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PEIRCE-L Digest 1326 - March 12, 1998
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From PEIRCE-L Forum, Jan 5, 1998, [name of author of message],
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Topics covered in this issue include:
1) Re: Logic Naturalized : Truth
by Joseph Ransdell
2) Re: Logic Naturalized?
by Howard Callaway
3) Re: Logic Naturalized : Truth
by "Mary Libertin"
4) Re: Absent Authors
by Peter_Skagestad[…]uml.edu (Peter Skagestad)
5) Re: Logic Naturalized?
by Tom Burke
6) Pepper list and Web page
by "Bill J. Harrell"
7) Re: Logic Naturalized : Truth
by Tom Burke
8) RE: Logic Naturalized : Truth
by Tom Burke
9) Re: Logic Naturalized : Truth
by joseph.ransdell[…]yahoo.com (ransdell, joseph m.)
10) Re: Logic Naturalized : Truth
by Tom Burke
----------------------------------------------------------------------
Date: Thu, 12 Mar 1998 06:40:59 +0000
From: Joseph Ransdell
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID: <3.0.1.16.19980312064059.5e1f8dcc[…]pop.ttu.edu>
In response to Howard Callaway, who said:
>The deeper question, of course, concerns the compatibility
>of the semantic conception of truth with Peirce's accounts
>of meaning, reference, and interpretation. But I do not see
>that we are forced to construe Tarskian semantics as anti-
>triadic. On the contrary, I think that in Tarskian seman-
>tics, one is concerned with the reference of signs to things
>in relation to an interpretation or interpretations. For
>instance, one could say that an argument is valid iff the
>conclusion is true (and thus relevant terms denote or refer
>to relevant objects/things) on every consistent or uniform
>interpretation which renders the premises true. It seems to
>me that Tarskian semantics makes essential use of a concep-
>tion of interpretation.
>
>Filling in the specifics of this conception of interpreta-
>tion is what may make the difference. Davidson's work helped
>to clarify the point that Tarski's theory of truth depends
>upon an implicit notion of translation or synonymy.
========END QUOTE FROM HOWARD CALLAWAY=======================
This seems right, on the face of it, and if so then I am initially inclined
to agree that there is no problem in assimilating the Tarskian conception.
This is certainly all to the good, if it works, and I should add that this
is the first time I have been able to see any real point to the Tarskian
conception, which always seemed to me hitherto to be only a sort of trivial
formal consequence of little philosophical interest if one did not accept
the idea that logic is concerned primarily with the properties of
languages. Since the semiotic conception of logic has seemed to me to
relegate the conception of "a language" to linguistics, with no special
role for it to play in logic, I have been unable to see why anyone would be
concerned with it who thought the semiotic conception to be the right one.
I don't mean that thare might not be important motivations for appealing to
it in purely formal (and thus essentially mathematical) inquiry, for
example, but I have been unable to see what distinctively logical purpose
is being served by it. But if you are right about this, Howard, then I can
understand that equivalence sentence-form as capturing -- iconically, as it
were -- something the importance of which I had already been aware
importance in Peirce's conception of the sign-relation, namely, that every
sign-object-interpretant relationship involves a "logical level" structure,
i.e. the interpretant is always and necessarily at a "higher" logical level
than the sign it interprets, though we may or may not have any reason to
make that explicit for this and that concrete (situational, contextual)
analytical purpose. This is in opposition to the positivist notion of the
object-language/meta-language distinction and is akin rather to the
scholastic doctrine of first, second, and possibly third (or higher)
intentionality, except that in Peirce the intentional level is dependent
on context rather than supposing an "absolute" or context-free first
intentionality, second intentionality, etc.
Well, this is surely too cryptic to be intelligible -- my mind is running
rapidly through the various ramifications of this which I have already
traced through to some extent independent of the present topic -- but I
have some material written up on this already which I will post as soon as
I get the chance. I will be much interested to see what Tom's and Cathy's
response to this is, as well as that of anyone else on the list, and it
occurs to me that Lee Auspitz' response would be especially helpful, too.
Lee seems to have an unusually extensive and deep acquaintance with
Tarski's work and an understanding of its original context which puts it in
a different light than it is often viewed. Lee is off the list to get some
writing done but monitors it with some regularity, anyway, I think. I'll
send him a note on this if we don't hear from him in a couple of days or so.
>It seems clear, in any case, that Peirce cannot avoid a
>syntax/semantics distinction in some form, since this is
>present wherever we distinguish distinct meanings or inter-
>pretations of the same word or expression.
I think perhaps Peirce really is (implicitly) drawing that or a funcionally
similar distinction when he distinguishes between speculative grammar and
critical logic, but I will have to address that topic in another message,
when I get the time.
Joe R.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Joseph Ransdell - joseph.ransdell[…]yahoo.com
Dept of Philosophy - 806 742-3158 (FAX 742-0730)
Texas Tech University - Lubbock, Texas 79409 USA
http://members.door.net/arisbe (Peirce website - beta)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
------------------------------
Date: Thu, 12 Mar 1998 14:04:42 +0100 (MET)
From: Howard Callaway
To: Multiple recipients of list
Subject: Re: Logic Naturalized?
Message-ID:
On Thu, 12 Mar 1998, Cathy Legg wrote:
> Yes but I was careful to explain what I meant by "revise" as "changing
> one's mind about what's a valid argument." Can Tom or anyone else give me an
> example of where that has happened in the history of logic?
Cathy,
Actually, I gave several examples in a posting of a week or two back.
The best one, I think, is that in Aristotle's logic we can move from
a universal statement, "All A's are B's" to "There are A's." But
in contemporary symbolic logic this is rejected.
Actually, this is much like the assumption of a "logically perfect
language," here, one in which no predicate terms go without objects
of which they are true. But unfortunately, we are not always in a
position to know whether our terms are true of something. This may
depend on further inquiry, and in the mean time, we may want to
draw out consequences of a particular theory.
Similarly, some logics allow us to argue from "Fa" to "(Ex)Fx,"
on the implicit assumption that every name "a," "b," "c," etc.,
must name something or other. But consider "Pegasus is a flying
horse (arguably true) therefore there is a flying horse." Other
logics block this kind of inference. Nor is this always a matter
of fictions. At one point there was a theory which attempted to
account for observed irregularities in the orbit of Mercury
by postulating a planet "Vulcan" inside the orbit of Mercury.
