ONT Re: Inquiry Into Inquiry
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Mishtu Banerjee wrote (MB):
Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):
MB: Perhaps, it is better to state "physicists do not trust just logic".
Neither do biologists, chemists, foresters, social scientists ...
MB: I would suspect this could happen several different ways:
MB: 1. A logical conclusion is reached that begins with assumptions that are
in error (mis-identification of basic elements, or primitive statements).
MB: 2. A logical conclusion is reached that does not fit observations which have
been repeatedly verified (which would lead someone to suspect point 1)
MB: 3. A logical conclusion is reached based on a limited view of logic (not
allowing for multivalued logics, fuzziness, vagueness, alternate logics,
etc. )
MB: Physicists, biologists, must rely on more than just logic, because they are
not dealing with closed systems or for-ordained conclusions. If they could
rely on just logic, they woulden't have to observe, do experiments, dream ...
MB: I think that when Jon refers to Logic, he might be referring to Peirce's more
general view (semiotic), of which formal logic is a subset. I sometimes think
of Peirce's logic as metalogic, in the sense of a study of logic, from outside
the bounds of formal logic. When Howard is referring to logic, he is referring
to formal logic.
MB: Boole "logically" proved the existence of god. Or so he claimed.
But you would have to accept his premises first. I think, Howard
and Jon -- you might be talking past each other, because you have
different premises.
MB: Howard repeatedly brings up the empirical nature of scientific inquiry.
This is also why I provided the empirically rich example from the history
of physics. It is the explanation of specific things, through general
principles, that lead again to new specific things to look for, that excites
scientists. Even theoretical physicists and biologists are embedded in
empirical minutae. They have to be, to be competent in their field.
MB: Perhaps, it is at this point -- the nature, role, and value of empiricism to inquiry --
that you and Howard have different premises?
When it comes to these old, war-torn, and weather-beaten words like "form" and "logic",
I think that an ordinary dictionary is the best guide to ordinary meaning and use,
with an eye out for the etymology that records their historical transformations.
But when it comes to forming a technical craft of observation, abstraction, and
application to matters that we really care about doing well, as if our lives
depended on it, as they say, then you all know that some alterations of
common sense customs and practices will almost inexorably fall due,
just as it happens in every field of diligence where people are
paying attention, trying to abstract the principles underlying
what works and what does not, and are hopeful of anticipating
improved applications in some way more speedy than sticking
by the guns of the first notion that enters their heads and
then waiting to see what the "Evolution Of Nature" (EON)
has to say about it.
That is the kind of logic that I am talking about.
It is "formal" in the sense that it pays a bit of
attention to the forms that inform the conduct of
reasoning. Howard, the best that I can guess, is
still talking about a picture of logic that a few
glossers of the subject crafted early in the 20th
Century and were apparently remarkably successful
in mass-marketing, that is to say, in reproducing
en masse and world-widely distributing throughout
the mundane mental furniture of several so-called
"modern" generations. So it's the Carnival Glass
image of logic. I reckon that it had its utility,
but there were alternatives before it, much to be
preferred, much more powerful in their potentials,
to my way of thinking, and these form the methods
of learning and reasoning that I quickly selected
as the most viable candidates in my field of view,
shortly after I set to steady work on the problem,
within a computational setting, some 20 years ago.
From what I have learned through this work in the meantime,
I can honestly say, with no hint of hyperbole, that all of
the logical calculi in common and widespread use today are
about as much use in logic as roman numerals in arithmetic.
There are many applications and vast extensions of "logic",
say, logical analogues of differential & integral calculus,
just for starters, than are not conceivable in a practical
way so long as our daily use of logic remains fixed within
its present prisons of notions and notations. For my part,
I am trying to develop what could be the future of inquiry.
Jon Awbrey
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HP: My simple historical description of a fundamental discovery
may appear obscure, but to achieve "sheer obfuscation" would
require more effort than I care to invest.
JA: What I call "obfuscation" is your repeated statements that "physicists do not trust logic".
I have never known a physicist who would say this, except possibly in jest. I have known
mathematicians who are skeptical and even a bit disparaging about the utility of applying
the "Big Guns" of logic to discovering "interesting and significant" truths of mathematics,
and I know in what sense they mean this. If you are saying that "a priori proof-theoretic,
syntactic and deductive reasoning" (APPTSAD) is not sufficient to carry empirical science,
this would hardly be a big shock to me. But I have consistently said from the very start
of our discusssion that "you have been talking to wrong logicians" if you have come to buy
that this is all there is to logic. I have painted, in what I think are moderately graphic
and colorful ways, my own view of the contemporary scene, that this extremely peculiar idea
of logic is a fluke of early 20th Century analytic philosophy, itself a backwash from the
mainstream of what logic has been about from its earliest sources, and ignorant even of
the radical transformations in the basic methodology that were effected by Peirce while
these tyros were yet in their cradles. Aside from this formalist, exclusively syntactic,
and proof-theoretic style of doing logic, there is also a meaningful, inclusively semantic,
and model-theoretic tradition that is still alive and kicking, in spite of the circumstance
that the self-conceived dominant tradition does not accord it even the courtesy of diplomatic
recognition. Still, it moves. And one of the first things that I discovered, much to my own
surprise, when I started trying to program reasoning tools is that the model-theortic vein
makes much better connection with the empirical data-driven aspects of logic and learning.
