Re: [peirce-l] Deacon's incompleteness and Peirce's infinity
Very rich post, Gary (F), thank you! I've recently been alerted to the importance of Deacon by Gary (R) and he is now 'on my list'. On the interesting issue of Deacon's 'Absence' which you raise in the last paragraph, I wonder whether the Absent is absent from Being or just the actual world. If the latter, perhaps it is not entirely inaccessible to a Peircean phaneroscopy fearlessly navigating the Platonic Universe. Cheers, Cathy On Mon, Mar 12, 2012 at 4:24 AM, Gary Fuhrman wrote: > Jon, Gary, Ben and List, > > ** ** > > There's another part of the *Minute Logic* which may be related to the > connection Jon is making between “objective logic” and “categories”. It is > definitely related to the argument in Terrence Deacon's *Incomplete Nature > *, which Gary R. suggested some time ago as worthy of study here. We > haven't found a way to study it systematically, but maybe it's just as well > to do it one post at a time. Or one thread at a time, if replies ensue.*** > * > > ** ** > > The central part of Deacon's argument presents “a theory of emergent > dynamics that shows how dynamical process can become organized around and > with respect to possibilities not realized” (Deacon, p. 16). Depending on > the context, he also refers to these “possibilities not realized” as > “absential” or “ententional”. His argument is explicitly anti-nominalistic > and acknowledges the reality of a kind of final causation in the physical > universe (“teleodynamics”). It has a strong affinity with Peirce's argument > for a mode of being which has its reality *in futuro*. In other words, he > argues for the reality of Thirdness without calling it that – indeed > without using Peirce's phaneroscopic categories at all. (Personally i doubt > that he is familiar enough with them to use them fluently, but maybe he > decided not to use them for some reason.) > > ** ** > > “Incompleteness” is a crucial concept of what i might call Deaconian > realism. In physical terms, it is connected with Prigogine's idea of > *dissipative > structures* (including organisms) as *far from equilibrium* in a universe > where the spontaneous tendency is *toward* equilibrium, as the Second Law > of thermodynamics would indicate. Teleodynamic processes take > incompleteness to a higher level of complexity, but i don't propose to go > into that now. Instead i'll present here a Peircean parallel to Deacon's > “incompleteness”. The connection lies in the fact that *incompleteness*is > etymologically – and perhaps mathematically? – equivalent to > *infinity*. > > ** ** > > First, we have this passage from Peirce's Minute Logic of 1902: > > ** ** > > [[[ I doubt very much whether the Instinctive mind could ever develop into > a Rational mind. I should expect the reverse process sooner. The Rational > mind is the Progressive mind, and as such, by its very capacity for growth, > seems more infantile than the Instinctive mind. Still, it would seem that > Progressive minds must have, in some mysterious way, probably by arrested > development, grown from Instinctive minds; and they are certainly > enormously higher. The Deity of the Théodicée of Leibniz is as high an > Instinctive mind as can well be imagined; but it impresses a scientific > reader as distinctly inferior to the human mind. It reminds one of the view > of the Greeks that Infinitude is a defect; for although Leibniz imagines > that he is making the Divine Mind infinite, by making its knowledge Perfect > and Complete, he fails to see that in thus refusing it the powers of > thought and the possibility of improvement he is in fact taking away > something far higher than knowledge. It is the human mind that is infinite. > One of the most remarkable distinctions between the Instinctive mind of > animals and the Rational mind of man is that animals rarely make mistakes, > while the human mind almost invariably blunders at first, and repeatedly, > where it is really exercised in the manner that is distinctive of it. If > you look upon this as a defect, you ought to find an Instinctive mind > higher than a Rational one, and probably, if you cross-examine yourself, > you will find you do. The greatness of the human mind lies in its ability > to discover truth notwithstanding its not having Instincts strong enough to > exempt it from error. ]] CP 7.380 ] > > ** ** > > This suggests to me that fallibility – which not even Peirce attributes to > God – is a highly developed species of incompleteness. The connection with > infinity, and with Thirdness, is further brought out in Peirce's Harvard > Lecture of 1903 “On Phenomenology”: > > ** ** > > [[[ The third category of which I come now to speak is precisely that > whose reality is denied by nominalism. For although nominalism is not > credited with any extraordinarily lofty appreciation of the powers of the > human soul, yet it attributes to it a power of originating a kind of ideas > the like of which Omnipotence has failed to
Re: [peirce-l] Categorical Aspects of Abduction, Deduction, Induction