One can argue that they had to make use of the theory containing
this empty name in order to test it, so that a prohibition of
empty names, in the interest of a "logically perfect language,"
is something that we cannot sometime judge of effectively.
At best we can do it retroactively. But that just means that
the notion of a "logically perfect language" seems inappropriate
to a logic of inquiry. All of this is an argument concerning the
validity of a generally accepted logical form. It seems to me
that many people have changed their minds about which logical
truths they recognize!
Cheers!
Howard
H.G. Callaway
Seminar for Philosophy
University of Mainz
------------------------------
Date: Thu, 12 Mar 1998 10:51:45 PST
From: "Mary Libertin"
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID: <19980312185145.11058.qmail[…]hotmail.com>
Concerning this interesting thread, I wonder if any of you who have read
Michael Shapiro's *A Sense of Grammar* could comment? Shapiro's book is
a Peircean discussion of grammar and could shed some light on this
debate.
Also, I'm curious about how the process of semiosis fits into the
current discussion, because I suppose Peirce would find the truth as
potential rather than fossilized, and something other than that which
would be found in the "accidents of Indo-European" languages, as in the
quote below. In short, I'm wondering whether the Tarski method
(specifically) or the semantic/syntactic distinction, generally, is in
some respects limiting?
Thanks for your consideration.
Mary Libertin
Department of English
Shippensburg University
mlibertin[…]hotmail.com or mliber[…]ark.ship.edu
______________________________________________________
Get Your Private, Free Email at http://www.hotmail.com
------------------------------
Date: Thu, 12 Mar 1998 15:17:29 -0800
From: Peter_Skagestad[…]uml.edu (Peter Skagestad)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Absent Authors
Message-ID: <35086D09.54FB[…]uml.edu>
Leon Surette wrote:
>
> Peter Skagestad -- who has thought more about these matters than I
> -- mentioned that " Paul Levinson has argued in various places that the
> monological character of text, complained of in the Phaedrus, is a function
> of its paper-based embodiment, and has been overcome by electronic text,
> which is inherently dialogical."
> I am pleased to have Levinson's support for the importance of the
> technology, but I am dubious about the claim that electronic text overcomes
> those features. It is true that electronic text is far more volatile than
> paper based text. And its dispersal is far more rapid -- permitting much
> quicker response. But it still does not permit interruption, like face to
> face communication. On the other hand, one can't get punched in the nose either.
OK, I do not disagree. But what is perhaps as important as rapid
dispersion is the malleability - or editability - of electronic text. To
take an obvious example, I can more easily respond to you by inserting a
few words into your e-mail message than if I were compelled to copy out a
quotation from you on paper. This makes electronic text inherently
"dialogical" in the sense of facilitating textual juxtaposition of
questions, answers, statements, objections, comments, counter-comment,
etc. but not of course in the sense in which a dialogue progresses in
real time, receiving its direction and hence a large part of its content
from its temporal progresssion.
> Peter himself pointed out other failures of match between electronic
> text and speech. However, he omits the salient one that speech cannot be
> reclaimed or revised, but only repeated or altered.
> Of course, I am speaking of face to face speech, not recorded
> speech.
No disagreement. This is indeed a salient feature of speech and I am
grateful to you for bringing it up. I can't pursue the topic at this
moment, but wanted to acknowledge your posting, however briefly.
Cheers,
Peter
------------------------------
Date: Thu, 12 Mar 1998 15:03:05 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized?
Message-ID:
At 8:07 AM -0500 3/12/98, Howard Callaway wrote:
>On Thu, 12 Mar 1998, Cathy Legg wrote:
>
>> Yes but I was careful to explain what I meant by "revise" as "changing
>> one's mind about what's a valid argument." Can Tom or anyone else give
>>me an
>> example of where that has happened in the history of logic?
>
>Cathy,
>
>Actually, I gave several examples in a posting of a week or two back.
>The best one, I think, is that in Aristotle's logic we can move from
>a universal statement, "All A's are B's" to "There are A's." But
>in contemporary symbolic logic this is rejected.
>
>Actually, this is much like the assumption of a "logically perfect
>language," here, one in which no predicate terms go without objects
>of which they are true. But unfortunately, we are not always in a
>position to know whether our terms are true of something. This may
>depend on further inquiry, and in the mean time, we may want to
>draw out consequences of a particular theory.
>
>Similarly, some logics allow us to argue from "Fa" to "(Ex)Fx,"
>on the implicit assumption that every name "a," "b," "c," etc.,
>must name something or other. But consider "Pegasus is a flying
>horse (arguably true) therefore there is a flying horse." Other
>logics block this kind of inference. ...
Another example is the move from classical logic to quantum logic in
physics. As I recall, it was determined that we should not accept the
distributivity rule as valid (as true in every model). I.e., it does not
follow from "A and (B or C)" that "(A and B) or (A and C)" (or vice versa
-- I don't remember which way it is that this classically valid
truth-functional argument form fails -- but the point is, it fails one way
or the other).
In Cathy's favor, we could say on the other hand that *in a classical
truth-functional logic*, the distributivity rule is valid, and nothing is
ever going to change that. This is perhaps a good illustration of what
Peirce means when he says:
CP5:565. Truth is that concordance of an abstract statement with
the ideal limit towards which endless investigation would tend to bring
scientific belief, which concordance the abstract statement may possess
by virtue of the confession of its inaccuracy and one-sidedness, and this
confession is an essential ingredient of truth.
I.e., the qualifying phrase "in a classical truth-functional logic" is that
essential "confession of one-sidedness" that renders the claim about the
validity of the distributivity rule true.
