the "philosophy" of the catholic church, jh? Like Aristotle and St. Thomas? Or something else. I doubt you want to get those dreadful germans or..anglo-Americans involved (most of whom were pro-science--e.g., empiricists, or Wm. James). That said I might agree there is an ideology of science of sort--at least the academic sorts. Like make shit which works, will make money, or help pulverize the enemy.
a great thomist once said to me there is something of value for thinking in all thinkers even nietzsche even shopenhauer who was far drearier than ole frederick--to make the effort to read and understand any man's insight into life is a way of judging your own it is a way of thinking away from didactic outlines....at least all the philosophers were trying to be free and that is a great object...i've benefitted from trying to comprehend kant and hegel but i can't bear to go back and read them now...better to read holderin and listen to bach
i suspect some amazing undergroud philosophy came out of russia maybe still untranslated...someone there must've tapped into the only real freedom
There is a type of thinking involved with philosophy that the Herd doesn't get--nor do techies. Analytical-- not just quantitative--but conceptual as well.
Schopenhauer's far too much of a pessimist for Mericans ,jh. They want ..sunny streets and don't worry be Happy. The philosophy of selling cars, or computers,or beer bimbos and football, or silicon valley Zen-Co. The Hegelians &marxists hated schopenhauer as well--gloominess, entropic, with hints of eastern religion, meditations on the character of Jesusetc. Schop. did not perceive a Disney-esque nature either---but savage, unrelenting. Not good for ...esprit de corps
Thomism is bewildering, even more so than.... St.Tom's guru Aristotle . tengo mucho trabajo--but here's one puzzle maybe you can resolve---universals are realized in the particular, for thomists right, as for Ari. The Form of a cat, or catness is in Cat A--along with the matter (DNA like..sort of--). Compounding of sorts--not just a random collection of atoms. And thats subject to the Ari. causes. Yet musn't St. Tom say ..Deus has the universal in mind, and in humans' minds too? (felines--a category). So the Uni. exists in 3 places?? And can't Deus..override or alter that??..and the causes, ie final cause.That was a problem for scholastics as well wasn't it. Aquinas nearly sounds ..deterministic and pagan).
in ways the ..platonic schema however abstract was a bit...more understandable -- St Tom and Ari. were IMHE attempting a sort of..primitive biology--not always successful--the fiendish Russell said something of the sort)
the plague takes full swing in the 14th century but thomas saw enough of squalor to be convinced of the reality of epidemics....maybe he conjectured a link to evil i don't know
aristotle and thomas were content to describe nature as it appears the whole movement to rip it apart and dissect it and get at the inner essence of the thing was really an enlightenment impulse...so yeah it might seem primitive but they were a lot less convinced that man was to be the "domination" of nature...in that regard far less arrogant than so-called modern science
I've been trying to figure out how to respond in a way that will advance the conversation. It occurs to me that this quote can, and arguably should, be turned on its head in classic Hegelian antithesis form, leaving room for a useful synthesis.
It seems to me that philosophy without science, which is to say, philosophy that does not observe the real world, nor test it's conclusions against the real world, is a vanity and a striving against the wind.
i with aristotle and the dumb ox contend stu that science is primordial philosophy that is a grounding in the real the natual world is fundamental it is the first cognitive impulse of the human it is the groundwork of intellection this is what aristotle perceives as physica the tangible phenomenal world incorporated through the senses into the mind...this is the upending to which i've been most disturbed and which i rail against
i follow what might be construed as the hierarchy of knowledge (a la maritain) the hierarchy extends from the groundwork of science of knowing through the senses and the intellect and rises naturally to a questioning of higher even transcendental truths (if i may)
thanks for the long contemplation on the lines stu
in my hierarchy mine alone for i seem to be the only one on earth holding to this sacred principle lost out on the windy prairie chanting to the wind like so much buffalo grass or so much windy gas
i aspire to the high point to the peak of knowledge and thomas takes us there he really really does just come along now children he takes us to the fine high fresh air of thinking and then contemplation...for philosphy what might be termed first philosophy is properly understood as a metaphysical proposition...in that we ask of the real world metaphysical questions....for instance...from whence did it come? actually begs a more theological perception...is there a God? such that all science in thomas's view is actually a participation in the transcendant mystery of god's creation....maybe that's why all the scientists are walking around with the glib " O WE KNOW SO MUCH " attitudes on their faces...restrain me lord from diatribe today....must be the coffee...where was i
thomas and i hold and i guess now that he's dead and only available to us in prayer and his extant writings that he didn't burn as if it were straw we alone hold we alone hold the kernel of truth which places our highest natural aspiration in mystery and our beginning in the real world...reason is the groundwork of all our contemplative efforts
and it is this that i find lacking in so much scientific writing this sense that this is rooted in mystery and our knowledge of it indicates our participation in the mystery of our being here at all
i guess i'm holding out for what might appear as really inspired science writing...i get some of that in wes jackson and wendell berry...i like fritjof capra...who else writes with some sort of ardent interest OK pierre tielhard de chardin and thomas berry and rachel carson people liek this strike me as possessing some sense of the transcendent inherent in reality....
hmh what should i do next i know
play my guitar................
nope i'm sticking to my statement science without philosophical bearing is mere scribbling it is a pandering to the humanist ideal of human sufficiency it is the degradation of the known world in the efforts to dominate and control nature it is the monster we most fear...but it appears like a commercial on tv which says....scientists have found such and such to be true in countless laboratory experiments trust us it's safe it's good for you we know smile now and go about your day with less worry for we have the knowledge for you we want you to be happy here scientists show that this little pill yadda yadda yadda...that's the forced presumptuous quasi-hopeful conveyance of knoweldge which horrifies me...i turn more and more from all of it in repulsion and fear... but that's just me sitting on butte on the prairie in the sage and dirt with a tome of summa contra gentiles chanting in the wind..ah well
philosophy without science, which is to say, philosophy that does not observe the real world, nor test it's conclusions against the real world, is a vanity and a striving against the wind.
Hegel would disagree ich denke. Not that he was anti-science (his writing on Leibniz, Newton, the calculus, and Laplace quite..profound) But he wasn't exactly a positivist. First philosophy (in Hegel ,something like dialectic...but he was aware of the Kantian a priori,etc) still proceeds .. before empiricism (IIRC Hegel thought Hume ....well he didn't care for him).
