by J. L. Speranza
THIS MEANT as commentary to Jones's commentary -- but system disallowed it. It's all about 'pulling oneself up by one's bootstraps' in special connection with something like Carnap's System CR and Grice's System Q which becomes Myro's System GHP.
Very good points. Indeed, System GHP is intended as a 'model' of, say, say English. I call it "H. P." to refer to 'highly plausible' or 'hopefully powerful' -- while sticking to the initials of Grice being H. P, Herbert Paul.
And you are right that it's not meant as a 'meta-language' in principle. Indeed, in defining System Q (which is the one that Grice himself created) he uses natural English, ordinary English, as the metalanguage for his Sysem Q (and Myro does the same when defining his System G -- on which System GHP is based. Consider:
"If phi is a formula, phi /\ psi is a formula".
That simple enough 'formation rule' for System GHP -- actually subscripts for the three elemnts of "phi /\ psi" would be needed -- may cover some complexity should we want to define it in the object-language of System GHP itself. For it involves a sort of predicate-calculus, and we are dealing with the propositional-calculus segment of System GHP. For " ... is a formula" is really quite a piece of work, if you ask me! In any case I would think that Grice intends his System Q to cover BOTH the object-language (L1) and the meta-language -- but I would need to revise this. Similarly, in WoW:first two pages of 'Logic and Conversation' when he paints the picture of the Formalist (alla Hilbert) as dealing with a 'set of formulae' which may be taken as axiomata, etc., he seems to be talking of 'system', as he indeed is, as the 'proper' set of formulae -- 'proper' in the sense of 'itself', not qua technical term in set-theory! -- rather than as the set of formulae cum editorial work that the meta-language L2 may provide. But this may be tricky. In any case, there seems to be some sort of regress in that if, as Grice thinks, the formalist's point in constructing L1 is to free the language of 'metaphysical excrescences', what would the point be if any such excrescence, metaphysical or other, is brought onto the system via the meta-language?
Tarksi is a good case in point, maybe -- for I thought his "Semantic definition of truth" FULL of metaphysics at the meta-level. And it may be something like an examination of work being done by Davidson at Berkeley that had Grice formulating Bootstrap in the first place! (I am referring to Davidson on his "Truth" essay in Synthese that apparently had a big influence on Strawson's student, Strawson). But will re-read stuff and elaborate (mean: think). Thanks for input.
Friday, June 4, 2010
Thursday, June 3, 2010
Carnap and Grice pulling ourselves up by their own bootstraps
by JLS
THIS WAS MEANT as comment to the previous post, but system disallowed it.
Good. Yes, there must be something Tarskian behind this. Grice refers only briefly to Tarski in WoW:55 re: "Monkeys can talk", when he writes: "A theory of truth has (as Tarski notes) to provide not only for occurrences of true in sentennces in whch what is being spoken of as true is specified [in the object-language] but also for occurrences in which no specification is given (e.g. The policeman's statement was true)."
(Grice thought that Strawson's and indeed Ramsey's (whom he also quotes on that same page) failed to provide for that.
But I'm not sure about the NL-FL (natural-formal language) distinction at this point. Yes, there must have been something along that line in the Carnap-Grice difference of outlook. But I would think that syntax, even in NL, allows for a pretty easy way to mark the object-language/meta-language distinction: the simple quotes or scare quotes --. So, even in terms of syntactic admissability (which you say you are laxer when it comes to something like a System, and like to indulge in the semantics-ontology interface) I would think Grice is seeing a bigger problem there.
