P. M. S. Hacker, Tutorial Fellow in Philosophy, St. John's, remarks:
"Carnap, unsurprisingly, is incredulous."
"Carnap's account of analyticity, he remonstrates, is intended as an *explication* of the philosophical concept of analyticity, as applied to an ordinary language such as English, which is indeed imprecise.
"Expressions in ordinary language do not have sharply defined meanings."
"Quine argues that he did not know whether
'Everything green is extended'
is analytic or not."
"Quine attributes his uncertainty to the unclarity of the term ‘analytic’ ("Two dogmas of empiricism," p. 32)."
"Carnap objects that the unclarity is due *not* to the term ‘analytic’, but to the fact that it is unclear, in an ordinary language such as English, whether the ‘green’ is applicable to a single spatio-temporal point, where a point is construed as lacking extension."
"An ordinary language such as English does not *talk* of points thus construed."
"Grice and Strawson (in their infamous, "In defence of a dogma") strengthen Carnap’s point.
"Grice and Strawson note that the *same* uncertainty attaches to the question of whether
'Everything green is extended'
is merely *true* -- never mind 'logically true.'"
"Quine could *hardly* complain, Grice and Strawson argue, that, even for Quine, ‘true’ is irremediably unclear."
"In a constructed language, as Carnap has it, one lays down meaning postulates in order to ensure clarity."
"Hence, IF it is a meaning postulate that
‘G’ (‘green’)
IS inapplicable to spatio-temporal points,
‘(x) (Ux z> ~ Gx)’
is analytic in L.
And so is
‘(x) (Gx z> Ex)’
(where ‘U’ signifies ‘unextended’ and ‘E’ ‘extended’).
"Analytic in L," Carnap argues, denotes a sentences whose truth depends on its meaning alone, and is thus independent of the contingency of facts, or ‘true in virtue of meaning’.
"Of course, it does not follow that such a statements cannot be revoked."
"One same entence can be analytic in one system, and synthetic in another."
"An analytic truth is unrevisable only that it remains 'analytically true' as long as the language rules, or indeed, postulates, are not changed."
"Carnap might have added that it is anything but obvious what it would be to *revise* one’s belief that every bachelor is unmarried, without changing the use, or meaning, if you prefer, of the expression!"
"The attribution of truth to a 'synthetic' sentence may change in the light of experience, even though the logical structure of the language does not change."
"The analytic/synthetic distinction may be drawn always and only with respect to a language system, i.e., a language organised according to explicitly formulated rules or postulates, not with respect to a historically given natural language [such as English]’
-- Carnap, ‘Quine on Analyticity’, in "Dear Carnap, Dear Van."
Friday, February 14, 2020
P. M. S. Hacker on Rudolf Carnap and H. P. Grice
"Carnap, unsurprisingly, was incredulous."
"Carnap's account of analyticity, he remonstrates, is intended as an *explication* of the philosophical concept of analyticity as applied to an ordinary language such as English, which is indeed imprecise, since expressions in ordinary language do not have sharply defined meanings."
"Quine argues that he did not know whether ‘Everything green is extended’ is analytic or not, and he attributed his uncertainty to the unclarity of the term ‘analytic’ (TDE 32)."
"Carnap objects that the unclarity is due *not* to the term ‘analytic’, but to the fact that it is unclear in an ordinary language such as English whether the term ‘green’ is applicable to a single spatio-temporal point, where a point is construed as lacking extension, since ordinary language does not talk of points thus construed."
"Grice and Strawson strengthen Carnap’s point in noting that the same uncertainty attaches to the question of whether it is true that everything green is extended - and Quine could hardly complain that the term ‘true’ is irremediably unclear."
"In a constructed language, one lays down meaning postulates in order to ensure clarity."
"Hence, if it is a meaning postulate that ‘G’ (‘green’) is inapplicable to spatio-temporal points, ‘(x) (Ux z> ~ Gx)’ is analytic in L, and so is ‘(x) (Gx z> Ex)’ (where ‘U’ signifies ‘unextended’ and ‘E’ ‘extended’).
"Analytic in L," Carnap argues, signifies sentences whose truth depends on their meanings alone, and is thus independent of the contingency of facts, or ‘true in virtue of meanings’.
"Of course, it does not follow that such statements cannot be revoked."
"The same sentence can be analytic in one system and synthetic in another."
"An analytic truth is unrevisable only in the sense that it remains analytically true as long as the language rules are not changed."