--TB
______________________________________________________________________
Tom Burke http://www.cla.sc.edu/phil/faculty/burket
Department of Philosophy Phone: 803-777-3733
University of South Carolina Fax: 803-777-9178
For a list of common LISTSERV User Commands see
http://www.cla.sc.edu/phil/faculty/burket/listserv.html
------------------------------
Date: Thu, 12 Mar 1998 15:49:47 -0500
From: "Bill J. Harrell"
To: peirce-l[…]ttacs6.ttu.edu
Subject: Pepper list and Web page
Message-ID: <3.0.1.32.19980312154947.006fb86c[…]ntcnet.com>
Peirce friends,
You may recall that I put up a Stephen Pepper list summer. After a brief
flurry of participation, much confusion based on some technical glichs I
hadn't yet figured out, the list pretty much died. It didn't help that I
entered a period in which it became impossible for me to devote any
attention to it. In any case I intend to give it another try and want to
invite you to subscribe to the list if you feel it would have any interest
for you. I have also put up a Pepper webpage which I would encourage you to
visit.
To join the list send an email letter to: Majordomo[…]majordomo.sunyit.edu
Put in message section: subscribe scpepper-l
Once notified of your successful subscription send messages to:
scpepper-l[…]sunyit.edu
This morning I posted the following message to scpepper-l which gives some
more information about the webpage:
>Pepper-listers:
>
>As I indicated a few days ago I am hoping to spend more time getting the
>Pepper list up and running. Over the past few days I have put up a Pepper
>webpage. My hope is to place Pepper related material(and some Pepper work
>itself) on that site or links to other sites which carry relevant
>material,etc. So far, the webpage is, of course, in a relatively primitive
>state, but it should evolve over the months. I hope you will visit the site
>and consider putting your Pepper work (published, in draft, etc.) at the
>site or a link to a site where it can be found. The web address is:
>
> http://www.sunyit.edu/~harrell/Pepper.htm
>
>In the mean time, I have put on the site two chapters of a manuscript of
>mine: _FIVE WORLD HYPOTHESES: A Primer on Stephen C. Pepper's
>Epistemological System with illustrations from the Arts, Humanities,
>Social, and Natural Sciences_. This manuscript is essentially a summary of
>Pepper's work, _World Hypotheses_ and _Concept and Quality_ with additional
>sections which take ideas from his work on Art as they fall under the
>various world hypotheses. I prepared this manuscript with two purposes in
>mind: first, I had hoped to use it to provide a Pepperian framework for
>several courses I was teaching -- most particularly, the history of social
>thought; second, I thought of it as a primer in Pepper which introduced
>Pepper to mainly sociologists/anthropologists and which would help that
>audience follow what I was trying to do in my sociological work which was
>grounded in the Pepperian categories developed in _WH_ and _Concept and
>Quality_.
>
>The two chapters I posted are the Introduction which describes Pepper's
>"root metaphor" method and the chapter on Formism. The other section
>describes the WH, Contextualism with some discussion of its possible
>applications in art and literature. Toward the end of this section I
>discuss M. Kundera's _The Art of the Novel_ ([43]-[57]). In this work
>Kundera interprets Kafka's work in the most illuminating way I have ever
>seen. I suggest that Kundera is a contextualist struggling with the
>limitations of that framework, especially since he believes that art is
>centrally relevant to not just toleration but substantive values. I quote
>Kundera from a section in which he uses Kafka to illuminate totalitarianism
>by showing the relationship between Stalinism and ordinary family
>practices. He describes a scene when a woman he knew who had resisted with
>great courage and at huge sacrifice the oppression of the state police, of
>Stalinism, and who was now attempting to bring her child under some sort of
>parental control.
>
>"She had forced him [her son] to identify with an absurd accusation, to
>'seek his offense', to make a public confession. I looked on dumbfounded,
>at this Stalinist mind-trial, and I understood all at once that the
>psychological mechanisms that function in great (apparently incredible and
>inhuman) historical events are the same as those that regulate private
>(quite ordinary and very human) situations."(p.109)[50]
>
>I realize some of you do not have web capabilities, if you don't and you
>are interested in these chapters, let me know and I will try to get them in
>a form that can be sent as an attachement to email.
>
>Bill
>
Bill J. Harrell
Dept. of Sociology & Anthropology
S.U.N.Y. Institute of Technology
Utica, NY 13504
Home: 1917 Holland Ave.
Utica, NY 13501
bharrell[…]ntcnet.com
harrell[…]sunyit.edu
------------------------------
Date: Thu, 12 Mar 1998 16:51:38 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID:
At 7:38 AM -0500 3/12/98, Howard Callaway wrote:
>On Thu, 12 Mar 1998, Hugo Fjelsted Alroe wrote:
>
>> The distinction between syntax and semantics, between provability and
>> truth, is a distinction between syntactical truth and semantic truth,
>> that is, between two kinds of truth. How does this relate to semeiotics?
>
>Hugo,
>
>There are several interesting points in your posting which I might like
>to address. However, time limits me to trying to say something about
>the paragraph I quote here. Basically, your opening puzzles me, since I
>don't think anyone would want to take up a distinction between "two
>kinds of truth" on the basis of the syntax/semantics distinction (unless
>this be the pure a priori formalist). So, in order to answer your question
>above, I'd first want to know the what and why of your notion of "two
>kinds of truth."
Hugo,
The passage from your post that Howard quoted also bothered me. As I see
it, the key distinction is between syntactic provability and semantic
*consequence*. Ultimately you are interested in arguments, not just
"truths". The standard way this is presented in first-order deductive
logic is, on the semantic side, to speak about models for a given language,
truth in a model, truth in every model (i.e., validity), and then
consequence (Q is a consequence of P just in case Q is true in any model in
which P is true), etc.. There is no notion of proof here.
The notion of proof is rather a syntactic notion pertaining to the grammar
of the language (or sign system?). I.e., can you devise a proof system --
a set of procedures for manipulating sentences according to certain rules
(including axioms) that hinge only on their
syntactic/grammatical(/diagrammatic?) form -- which allows you to
mechanicaly generate ("prove") all valid sentences (theorems). Your proof
system is *sound* if every sentence that you can prove from scratch is in
fact valid, and it is *complete* if every sentence that is valid can be
proved from scratch.