It would seem then that we do have an user of the L1 -- this may be a given. A system like System GHP, or System CR, aims at reconstructing or constructing a segment of "NL" (or the language of scientists in Carnap's construal) as it is used (provisos there). But what about L2? This is the system-analyst's job (There IS a discipline, 'systems analysis', no?, so I propose such a reference when we talk of approaching a System like System GHP or System CR --. A mere truth-functional equivalence, of the Tarski type, to allow for the specification of what the policeman said as true may be complexer than it sounds. For we will not be satisfied with 'Monkeys can talk is true' iff monkeys can talk. In 'elucidation' of various types, including philosophical, if we were asked to provide a truth-functional equivalence of "Monkeys can talk" we may rather be inspired to provide an excursus onto what we mean, in the object-language, by 'monkey', by 'talk', and by 'can'. Suppose we arrive at the conclusion that it means, 'Any specimen s of Pan troglodytes has a procedure in the repertoire which has a finite set of initial devices, together with semantic provisions for them, and a finite set of different syntactical operations or combinations, and an understanding of what the functions of those modes of combination are, so that s can generate an infinite set of utterances or complex devices, together with a correspodningly infinite set of things to be communicated by them" (apres WoW:296). Even here we would be using 'talk' in scare quotes, since apparently, Nim Chimsky may be said to 'talk' rather than talk -- i.e. the malleability of the phonetic apparatus seems to be missing.
But I don't think Grice was into specific claims in the object-language, "Monkeys can talk" that may need an elucidation in terms of the meta-language. Rather, as I believe Jones does, too with his interesting notion of semantic regress and meta-circular definitions, and the brilliant idea of the Scylla and Charidis -- bewteen meta-circularity and regressus ad infinitum -- the problem lies at the heart of the 'constructivist' enterprise.
In any case, it is a good reminder to keep a good eye on what logicians mean when they jump to metalogic (as some of them do) in a way that they think washes 'their hands' with respect to the object-language.
The 'order' index may be indicative too. System GHP, or System CR, may be thought of as a language, L1. But what about L2. As Grice describes System Q in his "Vacuous Names", he uses English, indeed, not System Q itself. But is this a mere 'abbreviatory' manoeuvre? We hope so. But are we sure? The point may be trickier. In an introduction or elimination rule for a connective, say, when a System like System GHP uses the very idea of 'valid' inference, isn't it a bit of an 'act of faith' that such openly 'meta-linguistic' operation will yield an expression in the object-language? In some logic tracts the meta-language (meta-logic) is so much richer that one doubts! Or consider the semantics, where it interfaces with the ontology (or metaphysics as Grice would prefer -- recall that Part II of WoW is entitled, "Explorations in semantics and metaphysics" --. When the meta-language (in System GHP) speaks of 'Corr (1)', correlation with truth, and 'Corr (0)' and correlation with falsity, as it provides the 'truth-tables' for each operator -- e.g. monadic or dyadic truth-functors -- what would THAT statement, i.e. the statement of each such correlation -- yield when expressed in the object-language. I AM hoping that Tarski was, as Jones said he was, 'premature' in rejecting meta-circularity. I am positive that Grice loved a circle! (WoW: Meaning Revisited -- last section, is all about Schiffer's allegations of circularity in Grice and he goes on to bring in the platonic "circle" as a case in point to prove Schiffer wrong!)
THIS WAS MEANT as comment to the previous post, but system disallowed it.
Good. Yes, there must be something Tarskian behind this. Grice refers only briefly to Tarski in WoW:55 re: "Monkeys can talk", when he writes: "A theory of truth has (as Tarski notes) to provide not only for occurrences of true in sentennces in whch what is being spoken of as true is specified [in the object-language] but also for occurrences in which no specification is given (e.g. The policeman's statement was true)."
(Grice thought that Strawson's and indeed Ramsey's (whom he also quotes on that same page) failed to provide for that.
But I'm not sure about the NL-FL (natural-formal language) distinction at this point. Yes, there must have been something along that line in the Carnap-Grice difference of outlook. But I would think that syntax, even in NL, allows for a pretty easy way to mark the object-language/meta-language distinction: the simple quotes or scare quotes --. So, even in terms of syntactic admissability (which you say you are laxer when it comes to something like a System, and like to indulge in the semantics-ontology interface) I would think Grice is seeing a bigger problem there.