"Carnap might have added that it is anything but obvious what it would be to revise one’s belief that every bachelor is unmarried, without changing the use (or meaning) of the expression."
"The attribution of truth to synthetic sentences may be changed in the light of experience, even though the logical structure of the language does not change."
"The analytic/synthetic distinction can be drawn always and only with respect to a language system, i.e. a language organised according to explicitly formulated rules, not with respect to a historically given natural language [such as English]’
-- Carnap, ‘Quine on Analyticity’, in "Dear Carnap, Dear Van."
"Carnap's account of analyticity, he remonstrates, is intended as an *explication* of the philosophical concept of analyticity as applied to an ordinary language such as English, which is indeed imprecise, since expressions in ordinary language do not have sharply defined meanings."
"Quine argues that he did not know whether ‘Everything green is extended’ is analytic or not, and he attributed his uncertainty to the unclarity of the term ‘analytic’ (TDE 32)."
"Carnap objects that the unclarity is due *not* to the term ‘analytic’, but to the fact that it is unclear in an ordinary language such as English whether the term ‘green’ is applicable to a single spatio-temporal point, where a point is construed as lacking extension, since ordinary language does not talk of points thus construed."
"Grice and Strawson strengthen Carnap’s point in noting that the same uncertainty attaches to the question of whether it is true that everything green is extended - and Quine could hardly complain that the term ‘true’ is irremediably unclear."
"In a constructed language, one lays down meaning postulates in order to ensure clarity."
"Hence, if it is a meaning postulate that ‘G’ (‘green’) is inapplicable to spatio-temporal points, ‘(x) (Ux z> ~ Gx)’ is analytic in L, and so is ‘(x) (Gx z> Ex)’ (where ‘U’ signifies ‘unextended’ and ‘E’ ‘extended’).
"Analytic in L," Carnap argues, signifies sentences whose truth depends on their meanings alone, and is thus independent of the contingency of facts, or ‘true in virtue of meanings’.
"Of course, it does not follow that such statements cannot be revoked."
"The same sentence can be analytic in one system and synthetic in another."
"An analytic truth is unrevisable only in the sense that it remains analytically true as long as the language rules are not changed."
"Carnap might have added that it is anything but obvious what it would be to revise one’s belief that every bachelor is unmarried, without changing the use (or meaning) of the expression."
"The attribution of truth to synthetic sentences may be changed in the light of experience, even though the logical structure of the language does not change."
"The analytic/synthetic distinction can be drawn always and only with respect to a language system, i.e. a language organised according to explicitly formulated rules, not with respect to a historically given natural language [such as English]’
-- Carnap, ‘Quine on Analyticity’, in "Dear Carnap, Dear Van."
P. M. S. Hacker on Rudolf Carnap and H. P. Grice
"Carnap, unsurprisingly, was incredulous. His account of analyticity, he remonstrated, was intended as an explication of the philosophical concept of analyticty
as applied to ordinary language, which is indeed impredse, since expressions in
ordinary language do not have sharply defined meanings. Quine had argued that
he did not know whether ‘Everything green is extended’ is analytic or not, and he
attributed his uncertainty to the unclarity of the term ‘analytic’ (TDE 32). Carnap
objected that the unclarity was due not to the term ‘analytic’, but to the fact that
it is unclear in ordinary language whether the term ‘green’ is applicable to a single
spatio-temporal point, where a point is construed as lacking extension, since ordinary language does not talk of points thus construed. (Grice and Strawson strengthened Carnap’s point in noting that the same uncertainty attaches to the question of
whether it is true that everything green is extended - and Quine could hardly
complain that the term ‘true’ is irremediably unclear.) In a constructed language,
one lays down meaning postulates in order to ensure clarity. Hence, if it is a
meaning postulate that ‘G’ (‘green’) is inapplicable to spatio-temporal points, then
‘(x) (Ux z> ~ Gx)’ is analytic in L, and so is ‘(x) (Gx z> Ex)’ (where ‘U’ signifies
‘unextended’ and ‘E’ ‘extended’). ‘Analytic in L’, Carnap argued, signifies sentences whose truth depends on their meanings alone, and is thus independent of
the contingency of facts, or ‘true in virtue of meanings’. Of course, it does not
follow that such statements cannot be revoked; the same sentence can be analytic
in one system and synthetic in another. An analytic truth is unrevisable only in the
sense that it remains analytically true as long as the language rules are not changed.
