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PEIRCE-L Digest 1327 - March 13, 1998
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Topics covered in this issue include:
1) Re: Logic Naturalized : Truth
by Tom Burke
2) Re: Logic Naturalized : Truth
by Hugo Fjelsted Alroe
3) daily archives available
by Joseph Ransdell
4) Re: Logic Naturalized
by piat[…]juno.com (Jim L Piat)
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Date: Fri, 13 Mar 1998 01:18:58 -0500
From: Tom Burke
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID:
At 8:15 PM -0500 3/12/98, ransdell, joseph m. wrote:
>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. ...
Perhaps I didn't make it clear enough, but I was using the term "proof" in
a much more limited sense than Peirce often does. I was trying to relate a
deductive and syntactic notion of proof as conceived in contemporary
logicians (so far as I understand it) -- which only goes to show how
complicated it is to make connections with Peirce. Peirce's use of the
term is much broader, including both deductive and inductive "proofs":
----
> CP2.782: [Proof:] An argument which suffices to remove all real
> doubt from a mind that apprehends it.
> It is either mathematical demonstration; a probable deduction of so
> high probability that no real doubt remains; or an inductive, i.e.,
> experimental, proof. No presumption can amount to proof. Upon the nature
> of proof see Lange, Logische Studien, who maintains that deductive proof
> must be mathematical; that is, must depend upon observation of
> diagrammatic images or schemata. Mathematical proof is probably
> accomplished by appeal to experiment upon images or other signs, just as
> inductive proof appeals to outward experiment.
----
I think it would be a mistake to conclude that contemporary deductive logic
is defective because it has a too narrow notion of proof (relative to
Peirce), or that Peirce is in the ozone because he has a too broad notion
of proof (relative to contemporary logic). Rather, the question is simply
how we might map these two conceptions onto each other, not getting blinded
by the common jargon used in either case to express different ideas. In
one sense, a contemporary notion of proof is too narrow; but on the other
hand, within this limited framework, it may have uncovered an important
distinction -- what we might distinguish as "syntactic demonstrability"
(instead of "provability", if that term sticks in your craw) versus
"semantic consequence" -- which Peirce did not appreciate. There may be
something to gain both ways!
----
>... 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.
No, not really. What I have described corresponds fairly closely to what
Peirce calls "mathematical proof", though I even hesitate to say that.
It's only one kind of proof in Peirce's sense; yet it's just about all that
contemporary mathematical logicians consider. So it's limited; but it is
what it is; and Peirce can nicely accommodate it, so long as we realize
it's not the whole story so far as our conception of "proof" goes.
I take it that the following passage from "Fixation" is what you are
referring to?
----
> CP5.375: ... That the settlement of opinion is the sole end of
> inquiry is a very important proposition. It sweeps away, at once, various
> vague and erroneous conceptions of proof. A few of these may be noticed
> here.
> 376. 1. Some philosophers have imagined that to start an inquiry it
> was only necessary to utter a question whether orally or by setting it
> down upon paper, and have even recommended us to begin our studies with
> questioning everything! But the mere putting of a proposition into the
> interrogative form does not stimulate the mind to any struggle after
> belief. There must be a real and living doubt, and without this all
> discussion is idle.
> 2. It is a very common idea that a demonstration must rest on some
> ultimate and absolutely indubitable propositions. These, according to one
> school, are first principles of a general nature; according to another,
> are first sensations. But, in point of fact, an inquiry, to have that
> completely satisfactory result called demonstration, has only to start
> with propositions perfectly free from all actual doubt. If the premisses
> are not in fact doubted at all, they cannot be more satisfactory than they
> are.
----
What Peirce is addressing here does not apply so much to contemporary
notions of deductive proof, though it may apply to some early incarnations
of Carnapian logic. It applies more directly to older conceptions of proof
associated with Euclidean geometry, say, where the basic propositions were
taken to be evidently true, and proofs simply displayed or uncovered
further truths on that basis. Contemporary logic still does not
acknowledge the context of "doubt and belief" in which "proof" operates,
but it no longer takes for granted the indubitability of initial axioms and
definitions.