It would seem then that we do have an user of the L1 -- this may be a given. A system like System GHP, or System CR, aims at reconstructing or constructing a segment of "NL" (or the language of scientists in Carnap's construal) as it is used (provisos there). But what about L2? This is the system-analyst's job (There IS a discipline, 'systems analysis', no?, so I propose such a reference when we talk of approaching a System like System GHP or System CR --. A mere truth-functional equivalence, of the Tarski type, to allow for the specification of what the policeman said as true may be complexer than it sounds. For we will not be satisfied with 'Monkeys can talk is true' iff monkeys can talk. In 'elucidation' of various types, including philosophical, if we were asked to provide a truth-functional equivalence of "Monkeys can talk" we may rather be inspired to provide an excursus onto what we mean, in the object-language, by 'monkey', by 'talk', and by 'can'. Suppose we arrive at the conclusion that it means, 'Any specimen s of Pan troglodytes has a procedure in the repertoire which has a finite set of initial devices, together with semantic provisions for them, and a finite set of different syntactical operations or combinations, and an understanding of what the functions of those modes of combination are, so that s can generate an infinite set of utterances or complex devices, together with a correspodningly infinite set of things to be communicated by them" (apres WoW:296). Even here we would be using 'talk' in scare quotes, since apparently, Nim Chimsky may be said to 'talk' rather than talk -- i.e. the malleability of the phonetic apparatus seems to be missing.
But I don't think Grice was into specific claims in the object-language, "Monkeys can talk" that may need an elucidation in terms of the meta-language. Rather, as I believe Jones does, too with his interesting notion of semantic regress and meta-circular definitions, and the brilliant idea of the Scylla and Charidis -- bewteen meta-circularity and regressus ad infinitum -- the problem lies at the heart of the 'constructivist' enterprise.
In any case, it is a good reminder to keep a good eye on what logicians mean when they jump to metalogic (as some of them do) in a way that they think washes 'their hands' with respect to the object-language.
The 'order' index may be indicative too. System GHP, or System CR, may be thought of as a language, L1. But what about L2. As Grice describes System Q in his "Vacuous Names", he uses English, indeed, not System Q itself. But is this a mere 'abbreviatory' manoeuvre? We hope so. But are we sure? The point may be trickier. In an introduction or elimination rule for a connective, say, when a System like System GHP uses the very idea of 'valid' inference, isn't it a bit of an 'act of faith' that such openly 'meta-linguistic' operation will yield an expression in the object-language? In some logic tracts the meta-language (meta-logic) is so much richer that one doubts! Or consider the semantics, where it interfaces with the ontology (or metaphysics as Grice would prefer -- recall that Part II of WoW is entitled, "Explorations in semantics and metaphysics" --. When the meta-language (in System GHP) speaks of 'Corr (1)', correlation with truth, and 'Corr (0)' and correlation with falsity, as it provides the 'truth-tables' for each operator -- e.g. monadic or dyadic truth-functors -- what would THAT statement, i.e. the statement of each such correlation -- yield when expressed in the object-language. I AM hoping that Tarski was, as Jones said he was, 'premature' in rejecting meta-circularity. I am positive that Grice loved a circle! (WoW: Meaning Revisited -- last section, is all about Schiffer's allegations of circularity in Grice and he goes on to bring in the platonic "circle" as a case in point to prove Schiffer wrong!)
Wednesday, June 2, 2010
Carnap and Grice pulling themselves up by their own bootstraps
--- by JLS
--- IN "PREJUDICES AND PREDILECTIONS", which is the title I prefer for "Reply to Richards", (online books), Grice speaks of "Bootstrap". I may have quoted verbatim what the principle amounts to in the Grice Club. From memory. It concerns Russell's neologisms:
object-language (here the hyphen is important and the idea of 'object' IS important)
meta-language.
Let's use L1 and L2 for those. Since this is really a System. We can deal with the first order System GHP, or first-order System CR, alternatively.