(He might have added that it is anything but obvious what it would be to revise
fine’s belief that bachelors are unmarried, without changing the use (or meaning)
c of the expression.) The attribution of truth to synthetic sentences may be changed
in the light of experience, even though the logical structure of the language does
not change. ‘The analytic/synthetic distinction can be drawn always and only with
respect to a language system, i.e. a language organised according to explicitly
formulated rules, not with respect to a historically given natural language’ (Carnap,
‘Quine on Analytidty’, in Dear Camap, Dear Van, pp. 427-32)."
Wednesday, August 8, 2018
Grice v. Carnap on what philosophy isn't
Here's a draft for "The City" which dates back a while. I stumbled across it and made a pass at bringing it to a close.
In (once) recent postings to the Grice club Speranza and I have touched anew a topic on which we have not wholly agreed in the past, perhaps in the manner in which Grice and Carnap might have differed.
At its most stark there is a radical difference between Carnap and Grice on the scope and nature of philosophy.
For Carnap philosophy is confined to a priori reasoning yielding analytic truths expressing necessary propositions, which he would rather have in some formal language by way of escaping the inescapable ambiguity and logical incoherence of natural languages.
Our knowledge of natural languages falls under Hume's "matters of fact", hence a posteriori, synthetic and contingent.
For Carnap the study of such things, a posteriori knowledge, is, by definition empirical science, and for this he is called scientistic.
Well perhaps not just for that. Its not just that he calls it science, but also that the "unity of science" demands that these phenomena be considered continuous with, and addressed by the same methods, as the rest of science.
I have tended to talk in a similar manner, at least some of the way.
So I talk about the study of natural languages as belonging to empirical science, even though I don't myself subscribe to the "unity" thesis.
(and I might add, that Carnap's pluralism is a reason to wonder how substantial the "unity of science" was for him).
Against this, Speranza, who knows more about natural language, philosophy of language, ordinary language philosophy and the science of linguistics (none of these to be confused) objects, quite rightly.
There are a few points here on which I will gently criticise Carnap (where others would do so enthusiastically).
A lot of it is "mere" terminology, some of it is demarcation, which is also terminology.
Thus, in my case if not in Carnap's, its little more than inept terminology to talk of all a posteriori knowledge as belonging to science, and it's worth pleading that if that's as far as it goes, then it doesn't really amount to Grice's devil of scientism.
On the other hand, insisting as Carnap did (though he did soften) that philosophy is confined to analytic pronouncements, is the kind of terminological eccentricity which appears as a controversial demarcation, and an intolerant ejection from the status of philosophy of much that philosophers have done.
The suggestion of dogmatism may be contested, for Carnap was more conspicuously pluralistic than he was an advocate of the unity of science, and these two are in tension.
The unity of science is most forcefully presented as a doctrine about language, as some kind of reductionism of the whole of language to one special language.
But Carnap's pluralism rejects the thesis that any language has a special status. He wants phenomenalistic, physicalistic and "theoretical" language all to be equally acceptable, and expected each science to have its own special language.
Grice has an incompatible principle which also looks as if it might be one of those terminological/demarcation things.
It might just be methodological, that all philosophical problems should be addressed in the first instance by a careful study of the relevant ordinary language, but it is hard not to see this as a refusal to accept as philosophy those kinds of problem for which ordinary language can provide no illumination, and thus as a matter of demarcation.
Could Grice really have believed that there are no philosophical problems for which a preliminary study of ordinary language is not valuable, or even relevant, and which his doctrine would therefore be excluding from philosophy?
By way of a speculative gesture I'm going to suggest a concession to which I think Carnap might possibly have been amenable, and a complementary concession which, if extracted from Grice, might draw the teeth from this conflict.
It's principally about adjustments to terminology and demarcation.
The demarcation issue concerns the respective scopes of philosophy and science, and the point to press upon Carnap is that the real world is rather messier than his principled division of academic disciplines along lines inspired by Hume's fork (but not actually in conformance with Hume's conception of philosophy). Not all scientists are concerned with empirical matters, there is such a thing, for example, as "theoretical physics", which is an entirely mathematical discipline concerned with the mathematical consequences of scientific theories such as the general theory of relativity, rather than with the empirical, experimental confirmation or falsification of scientific theories.
Likewise there always have been, and possibly always will be, kinds of philosophising which involve reasoning a posteriori to conclusions which are not purely logical, but which for one reason or another cannot be addressed by the methods of empirical science, or which will only become science after some kind of pre-scientific investigation (perhaps "conceptual elucidation") has rendered them fit for scientific investigation.