----
> ... You [TB] 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?
Wow. I don't understand why you want to politicize the discussion like
this all of a sudden. My argument up to now has been that we are forced to
acknowledge these "two admittedly quite different kinds of things" on the
strength of Goedelian incompleteness results -- not because of any
political compulsions.
I agree, at the same time, that academic logic has produced an intellectual
wasteland, not because the details of what these pseudo-philosophers are
doing in their small little world is incorrect so far as it goes, but that
they seem to think their little world is or somehow constrains the whole
wide world of philosophy. The most effective strategy in that regard, if
you really want to know what I think, is to take what they do and see if
and how it might be embedded in the broader and richer philosophy of logic
you find in Peirce's and Dewey's work -- on one hand then, to try to
vindicate their efforts to some extent (to butter them up?) while on the
other hand, to dislodge them in effect from a position of power, insofar as
their narrowness of thought will at that point become obvious. It would be
kind of like ultimately defeating a conquering aggressor over time by
simply absorbing them into the population and getting back to business as
usual. But to say all that is misleading, because it's not the basis for
any kind of justifiable argument. We should not put up with political
maneuverings from their side anymore, but not practice that kind of thing
in return, either. Just use the method of science, tenaciously, and
academic philosophy will get back on track! Maybe I'm just naive.
----
>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 didn't think I was "brushing it aside". Like I say, if the line I'm
taking is nothing more than falling back to Carnapian logic, then I'm
wrong. But post-1980s logic is no longer Carnapian (or Kleenean), and
that's the persepctive I'd like to think I'm trying to work with here. You
may be entirely right about Kleene and Goedel and Turing; but a lot of
water has passed under the bridge since then, and those kinds of historical
episodes have been resolved to a greater extent than you seem to
acknowledge.
> [snip snip, in the interest of brevity]
>... 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, ...
> [snip snip]
But if I'm not just reverting to a layered-rule formal system like Carnap
or Kleene -- which I assert I'm not -- then there's perhaps no fear of
reverting to positivism or otherwise "misrepresenting" anyone. For that
matter, I'd rather focus on the subject-matter of *logic*, to heck with
*who* did *what* or *who* misrepresented *whom*.
----
>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.
If you look at the Hyperproof proof system, you'll see that it's all
governed by rule-specified moves. But what they have, interestingly, is a
"heterogeneous representation system" -- diagrammatic plus sentential --
whose proof system cannot then be limited to purely sentential rules.
There are rules for manipulating diagrams as well, *and*, moreover, rules
for manipulating information back and forth between the two kinds of
representations. E.g., the "Observe" or "Apply" rules are rules just like
modus ponens is a rule, but they are not simply sentential rules.
Their system is much like a real-life situation where you have a map in
your hands and want to get to Bob's house. The map is a diagram. Someone
then tells you "Bob lives at 1111 42nd Street." That is information in
sentential form. A perfectly valid inference in this case -- very simple
indeed -- much like employing the "Apply" rule -- would be to draw a little
X or circle at the point on the map that corrsponds to 1111 42nd Street.
Going the other way, you may give this map to Sally and tell her what the X
marks. She takes it home, and Sandy asks her where Bob lives. She looks
at the map, and then does a little one-step inference using the "Observe"
rule and produces the sentential conclusion "Bob lives in the 1000 block of
42nd Street." Or she might produce other sentential information about "how
to get to Bob's house" by looking at the map and describing in English a
best route as pictured diagrammatically on the map.
What's intersting is how this back-and-forth inferencing involving both
diagrammatic and sentential information is rule-governed! That's the whole
point. This is just a small step, but it does kinda help to bust people
out of a narrow view of purely sentential "sign" systems.
----
>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, ...
I agree, ...
>... which is what
>you are describing in your description of syntactical proof above.
No way. I think you are just not interpreting what I've said correctly,
and/or I'm not making myself clear enough.
>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.
But this is just unfair. This makes it sound like one can either do pure
unadulterated Peircean logic, or else do small-minded positivistic 1930s
logic, and there's no other alternatives. I just don't buy that.