Every deductive *argument* can then be viewed in two ways: one on hand, you
can ask whether the purported conclusion Q must be true in any model where
the premises P are true? If so, the conclusion is a semantic consequence
of the premises -- often written "P |= Q". On the other hand, you can ask
whether the purported conclusion Q can be proven from the premises P using
the rules of proof. If so, it is provable from the premises -- often
written "P |- Q". For first-order languages with no otherwise special
axioms or interesting classes of models in mind, syntactic provability
("|-") and semantic consequence ("|=") nicely correspond -- i.e., the
system is both sound and complete. But if you are concerned with theorems
of arithmetic or similarly interesting classes of models with more specific
kinds of content, and throw certain corresponding axioms into your proof
system (so yes, Cathy, you have to make the proof system more interesting
to mirror richer kinds of semantic contents), then completeness goes by the
wayside. The moral is that semantic consequence and syntactic provability
do not always simply mirror one another. There are cases (languages,
domains of inquiry) where P|=Q but not P|-Q. They are really two different
things, not just two different ways to talk about one thing.
So anyway, what does this have to do with Peirce? Well, I'm not exactly
sure (once again), but ...
At 12:55PM 3/12/98, Mary Libertin wrote:
>Also, I'm curious about how the process of semiosis fits into the
>current discussion, because I suppose Peirce would find the truth as
>potential rather than fossilized, and something other than that which
>would be found in the "accidents of Indo-European" languages, as in the
>quote below. In short, I'm wondering whether the Tarski method
>(specifically) or the semantic/syntactic distinction, generally, is in
>some respects limiting?
.. I would use the term "limited" rather than "limiting". It is limiting
only if we take it to be the story, the whole story, and nothing but the
story to tell about logic, proof, consequence, etc.. It's limited, but the
question is just where and how it fits into a broader theory of inquiry,
etc.. This is not just a matter of fallibility of Tarskian logic, but
pertains to the fact that it is looking at only a small but real piece of
the elephant.
(Similarly, Galilean kinematics or Newtonian mechanics are limited as
physical theories, but they are not necessarily limiting. They are
limiting only if you take too seriously the kind of move often attributed
to Laplace and assume they are the last word on how to do physics or how to
think about physical subject matters. So it goes with much of contemporary
logic!)
--TB
______________________________________________________________________
Tom Burke http://www.cla.sc.edu/phil/faculty/burket
Department of Philosophy Phone: 803-777-3733
University of South Carolina Fax: 803-777-9178
For a list of common LISTSERV User Commands see
http://www.cla.sc.edu/phil/faculty/burket/listserv.html
------------------------------
Date: Thu, 12 Mar 1998 18:05:14 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: RE: Logic Naturalized : Truth
Message-ID:
At 7:25 AM -0500 3/12/98, Cathy Legg wrote:
>On the whole I agree with Joe and Anne that the syntax/semantics
>distinction is not sharp enough to be useful in talking about
>natural language. So, for instance, the statement, "All bachelors are
>unmarried" is a tautologously true, but is this due to "syntax" or to
>"semantics"? Well this depends how the statement is formalised...
Actually, "All bachelors are unmarried" is not strictly a tautology. In
propositional logic, it would be symbolized simply by a single
propositional symbol "P", and that does not have the form of a tautology
(like "P or not P" or "P implies P"). Nor is it a case of what Barwise and
Etchemendy call "first-order logical truth", being of the form "For all x,
Bx implies Ux" (whereas something like "(For all x, Bx) iff (not for some
x, not Bx)" is a f-o logical truth -- a case of deMorgan's laws for
quantifiers). The latter kind of validity hinges primarily on how we
interpret the quantifier terms (a la Tarski). The sentence "All bachelors
are unmarried" is rather a case of what they call *analytical truth* --
depending on the meanings of the predicate symbols. Its truth is due
essentially to the semantics for predicate symbols, which can be captured
syntactically only if you could come up with certain axioms for the
bachelorhood and unmarriedness predicate symbols which you could add to
your proof system. Natural language is grossly (wonderfully, richly)
incomplete insofar as such axioms are not usually formulatable for most
natural language predicate terms. Hence (snicker snicker) citing "All
bachelors are unmarried" as an example is a nice and easy proof of the
incompleteness of natural language -- i.e., here you have an analytical
truth which is not provable (unless you take it as an axiom itself, or
throw in some equivalent ad hoc axioms). Of course, even when you *can*
come up with a principled class of such axioms, e.g., for the fragment of
language for arithmetic, incompleteness is still possible.
----
>I think that the distinction *can* be defined clearly in certain formalised
>systems of logic, and there "syntax" refers to the explicitly defined
>rules (and maybe the axioms too, I'm not sure) of that logical system,
>while "semantics" refers to the *interpretation* given to the logical
>system, that is the way its variables (and predicates) are mapped onto
>"things in the world". The semantics is left open by the syntax - that
>is, other interpretations are possible.
>
>If we clarify the two terms in this way, then Goedel's result *is* purely
>syntactic, and I would refer Tom to chapter 3 of Mendelson, _Introduction
>to Mathematical Logic_, (New York : Van Nostrand, 1979.)
>
>> To say that it is purely a syntactic result is something else altogether.
>
>Not according to the definitions above. What definitions do you favour,
>Tom?
I guess I've outlined some of this in an earlier reply to Hugo. I would
add that "syntax" initially concerns the recursive techniques you use to
construct your language in the first place -- specifying basic grammatical
categories (constants, predicate symbols, function symbols, sentence
symbols, circles, shadings, or whatever), saying what a well-formed formula
or diagram is, what a sentence as opposed to a formula is, etc. The syntax
of "arguments" is then what you are talking about above.
----
>> Truth in Tarski's if not Goedel's sense is a semantic notion, and we can
>> talk about truth [] in a model or in "every" model [and consequence]
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Date: Thu, 12 Mar 1998 21:10:51 -0600 (CST)
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>> (i.e., in a semantic sense) independent of syntactic proof. On
>> one hand you have consequence relations in a semantic sense,
>
>Do you mean "necessary connections"? I was going to say that I think
>necessary vs. contingent connections is the really useful distinction in
>this vicinity, but it carves up logical space rather differently than
>"syntactic" vs. "semantic".