Peircers, I think it's true that some of the difficulties of this discussion may be due to different concepts of predicates, or different ways of using the word "predicate" in different applications, communities, and contexts. If I think back to the variety of different communities of interpretation that I've had the fortune or misfortune of passing through over the years, I can reckon up at least this many ways of thinking about predicates: 1. In purely syntactic contexts, a predicate is just a symbol, a syntactic element that is subject to specified rules of combination and transformation. As we pass to contexts where predicate symbols are meant to have meaning, most disciplines of interpretation will be very careful, at first, about drawing a firm distinction between a predicate symbol and the object it is intended to denote. For example, in computer science, people tend to use forms like "constant name", "function name", "predicate name", "type name", "variable name", and so on, for the names that denote the corresponding abstract objects. When it comes to what information a predicate name conveys, what kind of object the predicate name denotes, or finally, what kind of object the predicate itself is imagined to be, we find that we still have a number of choices: 2. Predicate = property, the intension a concept or term. 3. Predicate = collection, the extension of a concept or term. 4. Predicate = function from a universe domain to a boolean domain. It doesn't really matter all that much in ordinary applications which you prefer, and there is some advantage to keeping all the options open, using whichever one appears most helpful at a given moment, just so long as you have a way of moving consistently among the alternatives and maintaining the information each conveys. Regards, Jon SE = Steven Ericsson-Zenith SE: Ben and I appear to be speaking across each other and, possibly, agreeing fiercely. SE: Recall that in the 1906 dialectic Peirce is drawing a distinction between the wider usage of "Category" at the time, i.e., Aristotle's Categories considered by "you" in the dialog, and saying that he prefers to call these "Predicaments". Having made this distinction he then speaks about the indices that are his categories. SE: As I said earlier, the index in this case does not point to the elements of the category but the category itself. "There is Firstness" as opposed to "x is a first." The confusion may be that Ben thinks I am saying that a category is some set of indices to its members. That is not the case, a category stands alone and we can point to it (index). Icons are the selection mechanisms of properties of classes, not indices. SE: Predicaments are higher order, assertions about assertions, predicates of predicates, I prefer to say "predicated predicates" or "assertions about assertions" which is more generally understood today. SE: Being as careful as he is, I see no evidence to cause us to suppose that the categories that Peirce attributes to himself in 1906 are different than those he identifies as early as 1866. -- academia: http://independent.academia.edu/JonAwbrey inquiry list: http://stderr.org/pipermail/inquiry/ mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey word press blog 1: http://jonawbrey.wordpress.com/ word press blog 2: http://inquiryintoinquiry.com/ - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
Irving, all,
In my previous post I said that I would include the "full" Peirce quotes, but
for the first Peirce quote I included only the portion included in the Commens
Dictionary. For the full quote (CP 4.233), go here:
http://books.google.com/books?id=3JJgOkGmnjEC&pg=RA1-PA193&lpg=RA1-PA193&dq=%22Mathematics+is+the+study+of+what+is+true+of+hypothetical+states+of+things%22
- Original Message -
From: Benjamin Udell
To: PEIRCE-L@LISTSERV.IUPUI.EDU
Sent: Tuesday, March 13, 2012 6:11 PM
Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce
edition
Irving, Gary, Malgosia, list,
Irving, I'm sorry that I gave you the impression that I think that a lemma is
something helpful but unproven inserted into a proof. I mean a theorem placed
in among the premisses to help prove the thesis. Its proof may be offered then
and there, or it may be a theorem from (and already proven in) another branch
of mathematics, to which the reader is referred. At any rate it is as Peirce
puts it "a demonstrable proposition about something outside the subject of
inquiry."
The idea that theorematic reasoning often involves a lemma comes not from me
but from Peirce. Theorematic reasoning, in Peirce's view, involves
experimentation on a diagram, which may consist in a geometrical form, an array
of algebraic expressions, a form such as "All __ is __," etc. I don't recall
his saying anything to suggest that theorematic reasoning is particularly
mechanical. I summarized Peirce's views in a paragraph in my first post on
these questions, and I'll reproduce it, this time with the full quotes from
Peirce. He discusses lemmas in the third quote.