"Cheek by jowl" is definitely not the way to see the relationship between
Peirce's philosophy of logic and contemporary logic. I thought I had made
that clear. It's like Peirce is working on a huge painting along with all
sorts of other folks, and contemporary logicians have grabbed onto one
corner (where the signature happens to be, no less) and have focused only
on that one little piece of it. It's not as if they've messed up the
painting, but the work is just too narrow constrained.
----
>I am sure you are much better positioned than I to address these matters
>competently, Tom, ...
I'm not so sure about that.
>... 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.
Fer sure, my recent prolific e-activity will not lst for long. Spring
break will soon be over, alas (or should I say, thank heaven?).
--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: Fri, 13 Mar 1998 09:57:43 -0500
From: Hugo Fjelsted Alroe
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized : Truth
Message-ID: <3.0.2.32.19980313095743.0068b38c[…]vip.cybercity.dk>
Howard,
Just a short note, trying to answer your question:
>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."
First of all, I should have written 'aspects of truth', or 'grounds for
truth', or similar. By putting it this way, I wanted to indicate that the
distinction between syntactic provability and semantic truth is not
absolute in any sense, but rather a pragmatic distinction in inquiry, as I
went on to say. Maybe this view is a fad of mine; but I did agree with what
you (Howard) wrote in another mail this morning (12.mar) on the same
subject, so perhaps I am just not explaining myself very well.
We might say that the truth of any proposition in inquiry is based partly
on syntax and partly on semantics, and my point is, that this distinction
is purely pragmatic. In an ongoing inquiry what was syntactic may later be
seen as semantic and what was semantic may later be seen as syntactic, this
is just another way of saying that everything is potentially questionable
in inquiry. Given truth is a regulative principle in inquiry, - that which
infinite inquiry would approach, and given some pragmatic distinction
between the at-the-moment-questioned and the at-the-moment-unquestioned,
which I take to be the distinction between syntax and semantics if these
terms are to be used in inquiry. Given this, it seems wrong to see semantic
truth and syntactic provability as two different things, something taken to
be syntactically provable is not in principle different from something
taken to be semantically true with respect to the pragmatic concept of
truth in ongoing inquiry. This is why I said 'two kinds [aspects] of
truth'.
As an aside, I dont think the above implies that there is nothing we may
call pure syntax, only that there is no pure syntax in inquiry. The
construction of some syntactic structure is not in itself part of inquiry
(I suppose Peirce would call this mathematics), though the syntactical
structure may of course at any part become part of inquiry. And becoming
part of inquiry, the syntax necessarily gains a semantic aspect, so to say,
it is taken to mean something, and in this respect, it can be questioned.
We could move further in this direction, I think, relating to another
subject in this thread, the question of revision of logic, or more
generally, the question of revision of theories (a la Poppers
falsificationism), but I will wait and see if I have made my point more
clear and if this invites more critique. -- I may have abused the concepts
of syntax and semantics, and I am certainly not keeping to Tarskis more
formal use; but I do not see anything but a pragmatic use of this
distinction in inquiry. From what you say later on in your reply, we seem
to agree on this. Please excuse me if I have confused the discussion with
unnecessary terms.
Thanks for the other comments in your reply, and thanks to Tom Burke for
his further comments, I will need a little time to read those in context of
the rest of the vivid discussion on this thread, then I might have more to
say.
Regards
Hugo
------------------------------
Date: Fri, 13 Mar 1998 08:23:50 +0000
From: Joseph Ransdell
To: peirce-l[…]TTACS.TTU.EDU
Subject: daily archives available
Message-ID: <3.0.1.16.19980313082350.3da783da[…]pop.ttu.edu>
Just a reminder that the daily compilation of the archives -- verbatim
records of discussion on peirce-l, somewhat misleadingly called "digests"
-- are being made available on the website arisbe going back for the better
part of a month at any given time. I am sometimes slow in getting them
posted but at present it is up to date through yesterday, going back to Feb
17th, with the most recent posts (two or three of them) not yet available.