Im for ...Wendell Berry jazz but..in ways oppose the overly sentimental Disney-view of nature--or "Franciscan" for that matter. So in terms of philosophical-poker, find Schopenhauer useful--he might reminds us of death,chaos, dissipation (tho I don't think he was quite an atheist ala Darwin tc) and was not too down with Hegelian heroics (which was still...protestant. Hegel loudly proclaimed his lutheran faith as well ). Schop. has in a sense broken with zionist-protestant tradition IMHE. Hegel vs Schopenhauer deathmatch.
(which is also to say.. greeks are profound--lets have Biff and Bunny read The Republic!--- but so ancient obscure amd difficult. And Hegel (andreally allthegermans)knew the greek philosophers quite well (unlike say..British empiricists). Hegel's lectures on Plato and Aristotle are worth a perusal once a year or so (tho he wasn't too enamored of Aquinas) .
i with aristotle and the dumb ox contend stu that science is primordial philosophy that is a grounding in the real the natual world is fundamental it is the first cognitive impulse of the human it is the groundwork of intellection this is what aristotle perceives as physica the tangible phenomenal world incorporated through the senses into the mind
Scientific knowledge is philosophical in its character, and clearly an important part of the synthesis must be to acknowledge this fact that both sides of the argument often forget.
The power of science comes from its character as a specialized philosophy, a philosophy that accepts certain limits (e.g., explicitly in terms of the structure of a permissible argument, and therefore implicitly in terms of the subject matter it can address) in return for greater proof-theoretic power within those limits.
Let me suggest that this explains in part the the occasional arrogance and overreach of some scientists: Science as a methodology has been extraordinarily successful in answering certain types of questions. Scientists who see the limits of science as natural and comfortable are inclined to identify the class of all questions science can answer with the class of all questions. J, who knows enough set theory to understand the reference, might view this analogous to Gödel's V=L hypothesis, as in, S=P, science equals philosophy. It is internally consistent, and therefore it is irrefutable to its adherents, but it's clearly seen to be misguided from the vantage point of a "more complete" system.
Of course, not all scientists feel that the intellectual limits of science are comfortable or natural, and may are perfectly happy to acknowledge that non-scientific classes of questions (e.g., ethical and/or theological) are natural and important, but are outside of the box in which science works.
J writes,
Hegel would disagree ich denke. Not that he was anti-science (his writing on Leibniz, Newton, the calculus, and Laplace quite..profound) But he wasn't exactly a positivist.
I was invoking Hegel's methods, not his specific positions. But I do think that Mathematics is a serious challege to the anti-thesis as I stated it. After all, analogies to statements that reflect an incomplete understanding are likely to reflect an incomplete understanding :-). But Math too, it must be noted, is a kind of specialized philosophy of very much the same kind as Science: it accepts the limits of a stronger notion of proof in return for greater certainty within its domain. One might argue (as I'm sure many have, and indeed I think I can safely invoke Aquinas here) that Theology too is a kind of specialized philosophy, i.e., one that admits the proposition that God exists as axiomatic, and one that accepts scripture and the writings of the fathers (to various degrees) as possessing important insight into the whys and what-fors of that fundamental theological dogma.
jh--when does ,or will the Pope or a leading catholic mention a Wendell Berry, tielhard de chardin or rachel carson, the berrigans, etc?
I don't perceive that sort of .. sensibility. The catholic business tends to be conservative--Scalia & Co., Boehner, Pat Buchanan--Tom Lasorda,etc. Not all--there have been many Catholic demos (ie, Boston, NY, Chi. politics were controlled by irish/italian catholics--eg, Kennedys. OR Tammany). But now many have turned GOP--like Christie, el Gordo. When Papa Bene. excommunicates Scalia and the rest of the right-wing pro-capitalist SC I will take Mass.
--Stu. Sounds something like Carnap, who probably had some influence on Goedel's continuum concept--tho' a rather different issue. (many don't realize how platonic--even mystical-- Goedel himself was. One problem I have with set theorists--they believe those sets of cardinals and ordinals as existing in some platonic heaven. And most people have an naive understanding of Goedel's incompleteness proofs--he didn't overthrow First Order logic, for one .....there may be assumptions in systems (arithmetic) that cannot be proven--but the system stilll works--sort of like you have 1000 operations/functions/arguments, and 990 of them work fine--youd probably say the system works alright,and then ...eliminiate/prevent the ones that don't (mostly a self-referential issue ala the Halting problem (at least when applied to computability).
For Carnap all real philosophical questions were ..at bottom ,scientific,ie verifiable. If not they were..meaningless. So, "ethics" aka normativity was meaningless according to Carnap (as youve probably heard)--which I disagree with. We might not be able to account for Justice in some perfect axiomatic fashion, but we, or at least rational people know it when it's..missing. (say via recent SC decisions)
THE CHURCH BLESS HER WARM WARM HEART ALWAYS HOLDS OUT FOR CONVERSION FOR PEOPLE TO SEE THE LIGHT EVEN IF ON THE DEATHBED o sorry didn't mean to hit the caps button key whatever listenin to tony rice and norman blake
you hit at the kernel idea there J this madness for deduction for impirical certainty it's the curse of epistemology it's like some desperate disease one can't rid herself from that there's got to be a an answer and if there's not well i'll state one anyway and call that the answer it's madness HELP MISTER WIZARD...but it reminds me
as i said the church is no stranger to intellectual presumption but most of the problem is the misapprehension by people on the outside the church's main business is charity it is taking care of the blisters and soars amid humanity and stating the importance of that in the public forum...intellectual integrity is big too
jesus wasn't just jesting with the criminal who was cranked and crucified next to him who pleaded to be remembered
someone going afoul in the public forum is like someone going afoul anywhere it's to be expected power corrupts these people do get forgiveness i don't care what dante said i mean we have rewritten the cosmology he heald to but we need to read dante anyway for above all his world is one of necessary enchantment
is there a divine comedy for the 21st century
maybe bill gates and steve jobs will be in the ice of hell for presuming to control human understanding in ways far worse than the magisterium ever did but perhaps the mercy would be those guys were benighted too how could they have known
it's interesting to consider what will happen when 7 billion people come face to face with the need for mercy mercy more than food and drugs
all in all things are working pretty well right now
still if people are not striving for freedom of thought they are striving for epistemlogical imprisonment and that can't be good
just like with the chosen people freedom of thought requires a few laws
somehow this conversation seems crazy o but what the hell
You seem to have some confusions about the incompleteness theorem.