Peirce held that the most important division of kinds of deductive reasoning is
that between corollarial and theorematic. He argued that, while finally all
deduction depends in one way or another on mental experimentation on schemata
or diagrams,[1] still in corollarial deduction "it is only necessary to imagine
any case in which the premisses are true in order to perceive immediately that
the conclusion holds in that case," whereas theorematic deduction "is deduction
in which it is necessary to experiment in the imagination upon the image of the
premiss in order from the result of such experiment to make corollarial
deductions to the truth of the conclusion."[2] He held that corollarial
deduction matches Aristotle's conception of direct demonstration, which
Aristotle regarded as the only thoroughly satisfactory demonstration, while
theorematic deduction (A) is the kind more prized by mathematicians, (B) is
peculiar to mathematics,[1] and (C) involves in its course the introduction of
a lemma or at least a definition uncontemplated in the thesis (the proposition
that is to be proved); in remarkable cases that definition is of an abstraction
that "ought to be supported by a proper postulate.".[3]
1 a b Peirce, C. S., from section dated 1902 by editors in the "Minute Logic"
manuscript, Collected Papers v. 4, paragraph 233, quoted in part in
"Corollarial Reasoning" in the Commens Dictionary of Peirce's Terms,
2003-present, Mats Bergman and Sami Paavola, editors, University of Helsinki.:
How it can be that, although the reasoning is based upon the study of an
individual schema, it is nevertheless necessary, that is, applicable, to all
possible cases, is one of the questions we shall have to consider. Just now, I
wish to point out that after the schema has been constructed according to the
precept virtually contained in the thesis, the assertion of the theorem is not
evidently true, even for the individual schema; nor will any amount of hard
thinking of the philosophers' corollarial kind ever render it evident. Thinking
in general terms is not enough. It is necessary that something should be DONE.
In geometry, subsidiary lines are drawn. In algebra permissible transformations
are made. Thereupon, the faculty of observation is called into play. Some
relation between the parts of the schema is remarked. But would this relation
subsist in every possible case? Mere corollarial reasoning will sometimes
assure us of this. But, generally speaking, it may be necessary to draw
distinct schemata to represent alternative possibilities. Theorematic reasoning
invariably depends upon experimentation with individual schemata. We shall find
that, in the last analysis, the same thing is true of the corollarial
reasoning, too; even the Aristotelian "demonstration why." Only in this case,
the very words serve as schemata. Accordingly, we may say that corollarial, or
"philosophical" reasoning is reasoning with words; while theorematic, or
mathematical reasoning proper, is reasoning with specially constructed
schemata. (' Minute Logic', CP 4.233, c. 1902)
2. Peirce, C. S., the 1902 Carnegie Application, published in The New Elements
of Mathematics, Carolyn Eisele, editor, also transcribed by Joseph M. Ransdell,
see "From Dr
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
Irving, Gary, Malgosia, list,
Irving, I'm sorry that I gave you the impression that I think that a lemma is
something helpful but unproven inserted into a proof. I mean a theorem placed
in among the premisses to help prove the thesis. Its proof may be offered then
and there, or it may be a theorem from (and already proven in) another branch
of mathematics, to which the reader is referred. At any rate it is as Peirce
puts it "a demonstrable proposition about something outside the subject of
inquiry."
The idea that theorematic reasoning often involves a lemma comes not from me
but from Peirce. Theorematic reasoning, in Peirce's view, involves
experimentation on a diagram, which may consist in a geometrical form, an array
of algebraic expressions, a form such as "All __ is __," etc. I don't recall
his saying anything to suggest that theorematic reasoning is particularly
mechanical. I summarized Peirce's views in a paragraph in my first post on
these questions, and I'll reproduce it, this time with the full quotes from
Peirce. He discusses lemmas in the third quote.