The address is
http://members.door.net/arisbe/menu/people/peirce-l/digests.htm
Joe Ransdell
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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: Fri, 13 Mar 1998 11:16:38 -0500
From: piat[…]juno.com (Jim L Piat)
To: peirce-l[…]ttacs6.ttu.edu
Subject: Re: Logic Naturalized
Message-ID: <19980313.111639.9302.1.piat[…]juno.com>
Folks,
I'm still trying to follow along with this interesting discussion and
better understand the nature and subject of logic -- What does logic
describe? Here's my loose and no doubt somewhat addled interpretation
of Peirce's grounds for the validity of deduction.
Deduction provides that if both A and B are equivalent to C, then A and B
are also equivalent to each other. But what do we mean by equivalence
in this context? From a pragmatic standpoint I believe the statement
that A and B are equivalent means that for some purpose A can be
substituted for B without making a difference in the outcome. Thus, to
say both A and B are equivalent to C is to say, in effect, that for
practical purposes we are only dealing with one - not three- things. We
are dealing with one thing called by three different names. At its core
deduction is no more than a resentment or reminder of this banality.
What is common to A, B and C is their pragmatic meaning or essence. In
other words, deduction is simply another way of stating the belief that
physical reality is comprised of unchanging essences which may be called
by different names when observed under different circumstances. For
example, the essence of the number three is permanent even though it may
take many forms (i e observed under many circumstances or referred to in
many ways) such as (8 - 5) or (2 + 1) and so on. In reality it is not
essence that changes but the view we take of it.
Or to put the matter still another way, deduction is based upon a belief
about reality. A belief that is either an a priori assumption or
empirically falsifiable. Essentially the belief is that physical reality
is comprised of immutable essences that can be called by different names
under different circumstances. What makes deduction so believable, so
self-evidently, necessarily so - is the fact that deduction rests upon
our most fundamental belief about the nature of reality: A rose by any
other name would smell as sweet. For those who do not recognize this
core belief deduction remains a puzzle: A seemingly inexplicable human
capacity to discern some sort of mystical logical property at the very
heart of necessity and reality. But viewed as a statement or reminder
about the permanence of essences, deduction becomes simply the
application of another belief, albeit a very basic one.
Peirce tells us that beliefs are based upon authority, tenacity, a priori
and science. So it is with the belief exemplified in deduction. Perhaps
some defend this core belief on the grounds of authority, but most seem
to believe that the essential constancy of essences is an a priori
necessary condition for reality - any reality. For most, to deny that
the same thing can be (indeed is) observed at different times and places
is to deny what seems to be the very bedrock of reality. Not simply the
contingent bedrock of the reality we happen to inhabit but the necessary
bedrock of any conceivable reality. Without permanence of essence across
the plurality of circumstances, it is difficult for us to imagine what
any reality could consist of or how, if it did exist, we might be able to
conceive it. Thus, even though we routinely encounter circumstances in
which the essence of things seem to have inexplicably changed we
generally do not attribute these events to a change in essence. Instead
we look for a change in circumstance, because as stated above to allow
unstable essences undermines the notion of an orderly and knowable world.
Nevertheless, some -including existentialists and at times Peirce
himself- have argued that not only is there chance (inexplicable
discontinuity of essences or other continuum) in the physical world, but
also that man himself (as free) is an instance in which essence is not
fixed. A man is never equivalent to himself, but is forever in the
process of becoming himself. For man existence precedes essence and
foolish consistency is the hobgoblin of small minds. So whether
deduction rests upon a priori or a posteriori considerations; or even
whether deduction is universally applicable remain open questions.
In conclusion: Deduction is simply an acknowledgement and exercise of
the belief that an essence is immutable, even though we may call an
essence by different names depending upon the circumstances. Whether
this belief is supported mainly by the a priori consideration that
constancy of essence is a necessary precondition for a conceivable or
coherent reality - or supported mainly by the a posteriori experience of
reality is difficult to determine. Deductions involving man's glassy
essence are particularly suspect.
This done wore me out but I think I've learned something even if I'm
wrong!
Jim Piat
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