First order logic is sound and complete, i.e., entailment is equivalent to provability. The issue with incompleteness revolves not around the deductive power of first order logic, but instead around its expressive power.
A trivial corollary of the incompleteness theorem is that the first order sentences of true arithmetic is not a computably enumerable set. Paradoxically, this entails another kind of incompleteness theorem for logics that are at least as powerful as first order logic: either they can't computably axiomatize arithmetic, or they don't have a computable set of axioms. In effect, if you're at least as powerful as FOL, you can be expressively complete or deductively complete, but you can't be both.
As for JH's remarks about certainly... I think that certainty is only to be found in Mathematics (which might in fact be characterized as the special philosophy of certain knowledge), but it comes at the cost that there is no necessary connection between mathematical knowledge and the real world. Hence, Wigner's famous article on the “unreasonable effectiveness of mathematics in the natural sciences.” Most mathematicians know this, and to the extent that they're platonists, they're honest enough to understand their worlds may be entirely artificial constructions.
No you misread me. The point is many people think Goedel disproved all logic, including FOL. When that isn't the case . He actually has completeness proof for FOL (sound and complete--.if it's a valid deduction the system shows it as such). 2nd order logic and "modal" logics are incomplete. Peano axioms as well (at least with 2nd order original form). via FOL Peano axioms holds. G. doesn't ..defeat Whitehead-Russell really (who arguably just said..mathematics was logical, not that it was complete).
Of Set theory ..I know ein bisschen but actually object(from somewhat nominalist grounds, ala Quine ...points contra-Cantor, and infinity ,really--not that I really like Quine ,who was like his mentor Carnap part of the reductionist mafia--)
I don't think that jh is necessarily happy with us turning his comments section into an opportunity to argue mathematical foundations, but I'll hope he'll grant us just a bit more license.
2nd order logic and "modal" logics are incomplete.
It all depends on what you mean by "incomplete." E.g., intuitionistic propositional logic is complete w.r.t. Kripke semantics, much as classical propositional logic is complete w.r.t. boolean valued semantics, or FOL is complete w.r.t. Tarski semantics.
Peano axioms as well (at least with 2nd order original form)
Actually, 2nd order PA is a complete axiomatization of arithmetic, a consequence of Dedekind's rigidity theorem (any two minimal sets with a successor-like function must be isomorphic). The problem is that it's a useless completeness, because while the axioms are (semantically) complete, the proof system necessarily is not.
I know some set theory, more than a bit, but it's pretty far removed from my specialties (computability theory, complexity theory, and randomness). Even so, as much as the formalist position is satisfying from a foundational point of view, I believe that every mathematician is a platonist when they're actually engaged in the doing of mathematics. Of course, it's an artificial platonism, but I think it's platonism still: this is visible whenever a mathematician talks of mathematical intuition, and without mathematical intuition, mathematics is all but impossible.
OK, and I didn't intend to go into another MF/logic swordfight but you mentioned Goedel (overrated figure IMHE..not to say mad). Re Propositional logic--an argument's only as good as its premises. Isn't that soundness actually? Use only true, ie tautological premises and there are no problems.
That said , I agree somewhat that analytical phil. biz (including set theorists) like academic science might be considered culpable as per jh's original statement. That was my original point, not stated very well. Im not a postmodernist or ..a luddite but have come to realize that formalization tends to help corporate Oppression for lack of better term (and that can be verified,even)--e.g. set theorists working with the holy sets of ordinals when ...peoples are starving or rioting in the street. . Misapplied Techne, per Heidegger.
OK, and I didn't intend to go into another MF/logic swordfight but you mentioned Goedel (overrated figure IMHE..not to say mad).
I don't consider this to be a sword fight. It seems to me that it's been a very civil conversation. As for Gödel, he was certainly mad. But he was also certainly a seminal figure in modern logic. I'm certainly well aware of antecedents to the completeness theorem. Wiki sites Skolem, but what Wiki doesn't know is that Skolem borrowed from Lowenheim's paper, but very few people have actually read Lowenheim, and fewer still have understood him. I remember having to explain it to Burt Dreben at a party at Jerry Sacks'. This is relevant because, IIRC, Dreben wrote the introduction to Lowenheim's paper in van Heijenoort. My theory is that Skolem was the referee for Lowenheim's paper. He was certainly in the right place at the right time (Gottingen, 1914).
But even if you minimize the creative content of the completeness theorem there's a lot more that Gödel did. The incompleteness theorem, and with it the foundations for modern theories of computation. The relative consistency of the axiom of constructivity (V=L), and with it the relative consistency of the Continuum Hypothesis. A solution to Einstein's equations that permits time travel.
As a practicing mathematician, it always comes down to this: would I trade my theorems for his? In a heartbeat, sir. In a heartbeat.
Re Propositional logic--an argument's only as good as its premises. Isn't that soundness actually? Use only true, ie tautological premises and there are no problems.
This is confused. Propositional logic is the logic of and, or, and not, i.e., no quantifiers. And there's not much use using tautologies as premises: if they're tautologies, you can derive them from the axioms.
That said , I agree somewhat that analytical phil. biz (including set theorists) like academic science might be considered culpable as per jh's original statement. That was my original point, not stated very well.
I'm not sure I get this point, either from what you've written, or from what JH has written. That specialists care mostly about their specialties? That ought to qualify as a sociological tautology.
Im not a postmodernist or ..a luddite but have come to realize that formalization tends to help corporate Oppression for lack of better term (and that can be verified,even)--e.g. set theorists working with the holy sets of ordinals when ...peoples are starving or rioting in the street.