Peirce held that the most important division of kinds of deductive reasoning is
that between corollarial and theorematic. He argued that, while finally all
deduction depends in one way or another on mental experimentation on schemata
or diagrams,[1] still in corollarial deduction "it is only necessary to imagine
any case in which the premisses are true in order to perceive immediately that
the conclusion holds in that case," whereas theorematic deduction "is deduction
in which it is necessary to experiment in the imagination upon the image of the
premiss in order from the result of such experiment to make corollarial
deductions to the truth of the conclusion."[2] He held that corollarial
deduction matches Aristotle's conception of direct demonstration, which
Aristotle regarded as the only thoroughly satisfactory demonstration, while
theorematic deduction (A) is the kind more prized by mathematicians, (B) is
peculiar to mathematics,[1] and (C) involves in its course the introduction of
a lemma or at least a definition uncontemplated in the thesis (the proposition
that is to be proved); in remarkable cases that definition is of an abstraction
that "ought to be supported by a proper postulate.".[3]
1 a b Peirce, C. S., from section dated 1902 by editors in the "Minute Logic"
manuscript, Collected Papers v. 4, paragraph 233, quoted in part in
"Corollarial Reasoning" in the Commens Dictionary of Peirce's Terms,
2003-present, Mats Bergman and Sami Paavola, editors, University of Helsinki.:
How it can be that, although the reasoning is based upon the study of an
individual schema, it is nevertheless necessary, that is, applicable, to all
possible cases, is one of the questions we shall have to consider. Just now, I
wish to point out that after the schema has been constructed according to the
precept virtually contained in the thesis, the assertion of the theorem is not
evidently true, even for the individual schema; nor will any amount of hard
thinking of the philosophers' corollarial kind ever render it evident. Thinking
in general terms is not enough. It is necessary that something should be DONE.
In geometry, subsidiary lines are drawn. In algebra permissible transformations
are made. Thereupon, the faculty of observation is called into play. Some
relation between the parts of the schema is remarked. But would this relation
subsist in every possible case? Mere corollarial reasoning will sometimes
assure us of this. But, generally speaking, it may be necessary to draw
distinct schemata to represent alternative possibilities. Theorematic reasoning
invariably depends upon experimentation with individual schemata. We shall find
that, in the last analysis, the same thing is true of the corollarial
reasoning, too; even the Aristotelian "demonstration why." Only in this case,
the very words serve as schemata. Accordingly, we may say that corollarial, or
"philosophical" reasoning is reasoning with words; while theorematic, or
mathematical reasoning proper, is reasoning with specially constructed
schemata. (' Minute Logic', CP 4.233, c. 1902)
2. Peirce, C. S., the 1902 Carnegie Application, published in The New Elements
of Mathematics, Carolyn Eisele, editor, also transcribed by Joseph M. Ransdell,
see "From Draft A - MS L75.35-39" in Memoir 19 (once there, scroll down):
Deduction is only of value in tracing out the consequences of hypotheses,
which it regards as pure, or unfounded, hypotheses. Deduction is divisible into
sub-classes in various ways, of which the most important is into corollarial
and theorematic. Corollarial deduction is where it is only necessary to imagine
any case in which the premisses are true in order to perceive immediately that
the conclusion holds in that case. Ordinary syllogisms and some deductions in
the logic of relatives belong to this class. Theorematic
Re: [peirce-l] Book Review: "Peirce and the Threat of Nominalism"
Glad to hear, Cathy - thanks. I agree with your assessment and, based only on what Houser presents, his criticisms. The book itself is probably a worthwhile read, perhaps worthy of further review here. From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf Of Catherine Legg Sent: Tuesday, March 13, 2012 4:43 PM To: PEIRCE-L@LISTSERV.IUPUI.EDU Subject: Re: [peirce-l] Book Review: "Peirce and the Threat of Nominalism" Michael I just read the book review from Nathan Houser you shared - it is lucidly written over 6 pages and gives a commanding overview of Peirce's realism. I really enjoyed reading it, thanks for posting it. Cathy On Fri, Mar 9, 2012 at 6:13 PM, Michael DeLaurentis wrote: If there has already been a post about this, my apologies. Book review just in on CSP and nominalism. Michael J DeLaurentis - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU _ No virus found in this message. Checked by AVG - www.avg.com Version: 2012.0.1913 / Virus Database: 2114/4868 - Release Date: 03/13/12 - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