HP: I have always found that the normal meaning of
"logical consequents of a formal model" refers to all
and only the syntactic mathematical symbol manipulations
that are independent of any interpretation (such as solving
an equation or integration).
JA: Again, a statement like this tells me that the things you have "always found"
are due to your having spent all your time looking under the same lamp post.
JA, quoting Chang & Keisler:
Here is another:
| We say that [a sentence] p is a 'consequence'
| of [a set of sentences] S, in symbols S |= p,
| iff every model of S is a model of p.
|
| A set G of sentences is called a 'theory'.
|
| A theory is said to be 'closed'
| iff every consequence of G belongs to G.
|
| A set D of sentences is said to
| be a 'set of axioms for' a theory G
| iff G and D have the same consequences.
|
| A theory is called 'finitely axiomatizable'
| iff it has a finite set of axioms.
|
| Since we may form the conjunction of a finite
| set of axioms, a finitely axiomatizable theory
| actually always has a single axiom.
|
| C.C. Chang & H.J. Keisler, 'Model Theory',
| North-Holland, Amsterdam, Netherlands, 1973,
| pages 11-12.
|
| http://suo.ieee.org/ontology/msg02624.html
HP: What I mean by physicists not trusting logic does not mean that
they lack confidence in these syntactic operations of logic and
mathematics. This is the easiest part of inquiry to follow,
just because it is syntactically well-defined and free of
interpretational interference.
HP: What they do not trust is that the logical precision and the logical consequents
of the formal model have any necessary relation to its empirical validity.
HP: Hertz's condition for an acceptable model is the essential empirical condition,
but it is by no means a sufficient condition. How the formal model is interpreted
or what the consequents mean is an entirely different question. As I said, it is not
necessary that the model mean anything in order to derive the "logical consequents".
That is what is normally meant in mathematics by a formal system.
JA: This is not how logicians and mathematicians use the word "model".
Maybe some physicists use it to mean a set of axioms and equations --
and equations do not make sense without the axioms that define the
mathematical domains in which their constants reside and over which
their variables range -- but logic and math people originally used
the word "model" to mean that of which a theory holds, and yes, the
Principians have warped the sense of that beyond all recognition, too,
but soon it will all be over with them, and we can all go back to a logic
that appreciates beauty and also makes sense, all in one and the same moment.
HP: But in the total process of inquiry, of course interpretation is always going on.
That is why additional criteria of universality (invariance and symmetry), aesthetic
criteria (simplicity, elegance), and alternative interpretations are essential for
evaluation of the model and for suggesting further experiments and inquiry.
HP: Here is a description of inquiry by Heisenberg showing
how obscure and uncertain the whole process is:
WH: | What quite frequently happens in physics is that, from seeing some part of [a particular]
| experimental situation, you get a feeling of how the general experimental situation is.
| That is, you get some kind of picture. Well, there should be quotation marks around the
| word 'picture.' This 'picture' allows you to guess how other experiments might come out.
| And of course you try to give this picture some definite form in words or mathematical
| formula. Then what frequently happens later on is that the mathematical formulation of
| the 'picture' or the formulation of the 'picture' in words, turns out to be rather wrong.
| Still, the guesses were rather right. That is, the actual 'picture' which you had in mind
| was better than the rationalization which you tried to put down in the publication. That is,
| of course, a quite normal situation, because the rationalization, as everybody knows, is always
| a later stage and not the first stage. So first one has what one may call an impression of how
| things are connected, and from this impression you may guess, and you have a good chance of
| guessing the correct things. But then you say, 'Well, why do you guess this and not that?'
| [and so on, with more and more refined guesswork, rationalization, formalization, and testing].
JA: Let's compare that with Peirce's image of the "skeleton diagram, or outline sketch" that
one uses in the form of "abstractive observation" on which mathematical reasoning relies.
For Peirce, as for any platonically real thinker -- in spite of the host of historical
distortions that moderns tend to project on the ancient scene -- mathematics itself is
a partly empirical and a highly experimental science. It is one of the reasons that
Peirce would hardly have blinked at Gödel's incompleteness theorems. What would be
so surprising about the fact that we cannot know it all about a real rich domain?
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| Logic, in its general sense, is, as I believe I have shown, only another name for
|'semiotic' ([Greek: semeiotike]), the quasi-necessary, or formal, doctrine of signs.
| By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the
| characters of such signs as we know, and from such an observation, by a process which
| I will not object to naming Abstraction, we are led to statements, eminently fallible,
| and therefore in one sense by no means necessary, as to what 'must be' the characters
| of all signs used by a "scientific" intelligence, that is to say, by an intelligence
| capable of learning by experience. As to that process of abstraction, it is itself
| a sort of observation. The faculty which I call abstractive observation is one which
| ordinary people perfectly recognize, but for which the theories of philosophers sometimes
| hardly leave room. It is a familiar experience to every human being to wish for something
| quite beyond his present means, and to follow that wish by the question, "Should I wish for
| that thing just the same, if I had ample means to gratify it?" To answer that question, he
| searches his heart, and in doing so makes what I term an abstractive observation. He makes
| in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what
| modifications the hypothetical state of things would require to be made in that picture, and
| then examines it, that is, 'observes' what he has imagined, to see whether the same ardent
| desire is there to be discerned. By such a process, which is at bottom very much like
| mathematical reasoning, we can reach conclusions as to what 'would be' true of signs
| in all cases, so long as the intelligence using them was scientific. (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editors' Note: From an unidentified fragment, c. 1897.