The concession for Carnap is to give up his simplistic conception of the words "science" and "philosophy", and allow that these be decoupled from the rigid association which he preferred between these disciplines and the search for synthetic and analytic truth respectively.
Carnap was capable of making this kind of terminological adjustment, bowing thus to necessity. He did in fact concede on the scope of philosophy, and he also gave signs of conceding on the usage of the term "logical truth".
Certainly he did shift his usage of the technical term L-truth which for many years stood for "logical-truth" in the broad sense in which for Carnap took to be the same as analyticity. In the transition from the first edition of Meaning and Necessity and the paper on "Meaning Postulates" which was to be included as an appendix in the second edition, he shifts to using the term "L-truth" for a narrow conception of logical truth and introduces the term "A-truth" for analyticity and the broad conception.
There is no sign that he is personally inclined to take the narrow view, but by this time it perhaps seems a fait accompli, that the community now takes the narrow view (without in general recognising that this is mere terminology).
Turning back to Grice, the concession we need is that, even if a study of the relevant ordinary language were allowed as an important preliminary (to philosophical insight), maybe sometimes there isn't any. Surely there may be recondite and esoteric corners of mathematics or physics so far removed from everyday life that terminological issues can only be progressed through a detailed analysis of the scientific origins of the particular esoteric language. Must these corners of science be devoid of philosophy?
In (once) recent postings to the Grice club Speranza and I have touched anew a topic on which we have not wholly agreed in the past, perhaps in the manner in which Grice and Carnap might have differed.
At its most stark there is a radical difference between Carnap and Grice on the scope and nature of philosophy.
For Carnap philosophy is confined to a priori reasoning yielding analytic truths expressing necessary propositions, which he would rather have in some formal language by way of escaping the inescapable ambiguity and logical incoherence of natural languages.
Our knowledge of natural languages falls under Hume's "matters of fact", hence a posteriori, synthetic and contingent.
For Carnap the study of such things, a posteriori knowledge, is, by definition empirical science, and for this he is called scientistic.
Well perhaps not just for that. Its not just that he calls it science, but also that the "unity of science" demands that these phenomena be considered continuous with, and addressed by the same methods, as the rest of science.
I have tended to talk in a similar manner, at least some of the way.
So I talk about the study of natural languages as belonging to empirical science, even though I don't myself subscribe to the "unity" thesis.
(and I might add, that Carnap's pluralism is a reason to wonder how substantial the "unity of science" was for him).
Against this, Speranza, who knows more about natural language, philosophy of language, ordinary language philosophy and the science of linguistics (none of these to be confused) objects, quite rightly.
There are a few points here on which I will gently criticise Carnap (where others would do so enthusiastically).
A lot of it is "mere" terminology, some of it is demarcation, which is also terminology.
Thus, in my case if not in Carnap's, its little more than inept terminology to talk of all a posteriori knowledge as belonging to science, and it's worth pleading that if that's as far as it goes, then it doesn't really amount to Grice's devil of scientism.
On the other hand, insisting as Carnap did (though he did soften) that philosophy is confined to analytic pronouncements, is the kind of terminological eccentricity which appears as a controversial demarcation, and an intolerant ejection from the status of philosophy of much that philosophers have done.
The suggestion of dogmatism may be contested, for Carnap was more conspicuously pluralistic than he was an advocate of the unity of science, and these two are in tension.
The unity of science is most forcefully presented as a doctrine about language, as some kind of reductionism of the whole of language to one special language.
But Carnap's pluralism rejects the thesis that any language has a special status. He wants phenomenalistic, physicalistic and "theoretical" language all to be equally acceptable, and expected each science to have its own special language.
Grice has an incompatible principle which also looks as if it might be one of those terminological/demarcation things.
It might just be methodological, that all philosophical problems should be addressed in the first instance by a careful study of the relevant ordinary language, but it is hard not to see this as a refusal to accept as philosophy those kinds of problem for which ordinary language can provide no illumination, and thus as a matter of demarcation.
Could Grice really have believed that there are no philosophical problems for which a preliminary study of ordinary language is not valuable, or even relevant, and which his doctrine would therefore be excluding from philosophy?
By way of a speculative gesture I'm going to suggest a concession to which I think Carnap might possibly have been amenable, and a complementary concession which, if extracted from Grice, might draw the teeth from this conflict.