Dear Irving, A digression, from the perspective of art. You quote probability theorist William Taylor and set theorist Martin Dowd as saying: > "The chief difference between scientists and mathematicians is that > mathematicians have a much more direct connection to reality." >> This does not entitle philosophers to characterize mathematical reality >> as fictional. Yes, I can see that. But how about a variant: The chief difference between scientists, mathematicians, and artists is that artists have a much more direct connection to reality. This does not prevent scientists and mathematicians to characterize artistic reality as fictional, because it is, and yet, nevertheless, real. This is because scientist's and mathematician's map is not the territory, yet the artist's art is both. Gene Halton -Original Message- From: C S Peirce discussion list [mailto:PEIRCE-L@LISTSERV.IUPUI.EDU] On Behalf Of Irving Sent: Tuesday, March 13, 2012 4:34 PM To: PEIRCE-L@LISTSERV.IUPUI.EDU Subject: Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition Ben, Gary, Malgosia, list It would appear from the various responses that. whereas there is a consensus that Peirce's theorematic/corollarial distinction has relatively little, if anything, to do with my theoretical/computational distinction or Pratt's "creator" and "consumer" distinction. As you might recall, in my initial discussion, I indicated that I found Pratt's distinction to be somewhat preferable to the theoretical/computational, since, as we have seen in the responses, "computational" has several connotations, only one of which I initially had specifically in mind, of hack grinding out of [usually numerical] solutions to particular problems, the other generally thought of as those parts of mathematics taught in catch-all undergrad courses that frequently go by the name of "Finite Mathematics" and include bits and pieces of such areas as probability theory, matrix theory and linear algebra, Venn diagrams, and the like). Pratt's creator/consumer is closer to what I had in mind, and aligns better, and I think, more accurately, with the older pure (or abstract or theoretical) vs. applied distinction. The attempt to determine whether, and, if so, how well, Peirce's theorematic/corollarial distinction correlates to the theoretical/computational or creator/consumer distinction(s) was not initially an issue for me. It was raised by Ben Udell when he asked me: "Do you think that your "theoretical - computational" distinction and likewise Pratt's "creator - consumer" distinction between kinds of mathematics could be expressed in terms of Peirce's "theorematic - corollarial" distinction?" I attempted to reply, based upon a particular quote from Peirce. What I gather from the responses to that second round is that the primary issue with my attempted reply was that Peirce's distinction was bound up, not with the truth of the premises, but rather with the method in which theorems are arrived at. If I now understand what most of the responses have attempted to convey, the theorematic has to do with the mechanical processing of proofs, where a simple inspection of the argument (or proof) allows us to determine which inference rules to apply (and when and where) and whether doing so suffices to demonstrate that the theorem indeed follows from the premises; whereas the corollarial has to do with intuiting how, or even if, one might get from the premises to the desired conclusion. In that case, I would suggest that another way to express the theorematic/corollarial distinction is that they concern the two stages of creating mathematics; that the mathematician begins by examining the already established mathematics and asks what new mathematics might be Ben Udell also introduces the issue of the presence of a lemma in a proof as part of the distinction between theorematic and corollarial. His assumption seems to be that a lemma is inserted into a proof to help carry it forward, but is itself not proven. But, as Malgosia has already noted, the lemma could itself have been obtained either theorematically or corollarially. In fact, most of us think of a lemma as a minor theorem, proven along the way and subsequently used in the proof of the theorem that we're after. I do not think that any of this obviates the main point of the initial answer that I gave to Ben's question, that neither my theoretical/computational distinction nor Pratt's "creator" and "consumer" distinction have anything to do with Peirce's theorematic/corollarial distinction. In closing, I would like to present two sets of exchanges; one very recent (actually today, on FOM, with due apologies to the protagonists, if I am violating any copyrights) between probability theorist William Taylor (indicated by '>') and set theorist Martin Dowd (indicated by '>>'), as follows: >> More seriously, any freshman
Re: [peirce-l] Book Review: "Peirce and the Threat of Nominalism"
Michael I just read the book review from Nathan Houser you shared - it is lucidly written over 6 pages and gives a commanding overview of Peirce's realism. I really enjoyed reading it, thanks for posting it. Cathy On Fri, Mar 9, 2012 at 6:13 PM, Michael DeLaurentis wrote: > If there has already been a post about this, my apologies. Book review > just in on CSP and nominalism. > > ** ** > > Michael J DeLaurentis > > ** ** > > > > ** ** > > ** ** > > - > You are receiving this message because you are subscribed to the PEIRCE-L > listserv. To remove yourself from this list, send a message to > lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body > of the message. To post a message to the list, send it to > PEIRCE-L@LISTSERV.IUPUI.EDU - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Mathematical terminology, was, review of Moore's Peirce edition