(But there is the caveat that 'second-order' does not really necessarily MEAN 'metalanguage').
So, let's grab the piece by Grice!
--- He writes:
It is p. 93 of P. G. R. I. C. E., ed. Grandy/Warner (Clarendon Press).
He is considering points which I have discussed in the club, as to levels of priority and levels of conceptual priority, and subscripting to levels of conceptual priority (reminiscing this PhD I was referring to recently at the Grice Club regarding the point of the "... means ..."). In any case, Grice is being VERY general here, and surely he doesn't have just '... means ...' as his focus. He is considering sense-data, and moral/legal notions, too. He is considering ontology and epistemology (ontological priority, epistemic ontology), etc. He writes:
"It is perhaps reasonable to regard such fine
distinction as indispensable if we are to succeed
in the business of pulling ourselves up by our
own bootstraps. In this connection it will be
relevant for me to say that I once invented
(though I did not establish its validity) a
principle which I labelled as Boostrap. The
principle laid down that when one is introducing
the primitive concepts of a theory formulated
in an object-language, one has freedom to use
any battery of concepts expressible in the
meta-language, subject to the condition that
counterparts of such concepts are
subsequently definable or otherwise derivable
in the object-language. So the more economically
one introduces the primitive object-language concepts,
the less of a task one leaves oneself for the morrow".
I propose the above vis a vis Jones's VERY intersting reflections, here and in the other two blogs, Grice Club and Carnap Corner, about the role of metalogic in the development of twentieth-century logic -- a topic that fascinates us both. And Jones's expertise allows him to utter some very bold and inspiring and truly exegetical claims in the direction where progress should lead to.
--- IN "PREJUDICES AND PREDILECTIONS", which is the title I prefer for "Reply to Richards", (online books), Grice speaks of "Bootstrap". I may have quoted verbatim what the principle amounts to in the Grice Club. From memory. It concerns Russell's neologisms:
object-language (here the hyphen is important and the idea of 'object' IS important)
meta-language.
Let's use L1 and L2 for those. Since this is really a System. We can deal with the first order System GHP, or first-order System CR, alternatively.
(But there is the caveat that 'second-order' does not really necessarily MEAN 'metalanguage').
So, let's grab the piece by Grice!
--- He writes:
It is p. 93 of P. G. R. I. C. E., ed. Grandy/Warner (Clarendon Press).
He is considering points which I have discussed in the club, as to levels of priority and levels of conceptual priority, and subscripting to levels of conceptual priority (reminiscing this PhD I was referring to recently at the Grice Club regarding the point of the "... means ..."). In any case, Grice is being VERY general here, and surely he doesn't have just '... means ...' as his focus. He is considering sense-data, and moral/legal notions, too. He is considering ontology and epistemology (ontological priority, epistemic ontology), etc. He writes:
"It is perhaps reasonable to regard such fine
distinction as indispensable if we are to succeed
in the business of pulling ourselves up by our
own bootstraps. In this connection it will be
relevant for me to say that I once invented
(though I did not establish its validity) a
principle which I labelled as Boostrap. The
principle laid down that when one is introducing
the primitive concepts of a theory formulated
in an object-language, one has freedom to use
any battery of concepts expressible in the
meta-language, subject to the condition that
counterparts of such concepts are
subsequently definable or otherwise derivable
in the object-language. So the more economically
one introduces the primitive object-language concepts,
the less of a task one leaves oneself for the morrow".
I propose the above vis a vis Jones's VERY intersting reflections, here and in the other two blogs, Grice Club and Carnap Corner, about the role of metalogic in the development of twentieth-century logic -- a topic that fascinates us both. And Jones's expertise allows him to utter some very bold and inspiring and truly exegetical claims in the direction where progress should lead to.
System GHP, System CR and Jones's Systems
By J. L. Speranza
JONES WROTE in his commentary to "System CR and System GHP"
"[Mine] is a first order set theory".