It's principally about adjustments to terminology and demarcation.
The demarcation issue concerns the respective scopes of philosophy and science, and the point to press upon Carnap is that the real world is rather messier than his principled division of academic disciplines along lines inspired by Hume's fork (but not actually in conformance with Hume's conception of philosophy). Not all scientists are concerned with empirical matters, there is such a thing, for example, as "theoretical physics", which is an entirely mathematical discipline concerned with the mathematical consequences of scientific theories such as the general theory of relativity, rather than with the empirical, experimental confirmation or falsification of scientific theories.
Likewise there always have been, and possibly always will be, kinds of philosophising which involve reasoning a posteriori to conclusions which are not purely logical, but which for one reason or another cannot be addressed by the methods of empirical science, or which will only become science after some kind of pre-scientific investigation (perhaps "conceptual elucidation") has rendered them fit for scientific investigation.
The concession for Carnap is to give up his simplistic conception of the words "science" and "philosophy", and allow that these be decoupled from the rigid association which he preferred between these disciplines and the search for synthetic and analytic truth respectively.
Carnap was capable of making this kind of terminological adjustment, bowing thus to necessity. He did in fact concede on the scope of philosophy, and he also gave signs of conceding on the usage of the term "logical truth".
Certainly he did shift his usage of the technical term L-truth which for many years stood for "logical-truth" in the broad sense in which for Carnap took to be the same as analyticity. In the transition from the first edition of Meaning and Necessity and the paper on "Meaning Postulates" which was to be included as an appendix in the second edition, he shifts to using the term "L-truth" for a narrow conception of logical truth and introduces the term "A-truth" for analyticity and the broad conception.
There is no sign that he is personally inclined to take the narrow view, but by this time it perhaps seems a fait accompli, that the community now takes the narrow view (without in general recognising that this is mere terminology).
Turning back to Grice, the concession we need is that, even if a study of the relevant ordinary language were allowed as an important preliminary (to philosophical insight), maybe sometimes there isn't any. Surely there may be recondite and esoteric corners of mathematics or physics so far removed from everyday life that terminological issues can only be progressed through a detailed analysis of the scientific origins of the particular esoteric language. Must these corners of science be devoid of philosophy?
Tuesday, August 7, 2018
Cognitive Architecture
Following a slow moving theme on which I posted here some 18 months ago, I wanted to write something about a kind of "cognitive architecture" in which I am now engaged, and I thought it might be suitable material for this blog.
Eternal truths, if such there be, are of course, once established, a kind of knowledge, and knowledge is the stuff of cognition. So, the place where one might hope to find eternal truths could be some ideally conceived cognitive system. A philosophical exposition of what eternal truth might be, how and where we might find it, and how it might be brought to bear in improving our mundane existence might be thought of as a kind of cognitive architecture, and also as a special species of philosophy, which I now like to call synthetic philosophy.
Having thus made a pass at arguing the relevance of this topic to the city of eternal truth, I will try to elucidate more carefully the kind of cognitive architecture which I think might serve the purpose. I'm going to do this by throwing a bunch of adjectives at it, and explaining how these are to be taken, so that we arrive at a more definite conception.
The first port of call in the exposition of this kind of cognitive architecture is philosophical, it is the articulation of a systematic philosophy in terms of which the cognitive system may be understood, and which will also form bedrock in the "belief system" of this cosmic cognitive system. Since this most closely relates to the philosophy of Rudolf Carnap, I will talk about it at the Carnap Corner Blog.
Eternal truths, if such there be, are of course, once established, a kind of knowledge, and knowledge is the stuff of cognition. So, the place where one might hope to find eternal truths could be some ideally conceived cognitive system. A philosophical exposition of what eternal truth might be, how and where we might find it, and how it might be brought to bear in improving our mundane existence might be thought of as a kind of cognitive architecture, and also as a special species of philosophy, which I now like to call synthetic philosophy.
Having thus made a pass at arguing the relevance of this topic to the city of eternal truth, I will try to elucidate more carefully the kind of cognitive architecture which I think might serve the purpose. I'm going to do this by throwing a bunch of adjectives at it, and explaining how these are to be taken, so that we arrive at a more definite conception.
- architecture - I think of this as the highest levels in the design of some system, concerned with the system as a whole, the principal subsystems and how these fit together, and all the considerations which might precede these matters in the development of the system, particularly, in the case of cognitive systems, a whole raft of considerations which are recognisably philosophical.