Ben, Gary, Malgosia, list It would appear from the various responses that. whereas there is a consensus that Peirce's theorematic/corollarial distinction has relatively little, if anything, to do with my theoretical/computational distinction or Pratt's "creator" and "consumer" distinction. As you might recall, in my initial discussion, I indicated that I found Pratt's distinction to be somewhat preferable to the theoretical/computational, since, as we have seen in the responses, "computational" has several connotations, only one of which I initially had specifically in mind, of hack grinding out of [usually numerical] solutions to particular problems, the other generally thought of as those parts of mathematics taught in catch-all undergrad courses that frequently go by the name of "Finite Mathematics" and include bits and pieces of such areas as probability theory, matrix theory and linear algebra, Venn diagrams, and the like). Pratt's creator/consumer is closer to what I had in mind, and aligns better, and I think, more accurately, with the older pure (or abstract or theoretical) vs. applied distinction. The attempt to determine whether, and, if so, how well, Peirce's theorematic/corollarial distinction correlates to the theoretical/computational or creator/consumer distinction(s) was not initially an issue for me. It was raised by Ben Udell when he asked me: "Do you think that your "theoretical - computational" distinction and likewise Pratt's "creator - consumer" distinction between kinds of mathematics could be expressed in terms of Peirce's "theorematic - corollarial" distinction?" I attempted to reply, based upon a particular quote from Peirce. What I gather from the responses to that second round is that the primary issue with my attempted reply was that Peirce's distinction was bound up, not with the truth of the premises, but rather with the method in which theorems are arrived at. If I now understand what most of the responses have attempted to convey, the theorematic has to do with the mechanical processing of proofs, where a simple inspection of the argument (or proof) allows us to determine which inference rules to apply (and when and where) and whether doing so suffices to demonstrate that the theorem indeed follows from the premises; whereas the corollarial has to do with intuiting how, or even if, one might get from the premises to the desired conclusion. In that case, I would suggest that another way to express the theorematic/corollarial distinction is that they concern the two stages of creating mathematics; that the mathematician begins by examining the already established mathematics and asks what new mathematics might be Ben Udell also introduces the issue of the presence of a lemma in a proof as part of the distinction between theorematic and corollarial. His assumption seems to be that a lemma is inserted into a proof to help carry it forward, but is itself not proven. But, as Malgosia has already noted, the lemma could itself have been obtained either theorematically or corollarially. In fact, most of us think of a lemma as a minor theorem, proven along the way and subsequently used in the proof of the theorem that we're after. I do not think that any of this obviates the main point of the initial answer that I gave to Ben's question, that neither my theoretical/computational distinction nor Pratt's "creator" and "consumer" distinction have anything to do with Peirce's theorematic/corollarial distinction. In closing, I would like to present two sets of exchanges; one very recent (actually today, on FOM, with due apologies to the protagonists, if I am violating any copyrights) between probability theorist William Taylor (indicated by '>') and set theorist Martin Dowd (indicated by '>>'), as follows: More seriously, any freshman philosopher encounters the fact that there are fundamental differences between physical reality and mathematical reality. Quite so. And one of these is noted by Hilbert (or maybe Hardy, anyone help?) >- "The chief difference between scientists and mathematicians is that mathematicians have a much more direct connection to reality." This does not entitle philosophers to characterize mathematical reality as fictional. Quite so; but philosophers tend to have a powerful sense of entitlement. the other, in Gauss's famous letter November 1, 1844 to astronomer Heinrich Schumacher regarding Kant's philosophy of mathematics, that: "you see the same sort of [mathematical incompetence] in the contemporary philosophers Don't they make your hair stand on end with their definitions? ...Even with Kant himself it is often not much better; in my opinion his distinction between analytic and synthetic propositions is one of those things that either run out in a triviality or are false." - Message from bud...@nyc.rr.com - Date: Mon, 12 Mar 2012 13:47:10 -0400 Fro
Re: [peirce-l] Proemial: On The Origin Of Experience