Well, I suppose there is an implicit notion of "necessary connection"
lurking here; but the notion of semantic consequence is relatively simple:
P is a consequence of Q iff P is true in every model in which Q is true. A
big problem with this -- which Putnam and others have had some fun with --
is that this can be merely contingent, depending on the space of models you
are looking at. So there are technical problems with this definition of
semantic consequence; but the point is that (1) it is simple and coherent,
and (2) it gets at something that is different from saying that P is
provable, given Q.
----
>> and on the other hand, you have
>> deducibility relations relative to a given proof system. Goedel's
>> completeness theorems were results concerning the correspondence between
>> these two kinds of relations; and sure enough, they line up in simpler
>> cases (truth-functional languages; first-order predicate calculi; etc.)
>> but they don't once your semantics is interesting enough [...]
>
>Why not "once your syntax is interesting enough"...?
Well, yes, you have to add axioms to your proof system (extend your proof
system) if you want to talk about interesting (restricted, more specific)
classes of models. So making the "syntax" more interesting goes hand in
hand with addressing more interesting semantic domains.
So are we getting anywhere with all this?
--TB
______________________________________________________________________
Tom Burke http://www.cla.sc.edu/phil/faculty/burket
Department of Philosophy Phone: 803-777-3733
University of South Carolina Fax: 803-777-9178
For a list of common LISTSERV User Commands see
http://www.cla.sc.edu/phil/faculty/burket/listserv.html
------------------------------
Date: Thu, 12 Mar 1998 19:11:03 -0600
From: joseph.ransdell[…]yahoo.com (ransdell, joseph m.)
To:
Subject: Re: Logic Naturalized : Truth
Message-ID: <002001bd4e1c$e643dd60$5ee6ead0[…]ransdell.door.net>
Tom, given what you say in your message to Hugo I am more than ever
convinced that although we might well want to recognize some sort of
syntactics/semantics distinction, it cannot be along the lines you
mention. When Peirce says in the "Fixation" article that he is
introducing a new conception of proof, he surely means one that
involves recognition of the reference to the interpretant as
essential -- which is to say that he is just not going to accept the
idea that
>The notion of proof is rather a syntactic notion pertaining to the
grammar
>of the language (or sign system?). I.e., can you devise a proof
system --
>a set of procedures for manipulating sentences according to certain
rules
>(including axioms) that hinge only on their
>syntactic/grammatical(/diagrammatic?) form -- which allows you to
>mechanicaly generate ("prove") all valid sentences (theorems).
That is just the opposite of the direction he is going and is marching
right back to Carnapian formalism. You go on later to say:
>. . . But if you are concerned with theorems
>of arithmetic or similarly interesting classes of models with more
specific
>kinds of content, and throw certain corresponding axioms into your
proof
>system (so yes, Cathy, you have to make the proof system more
interesting
>to mirror richer kinds of semantic contents), then completeness goes by
the
>wayside. The moral is that semantic consequence and syntactic
provability
>do not always simply mirror one another. There are cases (languages,
>domains of inquiry) where P|=Q but not P|-Q. They are really two
different
>things, not just two different ways to talk about one thing.
Why in the world would we want to hold on to these two admittedly quite
different kinds of things? In order to try to keep logicism alive? I
don't see the philosophical motive here. I don't think it is enough
just to say that that is what the formal logicians still swear by.
Academic logic is probably doomed to be forever controlled by these
people in spite of decades of demonstration of the intellectual
wasteland they represent. Once the dogmatists are thoroughly ensconced
in the power positions in academia they are impregnable: that is just
the way it works. I realize that you are anything but a defender of
dead traditions, Tom, but I am baffled by the apparent agreement with so
much of it and am trying to figure out what you are seeing in this
stuff. What am I overlooking here?
I was surprised to see you brushing aside as impertinent the possibility
I suggested that Goedel is being misrepresented by the formalists in
laying on him the syntax/semantics distinction as you describe it on the
grounds that
QUOTE TOM BURKE==================
Kleene and others were not just trying to give
watered-down accounts (reconstructions?) of what Turing and Goedel did,
but
to reconcile (reconstruct?) what they (Turing, Goedel) did and/with a
Tarskian conception of semantics. Whether it was Goedel himself
personally
or the overall community of logicians at the time who "established"
(i.e.,
settled on the belief) that syntax and semantics are not the same thing
is
really not the issue. But that's what Goedel's results eventually come
down to. (Similarly, what we often refer to as Newtonian physics is not
exactly what Newton himself did, but is the result of many inquirers
working out the details but otherwise appropriately calling the results
"Newtonian".)
END QUOTE=======================
I have thought quite a lot about Kleene's misrepresentation of Turing
and how to construe that without out imputing dishonesty to him. I
have no doubt that he was not being dishonest in representing Turing as
he did, according to his own conception of what intellectual honesty is,
but the fact is that he does not give the slightest indication at any
point that he has ensconced Turing within a conceptual framework which
Turing himself could have adopted explicitly if he thought it to his
purpose to do so. But all you have to do to see that Turing had no use
for it is to read Turing's article -- a marvel of intellectual lucidity
and wit, vastly superior sentence by sentence, and inference by
inference to any work of Kleene's I have seen -- to see that it would
only have been in a fit of madness that Turing would have agreed to
having that creaking intelllectual apparatus that Kleene was working
with -- the stock "formal system" of Carnap and the rest --loaded into
his own work. Yes, I know that Turing was in this country in the late
30's for a while, worked some with Church, and that Kleene probably knew
him personally, but I would have to see something more substantial than
that to believe that he thought Kleene had any right to reduce his work
intellectually to the calibre of own in that way, without even
indicating that this is what he was doing.
It seems to me that we have to respect a distinction between real
mathematicians, like Turing and Goedel, and "meta-mathematicians", like
Kleene, who are actually just formal logicians who seem to have been
able to convince others that they have a right to place themselves in a
"meta" position relative to the real thing and deconstruct and
reconstruct it from a vantage point of external observation in order to
show what is significant in it. But isn't the point to both Turing's
and Goedel's papers precisely that the formalistic program for
mathematics has no future and that the logical reconstruction of math a
la Russellian logicism is just out of the question? The fact that the
formalists just stayed on, anyway, after Goedel and Turing, reminds me
of something about a job I once had. I was one of a large number of
billing clerks in a huge room at Bethlehem Steel in San Francisco, all
doing identical tasks at what must have been 70 or 80 identical desks.
