Monday 31 May 2010

R. B. Jones's System C-R

by J. L. Speranza, of the Grice Club.
-- for the Carnap Corner.

WHEN Grice was invited (we trust) to honor Quine (SOME honoring: it came out in a book entitled, "Words and objections" -- SOME pun on Quine's alleged masterpiece), he talked of "System Q".

When Myro died, among his drafts was a few pages (which I MUST have somewhere) entitled, something like, "A sketch of System G, in gratitude to Paul Grice for the original idea". He had indeed previously referred to such a System in a piece Jones is familiar with. Or rather with a piece by Myro in a COLLECTION Jones is familiar with, since it includes Code's "Izzing and Hazzing" essay. This one is Myro's "Identity and Time", where, as I say, he also mentions this System G (as he later will in his unpublished drafts).

The point then? Well, I have gone on record for having extended Myro's System G, into what I call "System G-HP" where "HP" are meant as subscripts and where thus the hyphen is unnecessary. I don't know if Rudolf had another name than Rudolf, but then there's R. B. Jones's System C-R, which is, thus, System Carnap.

I propose that Speranza's System G-HP and JOnes's System C-R are IDENTICAL, which is a good way to the City!

More on this later, I hope. I have to go the City of Eternal Truth right now to drop the news!

Saturday 29 May 2010

Carnap and Grice in the history of logic (KEYWORD: "History of Logic")

-- by J. L. Speranza, of the Grice Club
---- for the Carnap Corner

I SHOULD DROP A NOTE IN "THE CITY of eternal truth", someday -- but the point is there. I am fascinated that Jones found that chapter on "Carnap and modern logic" (by Reck), in the Friede et al, Cambridge companion to Carnap -- of interest.

We should discuss a bit of a timeline here. As we move towards the overlapping of things.

From what _I_ see, "Whitehead/Russell" are central. This was 1910, but the whole thing was finished by 1913, only. Then there's the 1914 notebooks by Wittgenstein, which ARE important from a historical perspective.

Then of course we have anything EARLIER. Grice was OBSESSED by Russell, "On denoting" (Mind, 1905 -- which thus predates his collaboration with Whitehead) and I would think Carnap thought of Russell's theory of description of some value.

Then we can go EARLIER, to my pet: nineteenth-century logic. Frege, of course. But which WERE the general tracts by Frege: the conceptual notation, of course, which as Jones notes elsewhere (his website) is just Leibniz (and I'd add Wilkins) deja vue all over again!

---- Frege's PHILOSOPHICAL points were perhaps more 'minor'. Then there's PEANO, which Ruseell adopted, at least at the point of terminology --.

At an earlier time, the divergences between, say, British and Continental sources diverge. And I wouldn't know which German authors which are relevant to the History of GERMAN logic are of GENERAL importance. Stigwart perhaps. Then we should go back to KANT. Because after all, he wrote on Logic, too. People are too obsessed with his general theory of knowledge, but most of his points were purely logic, and it's very good to see that neo-Kantian is used, with a straight face, when talking Carnap.

Before that, we go to the scholastics which were pretty confused on a number of things, but not on ALL things. Kneale, "The Development of Logic" has been useful to me on this. And then, yes, we get to Aristotle! -- And categoricity without tears!

Carnap and Grice on constructivism

--- Thanks to Jones for referring to the essay, "Carnap and modern logic" in the volume co-edited by Friedman (Friedman was a close collaborator with Grice -- and a few pieces by Friedman and Grice and by Grice and Friedman need to be edited from the Grice collection -- tomorrow, perhaps). This to acknwoledge this footnote, 8, on one of that pages of that essay, where the author acknowledges 'constructionism' or 'constructivism', which we have discussed with Jones elsewhere (notably in the Grice Club). So the point is that THIS usage of 'constructivism' by the author of "Carnap and Modern Logic" is yet a different one.

He just means Brouwer, and what will later will transpire as 'intuitionism'. But it IS interesting to focus on why the earlier labels for this approach were indeed 'constructionism' or 'constructivism'. The author of that essay perhaps too hastily goes on to dimiss the point. Surely one can't have everything in an essay and the man had been INVITED to write it! But in any case, the author points that at SOME time, then, Carnap was viewing 'constructivism' as a 'third approach'.