I agree with that, Steven. We forget how many bad paths Einstein went down before he relied on a friend for key input when working on General Relativity. It's all in his notebooks from the time. John Professor John Collier Philosophy, University of KwaZulu-Natal Durban 4041 South Africa T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031 email: colli...@ukzn.ac.za>>> On 2012/03/13 at 08:38 AM, in message <5a506354-b312-4ebf-b5c9-7ee33401a...@iase.us>, Steven Ericsson-Zenith wrote: Thanks John. If the right question is asked and understood, then the answer is readily apparent if the data that confirms or denies it is accessible. In effect, the answers are all out there, we need only craft the right question. Scientific interpretation of data is but a process of question refinement and this can be generalized to all forms of "interpretation." Contrary to the common idea that interpretation is some posterior act. When we have the answer, we tend to forget the paths that either failed or were incomplete on our way to it. With respect, Steven -- Dr. Steven Ericsson-Zenith Institute for Advanced Science & Engineering http://iase.info On Mar 12, 2012, at 1:58 AM, John Collier wrote: > > > > > Professor John Collier > Philosophy, University of KwaZulu-Natal > Durban 4041 South Africa > T: +27 (31) 260 3248 / 260 2292 > F: +27 (31) 260 3031 > email: colli...@ukzn.ac.za>>> On 2012/03/06 at 11:03 PM, in message > <4a39e6c5-939f-49ba-bc6b-8af976028...@iase.us>, Steven Ericsson-Zenith > wrote: > > I'm not sure I would say that the Mars lander computational analysis of data > is "interpretation." It seems to me to be a further representation, although > one filtered by a machine imbued with our intelligence. Interpretation would > be the thing done by scientists on earth. > > As a former planetary scientist, I would agree in general with this, but I > also experienced new data that pretty much implied directly (along with other > well-known principles) that lunar differentiation had occurred. (Even then, > scientists had to interpret the results, but they were clear as crystal > relative to the question.) I relied on much less direct data (gravity > evidence and some general principles of physics and geochemistry) to argue > for the same conclusion. My potential paper was scooped, and I hadn't even > graduated yet. Both Harvard and MIT people in the field found my paper "very > interesting" but lost complete interest when I was retrospectively scooped by > firmer evidence. The moral is that nothing in science beats direct evidence, > even the most appealing hypothesis. Nonetheless, your book sound interesting. > > Regards, > John > > Please find our Email Disclaimer here-->: http://www.ukzn.ac.za/disclaimer > Please find our Email Disclaimer here: http://www.ukzn.ac.za/disclaimer/ - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
Re: [peirce-l] Proemial: On The Origin Of Experience
Thanks John. If the right question is asked and understood, then the answer is readily apparent if the data that confirms or denies it is accessible. In effect, the answers are all out there, we need only craft the right question. Scientific interpretation of data is but a process of question refinement and this can be generalized to all forms of "interpretation." Contrary to the common idea that interpretation is some posterior act. When we have the answer, we tend to forget the paths that either failed or were incomplete on our way to it. With respect, Steven -- Dr. Steven Ericsson-Zenith Institute for Advanced Science & Engineering http://iase.info On Mar 12, 2012, at 1:58 AM, John Collier wrote: > > > > > Professor John Collier > Philosophy, University of KwaZulu-Natal > Durban 4041 South Africa > T: +27 (31) 260 3248 / 260 2292 > F: +27 (31) 260 3031 > email: colli...@ukzn.ac.za>>> On 2012/03/06 at 11:03 PM, in message > <4a39e6c5-939f-49ba-bc6b-8af976028...@iase.us>, Steven Ericsson-Zenith > wrote: > > I'm not sure I would say that the Mars lander computational analysis of data > is "interpretation." It seems to me to be a further representation, although > one filtered by a machine imbued with our intelligence. Interpretation would > be the thing done by scientists on earth. > > As a former planetary scientist, I would agree in general with this, but I > also experienced new data that pretty much implied directly (along with other > well-known principles) that lunar differentiation had occurred. (Even then, > scientists had to interpret the results, but they were clear as crystal > relative to the question.) I relied on much less direct data (gravity > evidence and some general principles of physics and geochemistry) to argue > for the same conclusion. My potential paper was scooped, and I hadn't even > graduated yet. Both Harvard and MIT people in the field found my paper "very > interesting" but lost complete interest when I was retrospectively scooped by > firmer evidence. The moral is that nothing in science beats direct evidence, > even the most appealing hypothesis. Nonetheless, your book sound interesting. > > Regards, > John > > Please find our Email Disclaimer here-->: http://www.ukzn.ac.za/disclaimer > - You are receiving this message because you are subscribed to the PEIRCE-L listserv. To remove yourself from this list, send a message to lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body of the message. To post a message to the list, send it to PEIRCE-L@LISTSERV.IUPUI.EDU