Right across the aisle from mine was this guy who stood out from the
rest, though, in that all that he did every day was to study road maps
of the U.S., of which he had a complete collection in his file drawer.
It seems that he was the billing clerk for steel shipped to red China,
which had not had any trade with the U.S. for years, and the reason he
was still there was that when they told him years earlier that his job
was at an end he simply kept on showing up, clocking in, and sitting at
his desk. They didn't pay him for a few weeks but after a while they
decided it was less problematic to keep on paying him than to bring in
the police to remove him. (Maybe he had read Melville's "Bartleby the
Scrivener"!)
Okay, bad joke! But seriously, if appreciating Tarski's point really
does require buying into the notion of a layered-rule "formal system" --
which is what you now appear to be saying, since that is what Kleene
represents -- then we are clearly going back to positivism, not to
something that gets past it, and we surely want to reconsider whether we
are really doing justice to Goedel in regarding it as perfectly okay to
rely on that intellectual framework in characterizing what he does or
shows. I don't know that it does require that, and I thought at first
that you were suggesting that we could leave that stuff behind in
understanding the significance of Tarski. But if you are invoking that
then it is reasonable to suspicious of whether it is right to
characterize Goedel as having a syntactic conception of provability.
It also seems odd on the face of it to refer to Barwise et. al. in that
connection, too, when the conception of graphical proof involves the
claim that rigorous proof is possible that appeals to observational
moves, experimental in character, not reducible to rule-specified moves.
I can imagine that in developing this Barwise has come up with a
generalized conception of syntax that permits a distinction from
semantics, but we are surely no longer in the same intellectual universe
that the positivist logicians of the 30's were inhabiting, which is what
you are describing in your description of syntactical proof above.
There is good reason to think Barwise's intellectual universe surely
would be inhabitable by Peirce, but I don't see Peirce as cheek to jowl
with "metamathematicians" and the like.
I am sure you are much better positioned than I to address these matters
competently, Tom, and I don't mean to be appealing to a competence I
don't actually have but I do think I should push you on this a bit,
though I take it for granted that you have to work this sort of thing in
where you can, and have no obligation to respond immediately -- or
indeed, at all, as far as that goes; but I am particularly concerned
that you not feel a mistaken obligation to do what you have no time to
do right now. I respond to things when I can and when I can't I just
don't, and I take it for granted that people understand the limitations
we all work within.
Joe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Joseph Ransdell or <>
Department of Philosophy, Texas Tech University, Lubbock TX 79409
Area Code 806: 742-3158 office 797-2592 home 742-0730 fax
ARISBE: Peirce Telecommunity website - http://members.door.net/arisbe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
------------------------------
Date: Thu, 12 Mar 1998 22:14:02 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID:
At 7:46 AM -0500 3/12/98, Joseph Ransdell wrote:
>In response to Howard Callaway, who said:
>...
>>It seems clear, in any case, that Peirce cannot avoid a
>>syntax/semantics distinction in some form, since this is
>>present wherever we distinguish distinct meanings or inter-
>>pretations of the same word or expression.
>
>I think perhaps Peirce really is (implicitly) drawing that or a
>functionally similar distinction when he distinguishes between speculative
>grammar and critical logic, ...
This is an interesting thesis worth investigating. An alternative thesis
is that a syntax/semantics distinction in some form or other (with possible
embellishments, e.g., having to do with interpretation as yet another
essential concern) applies to each of these branches of logic by
themselves. Though this depends on which of Peirce's characterizations of
the three branches of logic you work with. Here again are a couple of
passages from CP which briefly describe these three branches:
----
> CP1.192: Logic is the theory of self-controlled, or deliberate,
> thought; and as such, must appeal to ethics for its principles. It also
> depends upon phenomenology and upon mathematics. All thought being
> performed by means of signs, logic may be regarded as the science of the
> general laws of signs. It has three branches:
> 1, Speculative Grammar, or the general theory of the nature and
> meanings of signs, whether they be icons, indices, or symbols;
> 2, Critic, which classifies arguments and determines the validity
> and degree of force of each kind;
> 3, Methodeutic, which studies the methods that ought to be pursued
> in the investigation, in the exposition, and in the application of truth.
> Each division depends on that which precedes it.
----
> CP2.93: Logic is the science of the general necessary laws of Signs
> and especially of Symbols. As such, it has three departments.
> Obsistent logic, logic in the narrow sense, or Critical Logic, is
> the theory of the general conditions of the reference of Symbols and other
> Signs to their professed Objects, that is, it is the theory of the
> conditions of truth.
> Originalian logic, or Speculative Grammar, is the doctrine of the
> general conditions of symbols and other signs having the significant
> character. It is this department of general logic with which we are, at
> this moment, occupying ourselves.
> Transuasional logic, which I term Speculative Rhetoric, is
> substantially what goes by the name of methodology, or better, of
> methodeutic. It is the doctrine of the general conditions of the reference
> of Symbols and other Signs to the Interpretants which they aim to
> determine. . . .
----
Earlier in CP2, helping to explain the latter characterization of the three
branches, Peirce writes:
----
> CP2.89: Originality is being such as that being is, regardless of
> aught else.
> Obsistence (suggesting obviate, object, obstinate, obstacle,
> insistence, resistance, etc.) is that wherein secondness differs from
> firstness; or, is that element which taken in connection with Originality,
> makes one thing such as another compels it to be.
> Transuasion (suggesting translation, transaction, transfusion,
> transcendental, etc.) is mediation, or the modification of firstness and
> secondness by thirdness, taken apart from the secondness and firstness;
> or, is being in creating Obsistence.