In the Gricean rewrite, the problem with constructionism, when applied to intuitionism, lies in things like the acceptance or not of something like DNE (double negation elimination). What construction you ACCEPT is a matter of YOUR intuitions. Brouwer was perhaps not sophisticated enough (I write that provocatively) to see the points that would later concern English-speaking philosophers (as I'm not!) but -- hey!

Or not hey!

---

Awody and Reck on Categoricity

Further to my last post about categoricity in relation to the Fraenkel-Carnap problem, I found a couple of interesting papers on the history which provide technical background.

My very concise "explication" of categoricity (and related concepts) can be seen spelt out more fully and very clearly by Awody and Reck in:
Completeness and Categoricity, Part I: 19th Century Axiomatics to 20th Century Metalogic with the history continued in Completeness and Categoricity, Part II: 20th Century Metalogic to 21st Century Semantics.

I have not read much yet, and I'm sure that it soon gets tough going, but it starts off gently, and comes in early with two points which I like.
The first is to point out the importance of Fraenkel and Carnap to the development of these topics.  The second is to say that higher order logics are good and that the tendency in parts of mathematical logic to focus exclusively on first order logic is not so good, either from the point of view of historical or contemporary understanding.

RBJ

Carnap and Modern Logic

There has been a very considerable development of Carnap scholarship over the last couple of decades with which I am myself mostly unacquainted, but which hopefully has now corrected the caricatures which were prevalent when Logical Positivism was first supposedly given a definitive refutation.

It remains the case that most of the material I read on Carnap regards Carnap's philosophy as centering around phenomenal reductionism (the Aufbau) or the verification principle, despite the small place which these occupy in the very readable (and short) but apparently not widely read Carnap autobiography.

It is therefore nice to see something contributing to a better understanding of Carnap's work relating to the real core of his philosophy.

Carnap and Modern Logic is a chapter from the recent "Cambridge Companion to Carnap" which is of great interest (at least) in filling in detail of the history of Carnap's logical work which would not otherwise be accessible to a wide audience.

It is of particular interest to me in providing details about the influence of Hilbert on Carnap, on which Carnap says little in his autobiography, but which, on the face of it, accounts for the most substantial differences between the approach to logic of Frege and Russell and that seen in Carnap, and which in some respects weaken (make more vulnerable to the Quinean attack) the resulting conception of logical truth/ analyticity.  I was assuming that the influence of Hilbert came via Schlick (I possibly hint on this in the draft Carnap/Grice conversation), but this work may tell me otherwise (when I have digested it).

RBJ

Categoricity and "The Fraenkel-Carnap Question"

The Fraenkel-Carnap question has today come to my notice, and I suspect this may be the source of the matters to which Speranza referred in an earlier post to Carnap Corner on categoricity.

The Fraenkel-Carnap question is (according to Weaver and George):

whether every finitely axiomatizable semantically complete second-order theory is categorical

I offer an "explication" of this as follows.

A theory is a set of sentences in some logical system.
A second order theory is a theory in a second order logic.
A theory is finitely axiomatisable if all the sentences in the theory are formally derivable from some finite subset if the sentences.
A theory is semantically complete if it "determines" the truth value of every sentence in the language, however this means semantically, not syntactically.
It means that every sentence in the language has the same truth value in every model of the theory, so semantically it is either true or false in the context of the theory, which does not mean that it is provable or disprovable, since second order logic is not complete.

Categorical has two meanings, a syntactic and a semantic meaning.
We know that the semantic meaning is the relevant one here since the answer to the question is otherwise too easy.

A theory is syntactically categorical if every sentence or its negation is in the theory.
A theory is semantically categorical if it has only one model up to isomorphism, this is sometimes qualified by cardinality, since a first order theory with an infinite model will have models of every infinite cardinality and no two models of different cardinality will be isomorphic.  So, often, categorical should be read: all models of the same cardinality are isomorphic.

One might naively suppose that a semantically complete theory will be semantically categorical, but the theory of "true arithmetic" provides a counter-example.  "true arithmetic" is the set of true sentences of first order arithmetic.
It is semantically complete, because every sentence or its negation is true, but it is not semantically categorical, it has non-standard countable models.