I think this is silly. Do you actually know any set theorists? It's a wonder they can feed themselves ;-). I'm not sure society would have anything to gain by assigning them to trying to feed others. Seriously -- different folks have different gifts. Some folks are gifted as helping others. Others are gifted at puzzling out formal systems. And the applications of mathematics are often delayed, but no less real for it. Consider, for example, the economic consequences of Boole's work. Or the current market value of the Peron-Frobenius theorem: $162.1B, the market cap of Google. People are being fed, but the paths aren't alway clear, least of all at the beginning.
no,you're confuseds stu--its not just the connectives, but the argument forms..Modus ponens ring a bell? (ie conditionals as well the rest) So the forms--or rules of inference, IIRC--apply to both propositional and predicate logic--ie, modus ponens works with propositions/statements or with quantifiers. Propositions ie premises are still subject to verification , unless tautological, ie true, even if trivial-- if 90 degree angle iff a right triangle.
the later points are via say Hegel and pragmatists, Feyerabend. Maybe Thoreau--ie ,contra-the positivist model which you had suggested a few comments up. The aged Russell himself called for wisdom, not just logic chopping ( or Uni of Chi. finance capitalism). Ie ,there can be philosophy which does not depend strictly on science/verification. Normativity matters (even in the sense--does it function or not..or is it just vaguely-platonic dreams). Ive met set theorists .Liked them less than I do formal logicians and mathematicians, other academics. In fact, I consider Cantor's theorems at least bunko,actually--Ive read some eggheads take them as theology, usually jewish . "Being" whatever it is ,is not..a few collections of digits, however large.
no,you're confuseds stu--its not just the connectives, but the argument forms..Modus ponens ring a bell?
Modus ponens isn't a premise, it's a rule of inference that's a part of the proof system. Premise == Hypothesis. Maybe I'm just making a technical distinction that you aren't. Yes, we use proof systems to make/characterized sound arguments, but those arguments (outside of school exercises) generally take place in contexts where the premises and the conclusions are non-tautological, i.e., particular to a context. The purpose of the proof is to assess the argument in-between, and render the judgement, "yes, if the hypotheses are granted, then so too must the conclusion be granted."
Ie ,there can be philosophy which does not depend strictly on science/verification.
My point exactly. Such philosophy isn't science, but isn't everything. I suspect we're agreeing in different words, and quibbling over details.
In fact, I consider Cantor's theorems at least bunko,actually--Ive read some eggheads take them as theology, usually jewish
There's a book that I've bought but not yet read that makes the point that much of the early impetus behind the study of the infinite came from Jewish scholars. I guess I should pull it up to the top of the stack. But I disagree with your assessment of Cantor. We might never fully know the infinite (and here, I would caution against the "infinite == God" pun, I'm talking "merely" about cardinality and completed abstract collections), but we can know it partially. Cantor's work is a seminal contribution in helping us gain access to that partial knowledge. And oddly enough, it comes from practical considerations -- the convergence of Fourier approximations to functions that have isolated discontinuities. What initially blew Cantor's mind was when he proved that if f is a function from [0,1] to the reals with countably many discontinuities, then the series of Fourier approximations to f converges pointwise to f. I'm not sure what the notion of convergence was (it's not pointwise at the points of discontinuity, probably convergence in measure). The implication, though, was that if you removed countable sets from the reals, there was still enough left to constrain the convergence of the series. That matters.
i'm impressed with stu's knowledge of goedel and settheory--he's in the analytical biz...a pro.... im not-- but...his point re "philosophy without science" seems nearly exactly what your quote was addressing--the carnapian view/verificationist--"test it's conclusions against the real world"". Doesn't that go against about any sort of religious-holistic POV? We believe in Justice--or for that matter, beauty-- regardless of what analytical phil. insists. didn't mean to clog the thread up with bickering. pace
the carnapian view/verificationist--"test it's conclusions against the real world"". Doesn't that go against about any sort of religious-holistic POV?
This is presumably a reaction to my
It seems to me that philosophy without science, which is to say, philosophy that does not observe the real world, nor test it's conclusions against the real world, is a vanity and a striving against the wind.
I think you're reading more into what I wrote than what I intended. I was not arguing that the only philosophy worth doing is science, but instead of against the position that science isn't important. Whereas I see it as grounding the larger philosophical enterprise in the real world, and so as serving a crucial role in a much larger conversation.
I suppose my point ultimately is this. Let's suppose that our theological musings lead us to the firm conclusion that earth is fixed and flat. Something has to adjust, and it's not going to be the world.
Did Gödel have a cat? Or are you thinking of Schrödinger?
It's unfortunate that you don't know Gödel's work, because I believe it would shed light on things that you care about. After all, you care about Aquinas, and ultimately the incompleteness theorem says something about the intrinsic limitations of Aquinas's rational philosophical method.
--Google uses some set theory in their search engine secret-sauce, Ive read. So it does seem to have applications--for technological capitalism at least. Probably the military as well. Similarly for formal logic. Thus, the analytical formalization--and reduction of language to syntax, really-- does serve Mammon in a sense. Im not opposed to it exactly, nor consider say a Quine a nazi (as some postmods do). It's more a matter of...how it is used. Even the Counterforce might need some UNIX skills. St Francis the hacker
--as the sentence indicates, I said Modus Ponens is an argument form (or rule of inference, as they say now). So the issue is whether a conclusion is valid--follows from premises, whether thats a syllogism or complex prenex statement with quantifiers and predicates. Even with Lewis Carrollian premises, one can have valid arguments. That was the point--for sound and valid deduction, premises must be true and conclusion valid. Sort of undergraduate-y but many even academics philosophers don't seem to get it.
Google uses some set theory in their search engine secret-sauce, Ive read.
Not set theory. It's actually graph theory restated as linear algebra. Imagine the internet as a complete graph whose nodes are web pages, and where each arc represents the probability that the target page will be visited immediately after the source page.
If we put a probability distribution on the set of nodes, we can then ask what the distribution will be after everyone takes one step. This can be formalized as a stochastic matrix, i.e., a matrix where every entry is non-negative and each column sums to one, acting on a probability vector. Perron-Frobenius says that such matrixes have a principal eigenvector that consists of non-negative real components. The interpretation of such an eigenvector is that it is a stationary distribution on the set of pages -- the probability that a long random walk will end at that page.
And that, modulo some difficult but fairly standard information retrieval indexing and retrieval, and a bit of web spidering, is Google.
As for the logic bit, I reiterate: we're agreeing, and the basic structure of the discussion has been that we've each become progressively more careful in our use of language.
but...actually the google search is still boolean, and boolean at least is basic or naive set theory--combine..."google executives" with AND "oppressors" and then--via probability function (probably related to what you say--the 'n-grams" ,that pop up on google) you get an new--set of oppressive google execs. But there is some advanced set theory jazz ala Stanford U as well (dont have time for the search). Stanford alums (likethe google boys) want to win, baybe.