----
It seems to me like this application of the three categories, at this level
of generalization or abstraction, is a way of mapping out the entire theory
of inquiry. The first branch of logic -- speculative grammar -- talks
about the full range of contemporary logical considerations -- terms,
propositions, assertions, arguments, representation, judgments, inference,
etc etc -- but not yet with regard to the context of inquiry in which such
things are employed -- i.e., "regardless of aught else". Just look at the
TOC for the section on speculative grammar. The discussion of "signs and
their objects" (230) is just one place where some connection with the
contemporary syntax/semantics stuff might be made:
----
> BOOK II. SPECULATIVE GRAMMAR
>
> CHAP. 1. ETHICS OF TERMINOLOGY 219
>
> CHAP. 2. DIVISION OF SIGNS
>
> 1. Ground, Object, and Interpretant 227
> 2. Signs and Their Objects 230
> 3. Division of Triadic Relations 233
> 4. One Trichotomy of Signs 243
> 5. A Second Trichotomy of Signs 247
> 6. A Third Trichotomy of Signs 250
> 7. Ten Classes of Signs 254
> 8. Degenerate Signs 265
> 9. The Trichotomy of Arguments 266
> 10. Kinds of Propositions 271
> 11. Represent 273
>
> CHAP. 3. THE ICON, INDEX, AND SYMBOL
> 1. Icons and Hypoicons 274
> 2. Genuine and Degenerate Indices 283
> 3. The Nature of Symbols 292
> 4. Sign 303
> 5. Index 305
> 6. Symbol 307
>
> CHAP. 4. PROPOSITIONS
> 1. The Characteristics of Dicisigns 309
> 2. Subjects and Predicates 315
> 3. Dichotomies of Propositions 323
> 4. A Pragmatic Interpretation of the Logical Subject 328
> 5. The Nature of Assertion 332
> 6. Rudimentary Propositions and Arguments 344
> 7. Subject 357
> 8. Predicate 358
> 9. Predication 359
> 10. Quantity 362
> 11. Universal 367
> 12. Particular 372
> 13. Quality 374
> 14. Negation 378
> 15. Limitative 381
> 16. Modality 382
>
> CHAP. 5. TERMS
> 1. That these Conceptions are not so Modern as has been
> Represented 391
> 2. Of the Different Terms applied to the Quantities of Extension
> and Comprehension 393
> 3. Of the Different Senses in which the Terms Extension and
> Comprehension have been accepted 395
> 4. Denials of the Inverse Proportionality of the Two Quantities,
> and Suggestions of a Third Quantity 400
> 5. Three Principal Senses in which Comprehension and Extension will
> be taken in this Paper 407
> 6. The Conceptions of Quality, Relation, and Representation,
> applied to this Subject 418
> 7. Supplement of 1893 427
> 8. Signification and Application 431
>
> CHAP. 6. THE GRAMMATICAL THEORY OF JUDGMENT AND INFERENCE
> 1. Judgments 435
> 2. Inference 442
----
Meanwhile, the following outline shows the range of "critical logic".
Taking the details of speculative grammar as given, it looks in general
terms at how different kinds of reasoning employ the various argument forms
to handle/manage/transform information (I can't think of a better term).
There is nothing more or less syntactic or semantic about critical logic
than about speculative grammar -- that's just not where the difference
lies. Rather the "obsistent" character of critical logic has to do with
principles according to which given information leads to subsequent
information -- an obsistence between what's given versus its potentials
(its significance, its meaning, in a non-Tarskian sense of those terms), or
what kinds of potentials might have given rise to it -- dealing with "that
element which taken in connection with Originality, makes one thing such as
another compels it to be." This somehow goes beyond the discussion of
inference from the standpoint of speculative grammar.
----
> BOOK III. CRITICAL LOGIC
>
> A. EXPLICATIVE REASONING
>
> CHAP. 1. THE ARISTOTELIAN SYLLOGISTIC
> 1. Pretensions of Demonstrative Reasoning 445
> 2. Rules and Cases 452
> 3. The Quadrant 455
>
> CHAP. 2. ON THE NATURAL CLASSIFICATION OF ARGUMENTS
> Part I
> 1. Essential Parts of an Argument 461
> 2. Relations between the Premisses and Leading Principle 465
> 3. Decomposition of Argument 468
> 4. Of a General Type of Syllogistic Argument 471
>
> Part II
> 1. Of Apagogical Forms 475
> 2. Of Contradiction 476
> 3. Of Barbara 478
> 4. Of the First Figure 479
> 5. Second and Third Figures 480
> 6. The Theophrastean Moods 500
> 7. Mathematical Syllogisms 507
>
> Part III
> 1. Induction and Hypothesis 508
> 2. Moods and Figures of Probable Inference 512
> 3. Analogy 513
> 4. Formal Relations of the Above Forms of Arguments 514
>
> CHAP. 3. EXTENSION OF THE ARISTOTELIAN SYLLOGISTIC
> 1. On a Limited Universe of Marks 517
> 2. General Canon of Syllogism 528
> 3. Hamilton's Quantification of the Predicate 532
> 4. Universe of Discourse 536
>
> CHAP. 4. NOTES ON EXPLICATIVE REASONING
> 1. Logical 537
> 2. Pure 544
> 3. Organon 547
> 4. Intention 548
> 5. Material Logic 549
> 6. Logical Contraposition and Conversion 550
> 7. Obversion 551
> 8. Syllogism 552
> 9. Middle Term and Middle 581
> 10. Premise and Premiss 582
> 11. Mnemonic Verses and Words 584
> 12. Reduction 585
> 13. Leading Principle 588
> 14. Nota Notę 590
> 15. Laws of Thought 593
> 16. Regular Proof 601
> 17. Pertinent 602
> 18. Implicit 603
> 19. Observation 606
> 20. Spurious Proposition 607
> 21. Opposition 608
> 22. Inconsistency 609
> 23. Reductio ad Absurdum 612
> 24. Fallacies 613
> 25. Insolubilia 618
>
> B. AMPLIATIVE REASONING
>
> CHAP. 5. DEDUCTION, INDUCTION, AND HYPOTHESIS
> 1. Rule, Case, and Result 619
> 2. Baroco and Bocardo; Hypothesis and Induction 626
> 3. Rules for Induction and Hypotheses 632
> 4. Empirical Formulae and Theories 636
> 5. On the Difference between Induction and Hypothesis 641
>
> CHAP. 6. THE DOCTRINE OF CHANCES
> 1. Continuity and the Formation of Concepts 645
> 2. The Problem of Probability 647
> 3. On Degrees of Probability 649
> 4. Three Logical Sentiments 652
> 5. Fundamental Rules for the Calculation of Chances 656
> 6. Notes on the Doctrine of Chances 661
>
> CHAP. 7. THE PROBABILITY OF INDUCTION
> 1. Rules for the Addition and Multiplication of Probabilities 669
> 2. Materialistic and Conceptualistic Views of Probability 673
> 3. On the Chance of Unknown Events 680
> 4. On the Probability of Synthetical Inferences 685
> 5. The Rationale of Synthetic Inference 690
>
> CHAP. 8. A THEORY OF PROBABLE INFERENCE
> 1. Probable Deduction and Probability in General 694
> 2. Statistical Deduction 698
> 3. Induction 702
> 4. Hypothetic Inference 704
> 5. General Characters of Deduction, Induction, and Hypothesis 708