Obviously Grice was familiar with this, since often he would refer to set-theoretical concepts -- mainly in his attack of 'Extensionalism', which just ignores all that Carnap said about intensions or the mere possibility of defining intensions in terms of extensions. This is the only treatment of a bete noire in his "Reply to Richards". He tires with the details soon enough and proposes to deal with the twelve betes noires en bloc, as offsprings of Minimalism -- in THIS connection set-theory rears its head again, in that, for example, 'set' IS a sort of 'abstract entity' -- and thus Nominalism has to be refined to deal with the acceptance of sets. At some point Grice would say, 'rejection of all abstract entitities except sets' or something like that (as he tries to reconstruct rather than deconstruct the position). But in any case, Grice would prefer to talk of 'predicate calculus'.
----
Notably in "Prejudices and predilections" he does mention the collocation, "first-order predicate calculus with identity" -- implicating that NO modal notions need be introduced -- which would have yielded a system like Kripke's System S.
When I look at the presentations of these calculus (the Praedikaet Calcul of the Germans -- based on the Propositional Calculus) I am sometimes intrigued by the ontological simplicity of it. It seems it is GOING to yield a pretty simple ontology -- i.e. the syntax (never mind semantics) is such, -- 'contrived' may be the word -- that it's no wonder that the ontology that it will be made to 'depend' on via the semantics will also be contrived.
Sometimes the way to distinguish a philosopher (such as Carnap, Grice, Jones, or Speranza) -- from a non-philosopher is to examine his reactions at the 'ontology', so I'm pleased that Jones likes to play with the ontologies and the semantics. The syntax, as Jones notes, has to reflect an ontology which will be as rich as we want it to make it -- to reflect what we see is the ontology of 'common sense' or 'ordinary language' or 'science' -- qua 'cathedral of learning'. This is QUITE a task!
In any case, Jones's use of 'first-order' merits a post, which I will entitle 'Bootstrap', soon.
JONES WROTE in his commentary to "System CR and System GHP"
"[Mine] is a first order set theory".
Obviously Grice was familiar with this, since often he would refer to set-theoretical concepts -- mainly in his attack of 'Extensionalism', which just ignores all that Carnap said about intensions or the mere possibility of defining intensions in terms of extensions. This is the only treatment of a bete noire in his "Reply to Richards". He tires with the details soon enough and proposes to deal with the twelve betes noires en bloc, as offsprings of Minimalism -- in THIS connection set-theory rears its head again, in that, for example, 'set' IS a sort of 'abstract entity' -- and thus Nominalism has to be refined to deal with the acceptance of sets. At some point Grice would say, 'rejection of all abstract entitities except sets' or something like that (as he tries to reconstruct rather than deconstruct the position). But in any case, Grice would prefer to talk of 'predicate calculus'.
----
Notably in "Prejudices and predilections" he does mention the collocation, "first-order predicate calculus with identity" -- implicating that NO modal notions need be introduced -- which would have yielded a system like Kripke's System S.
When I look at the presentations of these calculus (the Praedikaet Calcul of the Germans -- based on the Propositional Calculus) I am sometimes intrigued by the ontological simplicity of it. It seems it is GOING to yield a pretty simple ontology -- i.e. the syntax (never mind semantics) is such, -- 'contrived' may be the word -- that it's no wonder that the ontology that it will be made to 'depend' on via the semantics will also be contrived.
Sometimes the way to distinguish a philosopher (such as Carnap, Grice, Jones, or Speranza) -- from a non-philosopher is to examine his reactions at the 'ontology', so I'm pleased that Jones likes to play with the ontologies and the semantics. The syntax, as Jones notes, has to reflect an ontology which will be as rich as we want it to make it -- to reflect what we see is the ontology of 'common sense' or 'ordinary language' or 'science' -- qua 'cathedral of learning'. This is QUITE a task!
In any case, Jones's use of 'first-order' merits a post, which I will entitle 'Bootstrap', soon.
Subscribe to:
Posts (Atom)