The fact that first order logic is complete tells us that any semantically complete axiomatic theory will be syntactically categorical, but the above counterexample shows that this does not entail semantic categoricity.

In the case of second order logic, we forgo completeness of the deductive system for the sake of greater expressiveness in the semantics (leaving the syntax behind).
The consequence of the more expressive semantics is that second order arithmetic becomes semantically categorical, but the semantic expressiveness is not matched by any greater syntactic strength, so we don't have syntactic categoricity.  Consequently we now have a categorical "true second order arithmetic", and its no longer obvious where to look for a counter-example to the general thesis considered in the Fraenkel-Carnap question.

This seems to me to be a somewhat recondite problem in mathematical logic.

I cannot myself see that it has any philosophical significance.
Carnap apparently offered a proof of the conjecture which was flawed.
Some partial results have been proven, the unqualified conjecture remains unsolved.

RBJ

Sunday 16 May 2010

Chalmers' John Locke Lectures

What  great sign of revival in the respectability of Carnap is the devotion of the Oxford John Locke lectures, this year by Chalmers, to some kind of Aufbau-like project.

The last thing I saw of his was something on the distinction between verbal and substantive question, which I do think worth getting clear.

I doubt that he is the man to get to the core of Carnap's programme, which is not phenomenal reductionism, but its nice that he is contributing to the rehabilitation of Carnap.

I haven't actually looked at any of the material online (apart from the first abstract) but I may be back when I have.

RBJ

Saturday 1 May 2010

Categoricity in Carnap and Grice

Not sure what the concept stands for in Carnap, but I'm SURE 'category' is a BASIC category in Grice!


Title:Carnap, Completeness, and Categoricity: The 'Gabelbarkeitssatz' of 1928
Authors:Awodey, S
Carus, A W
Source:Erkenntnis: An International Journal of Analytic Philosophy, 54(2), 145-172. 28 p. 2001.
Document Type:Journal Article
Subjects:AXIOMATICS
CATEGORICITY
COMPLETENESS
LOGIC
LOGICISM
Persons as Subjects:CARNAP
GÖDEL, KURT
Abstract:In 1929 Carnap gave a paper in Prague on "Investigations in General Axiomatics"; a brief summary was published soon after. Its subject looks something like early model theory, and the main result, called the 'Gabelbarkeitssatz', appears to claim that a consistent set of axioms is complete just if it is categorical. This, of course, casts doubt on the entire project. Though there is no further mention of this theorem in Carnap's published writings, his 'Nachlass' includes a large typescript on the subject, 'Investigations in General Axiomatics'. We examine this work here, showing that it provides important insights into Carnap's development during this critical period.

Jan Dejonzka does Carnap (He did Grice)

This below, because I have on record gone to great lengths of lovely conversation with this lovely author, so I'm sure what he says is fun -- and true!


Observational Ecumenicism, Holist Sectarianism: The Quine-Carnap Conflict on Metaphysical Realism
Authors:Dejnozka, Jan
Source:Philo: A Journal of Philosophy, 9(2), 165-191. 27 p. FALL-Winter 2006.
Document Type:Journal Article
Subjects:ECUMENICALISM
EMPIRICISM
EQUIVALENCE
HOLISM
METAPHYSICS
NATURALISM
PRAGMATISM
REALISM
SECTARIANISM
Persons as Subjects:CARNAP, RUDOLF
QUINE, WILLARD VAN ORMAN
Abstract:Do any significant philosophical differences between Quine and Carnap follow from Quine's rejection of Carnap's analytic-synthetic distinction? Not if they both understand empirical evidence in merely observational terms. But it follows from Quine's rejection of the distinction that empirical evidence has degrees of holophrastic depth penetrating even into logic and ontology (gradualism). Thus, his reasons to prefer realism to idealism are holophrastically empirical. I discuss Quine's holist sectarian realism on private languages, externalism versus internalism, unobserved objects, unobservable abstract entities, bivalence, ecumenicism versus sectarianism, and on gradualism itself.