I still consider Wittgenstein (ie, the Tractatus) sort of a bridge between the analytical and ..holistic/continental sorts of thinker--like Frege he viewed logical form in nearly..spiritual sense--the "great mirror". Though the pious might not care for him--maybe St Ludwig's in the hell-lake of ice too.
The boolean ops are what are subsumed in "standard information retrieval." What makes Google searches interesting isn't that they can find a bazzilion hits for "google executives" AND "oppressors", it's that they can present the results of this search in an interesting order -- i.e., by getting the heaviest weighted pages to you first.
Before there was Google, there was Alta Vista and it's ilk, and to try to winnow down from a bazzilion pages (presented in arbitrary order) to the one page that matters, you'd have to provide more and more restrictive search terms. This had a high coefficient of suckage.
AFIAK, there's no "advanced set theory." It's not as if there aren't apostles of Lofti Zedah out there, it's just that this isn't what makes Google tick. Set theory is more a Berkeley thing than a Stanford thing, anyway.
--its essentially boolean with some trimmings, ie a probability function (seen in the graphs...bell curve anyone), which puts the more relevant info. first . Billionaires via...Boole! Maybe the Google execs should pay some royalities to the family trust or something.
--Brin and Page are Steinford U alums--and there are some ST guys there.
Brin and Page are Steinford U alums--and there are some ST guys there.
Who. 'tis a serious question. The only full-bore logicians I can see on the math websites are Solomon Fefferman, and he's emeritus (and has been since '04, per his CV), and Grigori Mints, whose primary appointment is in philosophy.
My experience is that logicians are thin on the ground, and it's a rare math department that has more than one, and when it has more than one, they're generally in a fairly similar area. Berkeley is a rare exception, since they manage to cover computability theory (Slaman, Harrington), set theory (Addison, Silver, Steele, Wooden), with room left over for a model theorist (Scanlon). Of course, they all talk to one another and get in one another's work.
36 comments:
the "philosophy" of the catholic church, jh? Like Aristotle and St. Thomas? Or something else. I doubt you want to get those dreadful germans or..anglo-Americans involved (most of whom were pro-science--e.g., empiricists, or Wm. James). That said I might agree there is an ideology of science of sort--at least the academic sorts. Like make shit which works, will make money, or help pulverize the enemy.
a great thomist once said to me there is something of value for thinking in all thinkers even nietzsche even shopenhauer who was far drearier than ole frederick--to make the effort to read and understand any man's insight into life is a way of judging your own it is a way of thinking away from didactic outlines....at least all the philosophers were trying to be free
and that is a great object...i've benefitted from trying to comprehend kant and hegel but i can't bear to go back and read them now...better to read holderin and listen to bach
i suspect some amazing undergroud philosophy came out of russia maybe still untranslated...someone there must've tapped into the only real freedom
thinking
jh
There is a type of thinking involved with philosophy that the Herd doesn't get--nor do techies. Analytical-- not just quantitative--but conceptual as well.
Schopenhauer's far too much of a pessimist for Mericans ,jh. They want ..sunny streets and don't worry be Happy. The philosophy of selling cars, or computers,or beer bimbos and football, or silicon valley Zen-Co. The Hegelians &marxists hated schopenhauer as well--gloominess, entropic, with hints of eastern religion, meditations on the character of Jesusetc. Schop. did not perceive a Disney-esque nature either---but savage, unrelenting. Not good for ...esprit de corps
thomas wrote amid the blooming horror of bubonic plague
A bit before the plague wasn't it.
Thomism is bewildering, even more so than.... St.Tom's guru Aristotle . tengo mucho trabajo--but here's one puzzle maybe you can resolve---universals are realized in the particular, for thomists right, as for Ari. The Form of a cat, or catness is in Cat A--along with the matter (DNA like..sort of--). Compounding of sorts--not just a random collection of atoms. And thats subject to the Ari. causes. Yet musn't St. Tom say ..Deus has the universal in mind, and in humans' minds too? (felines--a category). So the Uni. exists in 3 places?? And can't Deus..override or alter that??..and the causes, ie final cause.That was a problem for scholastics as well wasn't it. Aquinas nearly sounds ..deterministic and pagan).
in ways the ..platonic schema however abstract was a bit...more understandable -- St Tom and Ari. were IMHE attempting a sort of..primitive biology--not always successful--the fiendish Russell said something of the sort)
the plague takes full swing in the 14th century
but thomas saw enough of squalor to be convinced of the reality of epidemics....maybe he conjectured a link to evil
i don't know
aristotle and thomas were content to describe nature as it appears
the whole movement to rip it apart and dissect it and get at the inner essence of the thing was really an enlightenment impulse...so yeah it might seem primitive but they were a lot less convinced that man was to be the "domination" of nature...in that regard far less arrogant than so-called modern science
jh,
I've been trying to figure out how to respond in a way that will advance the conversation. It occurs to me that this quote can, and arguably should, be turned on its head in classic Hegelian antithesis form, leaving room for a useful synthesis.
It seems to me that philosophy without science, which is to say, philosophy that does not observe the real world, nor test it's conclusions against the real world, is a vanity and a striving against the wind.