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HP: I don't see ...
JA: No, you don't, and the rest of your sentence
shows that you are not even trying to look.
You find it more convenient to keep burning
this strawman that has no relation to Peirce.
HP: I don't see how any inquiry into inquiry can be trusted
within the logical confines of Peircean discipleship,
because logic is not the key and there is a paucity
of empirical data.
JA: Anecdotes and praising famous names hardly counts as empirical data.
I enjoy a rousing biographical narrative as much as the next person,
and will use it as a source of plausible hypotheses until something
better comes along, but human introspection is just as fallible and
just as specious as all of our other spections. Your philosophical
assumptions re "incorrigible morphisms" and "infallible intuitions"
are founded on a Cartesian-Kantian tradition that Peirce critiqued
in full just by way of cutting his baby-teeth in philosophy.
HP: One must observe real cases of how inquiry has actually been done.
A large part of the misconceived "logic of science" is the result
of bad pedagogy that teaches only the final equations or so-called
"logical results" of what was actually a long process of imaginative
inquiry. This leaves the student in total ignorance of the creative
process. The vast literature on the subject shows that this is a
psychological problem, not a logical problem. It is also important
to appreciate how greatly psychological influences on the creative
imagination have changed over the course of modern science.
JA: Look, I was interested enough in the psychological aspects of learning and reasoning
to pick up a Master's in Psych along the way, and I know something of the literature
and the methodology that actually prevails in several parts of that field, but you
are simply ignoring the critical difference between a descriptive science like
psychology and a normative science like logic.
HP: Historical case studies are the only way to see these changes.
In response to Mishtu's reporting of Bernard Cohen's discussion
of Kepler, I quoted Pauli: "The process of understanding nature
as well as the happiness than man feels in understanding it, that is,
in the conscious realization of new knowledge, seems thus to be based
on a correspondence, a 'matching' of inner images pre-existent in the
human psyche with external objects and their behavior." This comes from
an in-depth Jungian-influenced psychological study of Kepler that is worth
reading. [Wolfgang Pauli, "The influence of archetypal ideas on the scientific
theories of Kepler" in "The Interpretation of Nature and the Psyche" Bollingen
Series LI, Pantheon, NY, 1955. Reprinted in Enz and Meyenn. eds.,"Pauli, Writings
on Physics and Philosophy" Springer-Verlag]
JA: This all the stuff that I read in the 60's. But that was yesterday ...
HP: The art historian, Erwin Panofsky, has argued that the expression
of Galileo's ideas was biased by his aesthetic preferences, and,
incidentally, that the Church's irritation was grounded more in
his physical realism, dislike of allegory (in painting as well
as text) and rejection of Platonic dualism, rather than merely
over the earth's orbit. ["Galileo as a critic of the arts"
The Hague, M. Nijhoff, 1954.]
HP: Newton, of course, is another historical example of complex
psychological and religious influences on inquiry [e.g.,
Cohen and Westfall, eds., "Newton" Norton, NY 1995]
HP: Modern psychological biases are much more aesthetic than were the religious biases
of the past. A modern example of aesthetic disagreement over equivalent mathematical
formalisms (the logical consequents of both formalisms matched the experimental data) was
between Schoedinger and Heisenburg. Schoedinger was "discouraged, not to say repelled" by
Heisenburg's matrix formulation, while Heisenberg found Schoedinger's formulation "disgusting"
and its superior visualizability "trash". [Miller, "Imagery in Scientific Thought" Birkhauser,
Boston, 1984, p. 143] In spite of such diversepersonal opinions, both interpretations were
valuable in the further development of quantum theory.
HP: That's more than enough for one sitting. Let me just emphasize that I'm not promoting
the physicist's style of inquiry for every problem. There is no single style of inquiry,
even in physics. There are strong tendencies -- opportunism, looking at extremes, skepticism,
formalization -- but this style is not for all inquiries. Simple induction still works in some
cases, and formalization is not useful in some cases. Even in physics there are exceptions, like
Feynmann diagrams, a kind of semi-interpreted semi-formalism. What I do promote for anyone inquiring
about inquiry is that they study how great discoveries have actually been made.
JA: There are times for looking at the boundaries, the anomalous and the ab-normal cases:
It often happens that we learn much from the exceptions about the nature of the rule.
There are times for looking at the interiors, the regions where a realm is more ruly:
It can happen that a good guess is blocked by trying to cover both feather and stone.
JA: You pays your nickel, and youse takes your chances ...
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