From Vienna to Santa Fé, from Oxford to the Eternal City

--- No clear idea why Santa Fé is mentioned here...



Carnap and Language: From Vienna to Santa Fé (in Slovak)
Authors:Hanzel, Igor
Source:Organon F: filozofický casopis, 14(4), 470-497. 28 p. 2007.
Document Type:Journal Article
Subjects:LOGIC
METALANGUAGE
METALOGIC
SEMANTICS
SYNTAX
Persons as Subjects:CARNAP, RUDOLF
CHURCH, ALONZO
Abstract:The paper reconstructs three main stages in the development of Carnap's approach to language in the years 1931-1947. It starts with Carnap's approach to metalogic in his Viennese 'Zirkelprotokolle' (1931) and his 'Logische Syntax der Sprache' (1934) from the point of view of one-level approach to the relation between metalanguage and its object language. It then analyzes Tarski's turn to semantics in his paper presented at the Paris conference in September 1935, as well as the implications of his view for Carnap's approach to semantics from 1935 until 1943. Finally, it analyzes Church's rediscovery of Frege and its impact on Carnap's shift to the extension/intension distinction in his semantics in the years 1943-1947.

Martin Firiedman on Carnap and Grice

A Parting of the Ways: Carnap, Cassirer, and Heidegger
Reviewers:Bird, Graham
Source:Kantian Review, 12(2), 161-163. 3 p. 2007.
Reviewed Item:Friedman, Michael; (2000). A Parting of the Ways: Carnap, Cassirer, and Heidegger. Chicago: Open Court.
Document Type:Book Review


--- Martin Friedman was collaborator with Grice on topics of 'universalia', now deposited at Bancroft. He wrote on Carnap, too.

Gustav Bergmann on Carnap and Grice

This bit below informs me that G. Bergmann belonged in the Vienna Circle. He referred to Grice as an "English futilitarian". I suppose he has nicer things to say about Carnap!

---

Wiener Kreis: Texte zur wissenschaftlichen Weltauffassung von Rudolf Carnap, Otto Neurath, Moritz Schlick, Philipp Frank, Hans Hahn, Karl Menger, Edgar Zilsel und Gustav Bergmann
By: Stölzner, Michael, Uebel, Thomas. Reviewed by: Neuber, Matthias. Zeitschrift fuer philosophische Forschung, 62(4), 618-619, 2 p. Hamburg: Verlag Felix Meiner. October-December 2008. (AN PHL9065400)
Database: Philosopher's Index
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Essays by Carnap and Grice in J. Baillie, ed. "Contemporary Analytic Philosophy"

Title:Contemporary Analytic Philosophy
Authors:Baillie, James
Publication Information:Upper Saddle River: Prentice Hall; 1997.
Subjects:ANALYTIC
ATOMISM
EPISTEMOLOGY
LANGUAGE
Abstract:

"This anthology includes some of the most influential readings in 20th century analytic philosophy. Authors are Frege, Russell, Wittgenstein, Ayer, Schlick, Carnap, Moore, Ryle, Grice, Austin, Sellars, Quine, Tarski, Davidson, Krupke, Putnam. Each selection is given a detailed introduction, including biographical details, summary of the argument, criticism and recommendations for further reading."

One wonders that pieces.

Blurb for Ostertag's book that combines Carnap and Grice

When I found that Ostertag had managed to reproduce only PART of Grice's 'Vacuous Names' in this expensive MIT book, I was SO disappointed... Anyway, he includes Carnap, too, and one wonders what section.

"The debate over the proper analysis of definite descriptions, which began with Bertrand Russell's classic essay, continues to this day. While it is now widely acknowledged that, like the indexical expressions "I," "here," and "now," definite descriptions in natural language are context sensitive, there is significant disagreement as to the ultimate challenge this context-sensitivity poses to Russell's theory. This reader is intended both to introduce students to the philosophy of language via the theory of descriptions, and to provide scholars in analytic philosophy with ready access to some of the central contributions in this area. It includes classic works by Russell, Carnap, Strawson, Lambert, Donnellan, Grice, Peacocke, Kripke, Wettstein, Soames, Neale, and Schiffer."

The book is "Definite descriptions: a reader", MIT, 1998.