i with aristotle and the dumb ox contend stu
that science is primordial philosophy that is a grounding in the real the natual world is fundamental it is the first cognitive impulse of the human it is the groundwork of intellection
this is what aristotle perceives as physica the tangible phenomenal world incorporated through the senses into the mind...this is the upending to which i've been most disturbed and which i rail against
i follow what might be construed as the hierarchy of knowledge (a la maritain) the hierarchy extends from the groundwork of science of knowing through the senses and the intellect and rises naturally to a questioning of higher even transcendental truths (if i may)
thanks for the long contemplation on the lines stu
in my hierarchy mine alone for i seem to be the only one on earth holding to this sacred principle lost out on the windy prairie chanting to the wind like so much buffalo grass or so much windy gas
i aspire to the high point to the peak of knowledge and thomas takes us there he really really does just come along now children he takes us to the fine high fresh air of thinking and then contemplation...for philosphy what might be termed first philosophy is properly understood as a metaphysical proposition...in that we ask of the real world metaphysical questions....for instance...from whence did it come? actually begs a more theological perception...is there a God? such that all science in thomas's view is actually a participation in the transcendant mystery of god's creation....maybe that's why all the scientists are walking around with the glib " O WE KNOW SO MUCH " attitudes on their faces...restrain me lord from diatribe today....must be the coffee...where was i
thomas and i hold and i guess now that he's dead and only available to us in prayer and his extant writings that he didn't burn as if it were straw we alone hold we alone hold the kernel of truth which places our highest natural aspiration in mystery and our beginning in the real world...reason is the groundwork of all our contemplative efforts
and it is this that i find lacking in so much scientific writing this sense that this is rooted in mystery and our knowledge of it indicates our participation in the mystery of our being here at all
i guess i'm holding out for what might appear as really inspired science writing...i get some of that in wes jackson and wendell berry...i like fritjof capra...who else writes with some sort of ardent interest OK pierre tielhard de chardin and thomas berry and rachel carson people liek this strike me as possessing some sense of the transcendent inherent in reality....
hmh
what should i do next
i know
play my guitar................
nope
i'm sticking to my statement
science without philosophical bearing is mere scribbling
it is a pandering to the humanist ideal of human sufficiency it is the degradation of the known world in the efforts to dominate and control nature it is the monster we most fear...but it appears like a commercial on tv which says....scientists have found such and such to be true in countless laboratory experiments trust us it's safe it's good for you we know smile now and go about your day with less worry for we have the knowledge for you we want you to be happy here scientists show that this little pill yadda yadda yadda...that's the forced presumptuous quasi-hopeful conveyance of knoweldge which horrifies me...i turn more and more from all of it in repulsion and fear...
but that's just me
sitting on butte on the prairie in the sage and dirt with a tome of summa contra gentiles chanting in the wind..ah well
jh
philosophy without science, which is to say, philosophy that does not observe the real world, nor test it's conclusions against the real world, is a vanity and a striving against the wind.
Hegel would disagree ich denke. Not that he was anti-science (his writing on Leibniz, Newton, the calculus, and Laplace quite..profound) But he wasn't exactly a positivist. First philosophy (in Hegel ,something like dialectic...but he was aware of the Kantian a priori,etc) still proceeds .. before empiricism (IIRC Hegel thought Hume ....well he didn't care for him).
Im for ...Wendell Berry jazz but..in ways oppose the overly sentimental Disney-view of nature--or "Franciscan" for that matter. So in terms of philosophical-poker, find Schopenhauer useful--he might reminds us of death,chaos, dissipation (tho I don't think he was quite an atheist ala Darwin tc) and was not too down with Hegelian heroics (which was still...protestant. Hegel loudly proclaimed his lutheran faith as well ). Schop. has in a sense broken with zionist-protestant tradition IMHE. Hegel vs Schopenhauer deathmatch.
(which is also to say.. greeks are profound--lets have Biff and Bunny read The Republic!--- but so ancient obscure amd difficult. And Hegel (andreally allthegermans)knew the greek philosophers quite well (unlike say..British empiricists). Hegel's lectures on Plato and Aristotle are worth a perusal once a year or so (tho he wasn't too enamored of Aquinas) .
scuzi rant
jh & J,
Let me come at this a couple of different ways...
First, I agree with the substance of this:
i with aristotle and the dumb ox contend stu
that science is primordial philosophy that is a grounding in the real the natual world is fundamental it is the first cognitive impulse of the human it is the groundwork of intellection
this is what aristotle perceives as physica the tangible phenomenal world incorporated through the senses into the mind
Scientific knowledge is philosophical in its character, and clearly an important part of the synthesis must be to acknowledge this fact that both sides of the argument often forget.
The power of science comes from its character as a specialized philosophy, a philosophy that accepts certain limits (e.g., explicitly in terms of the structure of a permissible argument, and therefore implicitly in terms of the subject matter it can address) in return for greater proof-theoretic power within those limits.
Let me suggest that this explains in part the the occasional arrogance and overreach of some scientists: Science as a methodology has been extraordinarily successful in answering certain types of questions. Scientists who see the limits of science as natural and comfortable are inclined to identify the class of all questions science can answer with the class of all questions. J, who knows enough set theory to understand the reference, might view this analogous to Gödel's V=L hypothesis, as in, S=P, science equals philosophy. It is internally consistent, and therefore it is irrefutable to its adherents, but it's clearly seen to be misguided from the vantage point of a "more complete" system.
Of course, not all scientists feel that the intellectual limits of science are comfortable or natural, and may are perfectly happy to acknowledge that non-scientific classes of questions (e.g., ethical and/or theological) are natural and important, but are outside of the box in which science works.
J writes,
Hegel would disagree ich denke. Not that he was anti-science (his writing on Leibniz, Newton, the calculus, and Laplace quite..profound) But he wasn't exactly a positivist.
I was invoking Hegel's methods, not his specific positions. But I do think that Mathematics is a serious challege to the anti-thesis as I stated it. After all, analogies to statements that reflect an incomplete understanding are likely to reflect an incomplete understanding :-). But Math too, it must be noted, is a kind of specialized philosophy of very much the same kind as Science: it accepts the limits of a stronger notion of proof in return for greater certainty within its domain. One might argue (as I'm sure many have, and indeed I think I can safely invoke Aquinas here) that Theology too is a kind of specialized philosophy, i.e., one that admits the proposition that God exists as axiomatic, and one that accepts scripture and the writings of the fathers (to various degrees) as possessing important insight into the whys and what-fors of that fundamental theological dogma.
jh--when does ,or will the Pope or a leading catholic mention a Wendell Berry, tielhard de chardin or rachel carson, the berrigans, etc?
I don't perceive that sort of .. sensibility. The catholic business tends to be conservative--Scalia & Co., Boehner, Pat Buchanan--Tom Lasorda,etc. Not all--there have been many Catholic demos (ie, Boston, NY, Chi. politics were controlled by irish/italian catholics--eg, Kennedys. OR Tammany). But now many have turned GOP--like Christie, el Gordo.
When Papa Bene. excommunicates Scalia and the rest of the right-wing pro-capitalist SC I will take Mass.
