meaning.
Prima facie, then, there is a tension between inferentialism and revision of logic. It appears that the inferentialist idea is somehow wedded to anti-revisionism. A curious result indeed, since many inferentialists are revisionists (e.g. Dummett, Prawitz, Tennant). Crispin: "It the meaning-constitutive anti-revisionist were correct, there would be as little sense in the idea of challenging, say, Modus Ponens as challenging the definition of 'father' as male parent."
Yet, clearly there is more to the revisionism advocated by Dummett and others. In fact, a hesitation to accept a Wittgensteinean line of non-revisionism is precisely one of Dummett's motivations to study the logical constants. Both Dummett and Crispin share the following thought: Even if one accepts inferentialism, one might want to allow that an inferential practice can fail to determine a concept. The practice need not be in good standing, it might be inconsistent or pathological in some other sense. The meaning-determination has misfired. (Think, for example, of the intuitionist's case against classical negation.)
An approach not favoured by either Dummett nor Crispin is pandemic holism. In Crispin's paper this is associated with the plasticity of meaning: Granted, an inferential practice must be consistent (or at least non-explosive) to be in good standing, but nothing else is required. "Provided that a consistent practice is enjoined, both the logical expressions the rules concern, and the statements free of their special vocabulary which they enable us to connect via inference, will simply take on meaning in such a way as to be both intelligible and validly so connected respectively."
However, Crispin denies that consistency is any guarantee of determinacy of content (for logical constants). Tunk (the dual of tonk) is a connective with an elim-rule that is (in some sense) too weak. The point is that tunk is perfectly consistent; it simply does not allow us to infer all that we ought to be able to infer. (An analogous point can be made with quantifiers.) Another example is a consistent rule that requires the domain to be infinite. What is characteristic of these rules: they are consistent but inharmonious. Crispin suggests that for rules like these, it is not merely a matter of them being poor inferential rules, they fail to be meaning-determining. "Commonsense recoils: there are no such meanings to mean."
So why accept that these weird rules come short of content-fixing? This is where Crispin and I part ways, I think. For him a crucial part of the epistemology of logic is "the obviousness of the basic rules". This is a rather intractible phenomenological property a rule-set, and Crispin suggests that it plays a significant rule in meaning-determination. "[T]he virtue of harmony is that it seems to go with the ability of rules of inferential practice to create a concept in such a way that the phenomenology of obviousness kicks in".
Evidence is for this, I take it, is to be found in the phenomenological contrast between, say, disjunction and tunk. Yet, I am not entirely convinced. That the phenomenology of obviousness is connected to harmony rather than, for example, our familiarity with a practice seems to me to be unclear. Logicians are probably familiar with being introduced to new complex rules and axioms, working away almost blindly in the beginning, only to find that after a period of being entrenched we aquire a familiarity that sheds light on the concept behind the formalism. (Compare Gödel on perception and intuition in mathematics.)
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