> 6. Induction and Hypothesis; Indirect Statistical Inferences;
> General Rule for their Validity 715
> 7. First Special Rule for Synthetic Inference. Sampling must be
> Fair. Analogy 725
> 8. Second Special Rule for Synthetic Inference, that of
> Predesignation 735
> 9. Uniformities 741
> 10. Constitution of the Universe 744
> 11. Further Problems 751
>
> CHAP. 9. THE VARIETIES AND VALIDITY OF INDUCTION
> 1. Crude, Quantitative, and Qualitative Induction 755
> 2. Mill on Induction 761
>
> CHAP. 10. NOTES ON AMPLIATIVE REASONING
> 1. Reasoning 773
> 2. Validity 779
> 3. Proof 782
> 4. Probable Inference 783
> 5. Predesignate 788
> 6. Presumption 791
>
> APPENDIX. MEMORANDA CONCERNING THE ARISTOTELIAN SYLLOGISM 792
----
I didn't see a similar outline for "speculative rhetoric", but the
following paragraphs occur even earlier in CP2. Note the remark about
"relaxing the severity of our rule of excluding psychological matter,
observations of how we think, and the like" at this stage of logical
theory. At this point, given the details of speculative grammar and
critical logic, the focus now is on conditionsand methods of solving
problems -- how reasoning techniques are used in inquiry, to solve
problems, to understand how discovery takes place, etc. None of the
previous stuff makes proper sense outside of this broader context of
inquiry. I take it that the "the general conditions of the reference of
Symbols and other Signs to the Interpretants which they aim to determine"
are presented/supplied by the contexts of inquiry in which such symbols or
signs are employed???
----
> §5. SPECULATIVE RHETORIC
>
> 105. All this brings us close to Methodeutic, or Speculative
> Rhetoric. The practical want of a good treatment of this subject is
> acute. It is not expected that any general doctrine shall teach men much
> about methods of solving problems that are familiar to them. But in
> problems a little remote from those to which they are accustomed, it is
> remarkable how not merely common minds, but those of the very highest
> order, stumble about helplessly. No class of thinkers can by anybody be
> rated higher in heuretic genius than the mathematicians; and yet see how
> they have boggled over comparatively simple problems of unfamiliar kinds,
> such as Fermat's theorems, Steiner's theorems, the problem of
> map-coloring, the theory of knots.
> 106. Many persons will think that there are other ways of acquiring
> skill in the art of inquiry which will be more instructive than the
> logical study of the theory of inquiry. That may be; I shall not dispute
> it; for it would carry me far beyond the confines of my province. I only
> claim that however much one may learn in other ways of the method of
> attacking an unfamiliar problem, something may be added to that knowledge
> by considering the general theory of how research must be performed. At
> the same time, it is this theory itself, for itself, which will here be
> the principal object.
> 107. In coming to Speculative Rhetoric, after the main conceptions
> of logic have been well settled, there can be no serious objection to
> relaxing the severity of our rule of excluding psychological matter,
> observations of how we think, and the like. The regulation has served its
> end; why should it be allowed now to hamper our endeavors to make
> methodeutic practically useful? But while the justice of this must be
> admitted, it is also to be borne in mind that there is a purely logical
> doctrine of how discovery must take place, which, however great or little
> is its importance, it is my plain task and duty here to explore. In
> addition to this, there may be a psychological account of the matter, of
> the utmost importance and ever so extensive. With this, it is not my
> business here to meddle; although I may here and there make such use of
> it as I can in aid of my own doctrine.
> 108. Time was when a theorem could constitute a considerable
> contribution to mathematical science. But now new theorems are turned out
> wholesale. A single treatise will contain hundreds of them. Nowadays
> methods alone can arrest attention strongly; and these are coming in such
> flocks that the next step will surely be to find a method of discovering
> methods.Ż1 This can only come from a theory of the method of discovery.
> In order to cover every possibility, this should be founded on a general
> doctrine of methods of attaining purposes, in general; and this, in turn,
> should spring from a still more general doctrine of the nature of
> teleological action, in general.
> 109. Although the number of works upon Methodeutic since Bacon's
> Novum Organum has been large, none has been greatly illuminative. Bacon's
> work was a total failure, eloquently pointing out some obvious sources of
> error, and to some minds stimulating, but affording no real help to an
> earnest inquirer. THE book on this subject remains to be written; and
> what I am chiefly concerned to do is to make the writing of it more
> possible.
> 110. I do not claim that the part of the present volume which deals
> with Speculative Rhetoric will approach that ideal. As to the other parts
> of my book, this prefatory chapter commits me to producing a work of
> great importance or to being set down a drawler of nonsense. But for the
> methodeutic part, I only say that since my youth I have associated with
> strong thinkers and have never ceased to make it a point to study their
> handling of their problems in all its details. When I was young, no
> remark was more frequent than that a given method, though excellent in
> one science, would be disastrous in another. If a mere aping of the
> externals of a method were meant, the remark might pass. But it was, on
> the contrary, applied to extensions of methods in their true souls. I
> early convinced myself that, on the contrary, that was the way in which
> methods must be improved; and great things have been accomplished during
> my life-time by such extensions. I mention my early foreseeing that it
> would be so, because it led me, in studying the methods which I saw
> pursued by scientific men, mathematicians, and other thinkers, always to
> seek to generalize my conception of their methods, as far as it could be
> done without destroying the forcefulness of those methods. This statement
> will serve to show about how much is to be expected from this part of my
> work.
----
------------------------------
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