--Stu. Sounds something like Carnap, who probably had some influence on Goedel's continuum concept--tho' a rather different issue. (many don't realize how platonic--even mystical-- Goedel himself was. One problem I have with set theorists--they believe those sets of cardinals and ordinals as existing in some platonic heaven. And most people have an naive understanding of Goedel's incompleteness proofs--he didn't overthrow First Order logic, for one .....there may be assumptions in systems (arithmetic) that cannot be proven--but the system stilll works--sort of like you have 1000 operations/functions/arguments, and 990 of them work fine--youd probably say the system works alright,and then ...eliminiate/prevent the ones that don't (mostly a self-referential issue ala the Halting problem (at least when applied to computability).
For Carnap all real philosophical questions were ..at bottom ,scientific,ie verifiable. If not they were..meaningless. So, "ethics" aka normativity was meaningless according to Carnap (as youve probably heard)--which I disagree with. We might not be able to account for Justice in some perfect axiomatic fashion, but we, or at least rational people know it when it's..missing. (say via recent SC decisions)
THE CHURCH BLESS HER WARM WARM HEART ALWAYS HOLDS OUT FOR CONVERSION FOR PEOPLE TO SEE THE LIGHT EVEN IF ON THE DEATHBED o sorry didn't mean to hit the caps button key whatever listenin to tony rice and norman blake
you hit at the kernel idea there J this madness for deduction for impirical certainty it's the curse of epistemology it's like some desperate disease one can't rid herself from that there's got to be a an answer and if there's not well i'll state one anyway and call that the answer it's madness HELP MISTER WIZARD...but it reminds me
as i said the church is no stranger to intellectual presumption but most of the problem is the misapprehension by people on the outside the church's main business is charity it is taking care of the blisters and soars amid humanity and stating the importance of that in the public forum...intellectual integrity is big too
jesus wasn't just jesting with the criminal who was cranked and crucified next to him who pleaded to be remembered
someone going afoul in the public forum is like someone going afoul anywhere it's to be expected power corrupts these people do get forgiveness i don't care what dante said i mean we have rewritten the cosmology he heald to but we need to read dante anyway for above all his world is one of necessary enchantment
is there a divine comedy for the 21st century
maybe bill gates and steve jobs will be in the ice of hell for presuming to control human understanding in ways far worse than the magisterium ever did but perhaps the mercy would be those guys were benighted too how could they have known
it's interesting to consider what will happen when 7 billion people come face to face with the need for mercy mercy more than food and drugs
all in all
things are working pretty well right now
still if people are not striving for freedom of thought they are striving for epistemlogical imprisonment and that can't be good
just like with the chosen people
freedom of thought requires a few laws
somehow this conversation seems crazy
o but what the hell
jh
J,
You seem to have some confusions about the incompleteness theorem.
First order logic is sound and complete, i.e., entailment is equivalent to provability. The issue with incompleteness revolves not around the deductive power of first order logic, but instead around its expressive power.
A trivial corollary of the incompleteness theorem is that the first order sentences of true arithmetic is not a computably enumerable set. Paradoxically, this entails another kind of incompleteness theorem for logics that are at least as powerful as first order logic: either they can't computably axiomatize arithmetic, or they don't have a computable set of axioms. In effect, if you're at least as powerful as FOL, you can be expressively complete or deductively complete, but you can't be both.
As for JH's remarks about certainly... I think that certainty is only to be found in Mathematics (which might in fact be characterized as the special philosophy of certain knowledge), but it comes at the cost that there is no necessary connection between mathematical knowledge and the real world. Hence, Wigner's famous article on the “unreasonable effectiveness of mathematics in the natural sciences.” Most mathematicians know this, and to the extent that they're platonists, they're honest enough to understand their worlds may be entirely artificial constructions.
No you misread me. The point is many people think Goedel disproved all logic, including FOL. When that isn't the case . He actually has completeness proof for FOL (sound and complete--.if it's a valid deduction the system shows it as such). 2nd order logic and "modal" logics are incomplete. Peano axioms as well (at least with 2nd order original form). via FOL Peano axioms holds. G. doesn't ..defeat Whitehead-Russell really (who arguably just said..mathematics was logical, not that it was complete).
Of Set theory ..I know ein bisschen but actually object(from somewhat nominalist grounds, ala Quine ...points contra-Cantor, and infinity ,really--not that I really like Quine ,who was like his mentor Carnap part of the reductionist mafia--)
J,
I don't think that jh is necessarily happy with us turning his comments section into an opportunity to argue mathematical foundations, but I'll hope he'll grant us just a bit more license.
2nd order logic and "modal" logics are incomplete.
It all depends on what you mean by "incomplete." E.g., intuitionistic propositional logic is complete w.r.t. Kripke semantics, much as classical propositional logic is complete w.r.t. boolean valued semantics, or FOL is complete w.r.t. Tarski semantics.
Peano axioms as well (at least with 2nd order original form)
Actually, 2nd order PA is a complete axiomatization of arithmetic, a consequence of Dedekind's rigidity theorem (any two minimal sets with a successor-like function must be isomorphic). The problem is that it's a useless completeness, because while the axioms are (semantically) complete, the proof system necessarily is not.
I know some set theory, more than a bit, but it's pretty far removed from my specialties (computability theory, complexity theory, and randomness). Even so, as much as the formalist position is satisfying from a foundational point of view, I believe that every mathematician is a platonist when they're actually engaged in the doing of mathematics. Of course, it's an artificial platonism, but I think it's platonism still: this is visible whenever a mathematician talks of mathematical intuition, and without mathematical intuition, mathematics is all but impossible.
OK, and I didn't intend to go into another MF/logic swordfight but you mentioned Goedel (overrated figure IMHE..not to say mad). Re Propositional logic--an argument's only as good as its premises. Isn't that soundness actually? Use only true, ie tautological premises and there
are no problems.
That said , I agree somewhat that analytical phil. biz (including set theorists) like academic science might be considered culpable as per jh's original statement. That was my original point, not stated very well. Im not a postmodernist or ..a luddite but have come to realize that formalization tends to help corporate Oppression for lack of better term (and that can be verified,even)--e.g. set theorists working with the holy sets of ordinals when ...peoples are starving or rioting in the street. . Misapplied Techne, per Heidegger.
FIN
J,
OK, and I didn't intend to go into another MF/logic swordfight but you mentioned Goedel (overrated figure IMHE..not to say mad).