- cognitive - this tells us what the system is intended to do, viz. to acquire, hold, reason with and apply knowledge.
- synthetic - there are two distinct ways in which the proposed architecture should be considered synthetic. The first is that the architecture is not intended to be descriptive of any existing cognitive system, but rather prescriptive of various possibilities, which we offer for consideration as models for a future cognitive system which we might strive to realise. The second is that the system is intended to be in part manufactured, and ultimately, overwhelmingly manufactured. A third sense is that the aspects of the architecture which may be regarded as philosophical in character (e.g. the account of what in the system counts as knowledge) will be examples of this kind of philosophy which I am calling synthetic philosophy (a term I will elaborate on in due course).
- hybrid - the cognitive systems for which an architecture is offered are intended to be hybrid, a mix of organic and inorganic constituents. Initially the intelligence will be supplied by organic components (human brains), but eventually some inorganic subsystems will deserve to be considered intelligent as well.
- cosmic - If we first consider our globally networked computing machinery, together with all the human brains which in one way or another connect into that network, as being a computational system slowly morphing into a cognitive system, and think forward to a period between one million and one billion years in the future, when the physical reach of humanity and our progeny extends spatially over a significant part of our galaxy, then we have the context at which the proposed cognitive architecture is aimed. It is nevertheless intended to be immediately applicable, and hence an architecture for the transition from our present global system to a future cosmic system. The hybrid/cosmological pair are also intended to help de-anthropomorphise our conception of cognition, we are not concerned merely with human cognition, but with cognition in very different systems.
The first port of call in the exposition of this kind of cognitive architecture is philosophical, it is the articulation of a systematic philosophy in terms of which the cognitive system may be understood, and which will also form bedrock in the "belief system" of this cosmic cognitive system. Since this most closely relates to the philosophy of Rudolf Carnap, I will talk about it at the Carnap Corner Blog.
Sunday, February 12, 2017
To mock a mockinbird: Carnap, Grice, and Smullyan
Speranza
Smullyan shared some passions with Carnap and Grice, if you can believe it.
Smullyan, the author of a very influential, "First-Order Logic" believed, well, in the power of first-order logic.
His education was peripatetic. An MA followed by a PhD from Princeton on "Theory of Formal Systems."
His main contribution was puzzling: it was his puzzles.
He was an admirer of Goedel, and his list of favourite authors should please both a Carnapian and a Griceian: Dodgson (aka Lewis Carroll), Boole, Cantor, and a few others!
And he had a sense of humour.
When Grice left Oxford, he had to give some reason. He said he moved because he was looking for the assistance of logicians and he couldn't find ONE in Oxford!
This was a bit hyperbolic. He, for one, was one (Strawson credits him in "Introduction to Logical Theory" as the tutor "from whom I have never ceased to learn about logic"). In "Vacuous Names," Grice's convoluted exposition of a System to allow for names like "Marmaduke Bloggs," who refers the hero who climbed Mt. Everest on hands and knees ("the invention of journalists, as it happened," Grice adds), there is a passing reference to Smullyan. With Myro, and others, Smullyan provided Grice with a way to provide a neat exposition of first order predicate logic -- of which Smullyan was an expert.
The fact that both played the piano helped!
Smullyan shared some passions with Carnap and Grice, if you can believe it.
Smullyan, the author of a very influential, "First-Order Logic" believed, well, in the power of first-order logic.
His education was peripatetic. An MA followed by a PhD from Princeton on "Theory of Formal Systems."
His main contribution was puzzling: it was his puzzles.
He was an admirer of Goedel, and his list of favourite authors should please both a Carnapian and a Griceian: Dodgson (aka Lewis Carroll), Boole, Cantor, and a few others!
And he had a sense of humour.
When Grice left Oxford, he had to give some reason. He said he moved because he was looking for the assistance of logicians and he couldn't find ONE in Oxford!
This was a bit hyperbolic. He, for one, was one (Strawson credits him in "Introduction to Logical Theory" as the tutor "from whom I have never ceased to learn about logic"). In "Vacuous Names," Grice's convoluted exposition of a System to allow for names like "Marmaduke Bloggs," who refers the hero who climbed Mt. Everest on hands and knees ("the invention of journalists, as it happened," Grice adds), there is a passing reference to Smullyan. With Myro, and others, Smullyan provided Grice with a way to provide a neat exposition of first order predicate logic -- of which Smullyan was an expert.
The fact that both played the piano helped!
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