I don't consider this to be a sword fight. It seems to me that it's been a very civil conversation. As for Gödel, he was certainly mad. But he was also certainly a seminal figure in modern logic. I'm certainly well aware of antecedents to the completeness theorem. Wiki sites Skolem, but what Wiki doesn't know is that Skolem borrowed from Lowenheim's paper, but very few people have actually read Lowenheim, and fewer still have understood him. I remember having to explain it to Burt Dreben at a party at Jerry Sacks'. This is relevant because, IIRC, Dreben wrote the introduction to Lowenheim's paper in van Heijenoort. My theory is that Skolem was the referee for Lowenheim's paper. He was certainly in the right place at the right time (Gottingen, 1914).
But even if you minimize the creative content of the completeness theorem there's a lot more that Gödel did. The incompleteness theorem, and with it the foundations for modern theories of computation. The relative consistency of the axiom of constructivity (V=L), and with it the relative consistency of the Continuum Hypothesis. A solution to Einstein's equations that permits time travel.
As a practicing mathematician, it always comes down to this: would I trade my theorems for his? In a heartbeat, sir. In a heartbeat.
Re Propositional logic--an argument's only as good as its premises. Isn't that soundness actually? Use only true, ie tautological premises and there
are no problems.
This is confused. Propositional logic is the logic of and, or, and not, i.e., no quantifiers. And there's not much use using tautologies as premises: if they're tautologies, you can derive them from the axioms.
That said , I agree somewhat that analytical phil. biz (including set theorists) like academic science might be considered culpable as per jh's original statement. That was my original point, not stated very well.
I'm not sure I get this point, either from what you've written, or from what JH has written. That specialists care mostly about their specialties? That ought to qualify as a sociological tautology.
Im not a postmodernist or ..a luddite but have come to realize that formalization tends to help corporate Oppression for lack of better term (and that can be verified,even)--e.g. set theorists working with the holy sets of ordinals when ...peoples are starving or rioting in the street.
I think this is silly. Do you actually know any set theorists? It's a wonder they can feed themselves ;-). I'm not sure society would have anything to gain by assigning them to trying to feed others. Seriously -- different folks have different gifts. Some folks are gifted as helping others. Others are gifted at puzzling out formal systems. And the applications of mathematics are often delayed, but no less real for it. Consider, for example, the economic consequences of Boole's work. Or the current market value of the Peron-Frobenius theorem: $162.1B, the market cap of Google. People are being fed, but the paths aren't alway clear, least of all at the beginning.
no,you're confuseds stu--its not just the connectives, but the argument forms..Modus ponens ring a bell? (ie conditionals as well the rest) So the forms--or rules of inference, IIRC--apply to both propositional and predicate logic--ie, modus ponens works with propositions/statements or with quantifiers. Propositions ie premises are still subject to verification , unless tautological, ie true, even if trivial-- if 90 degree angle iff a right triangle.
the later points are via say Hegel and pragmatists, Feyerabend. Maybe Thoreau--ie ,contra-the positivist model which you had suggested a few comments up. The aged Russell himself called for wisdom, not just logic chopping ( or Uni of Chi. finance capitalism). Ie ,there can be philosophy which does not depend strictly on science/verification. Normativity matters (even in the sense--does it function or not..or is it just vaguely-platonic dreams). Ive met set theorists .Liked them less than I do formal logicians and mathematicians, other academics. In fact, I consider Cantor's theorems at least bunko,actually--Ive read some eggheads take them as theology, usually jewish . "Being" whatever it is ,is not..a few collections of digits, however large.
wow
i mean wow
i mean really wow
i mean really really wow
so wow i can hardly believe it
all i know about goedel is that he had a cat
jh
J,
no,you're confuseds stu--its not just the connectives, but the argument forms..Modus ponens ring a bell?
Modus ponens isn't a premise, it's a rule of inference that's a part of the proof system. Premise == Hypothesis. Maybe I'm just making a technical distinction that you aren't. Yes, we use proof systems to make/characterized sound arguments, but those arguments (outside of school exercises) generally take place in contexts where the premises and the conclusions are non-tautological, i.e., particular to a context. The purpose of the proof is to assess the argument in-between, and render the judgement, "yes, if the hypotheses are granted, then so too must the conclusion be granted."
Ie ,there can be philosophy which does not depend strictly on science/verification.
My point exactly. Such philosophy isn't science, but isn't everything. I suspect we're agreeing in different words, and quibbling over details.
In fact, I consider Cantor's theorems at least bunko,actually--Ive read some eggheads take them as theology, usually jewish
There's a book that I've bought but not yet read that makes the point that much of the early impetus behind the study of the infinite came from Jewish scholars. I guess I should pull it up to the top of the stack. But I disagree with your assessment of Cantor. We might never fully know the infinite (and here, I would caution against the "infinite == God" pun, I'm talking "merely" about cardinality and completed abstract collections), but we can know it partially. Cantor's work is a seminal contribution in helping us gain access to that partial knowledge. And oddly enough, it comes from practical considerations -- the convergence of Fourier approximations to functions that have isolated discontinuities. What initially blew Cantor's mind was when he proved that if f is a function from [0,1] to the reals with countably many discontinuities, then the series of Fourier approximations to f converges pointwise to f. I'm not sure what the notion of convergence was (it's not pointwise at the points of discontinuity, probably convergence in measure). The implication, though, was that if you removed countable sets from the reals, there was still enough left to constrain the convergence of the series. That matters.
scuzi jh.
i'm impressed with stu's knowledge of goedel and settheory--he's in the analytical biz...a pro.... im not-- but...his point re "philosophy without science" seems nearly exactly what your quote was addressing--the carnapian view/verificationist--"test it's conclusions against the real world"". Doesn't that go against about any sort of religious-holistic POV? We believe in Justice--or for that matter, beauty-- regardless of what analytical phil. insists. didn't mean to clog the thread up with bickering.
pace
grr... I make my fair share of typographical errors, but this one affects meaning.
What I meant to write: Such philosophy isn't science, but science isn't everything.
Sorry about that.
Oh, and that grr was a me, not at J's intervening comment.
J,
Ah! now we're to the point of it...
the carnapian view/verificationist--"test it's conclusions against the real world"". Doesn't that go against about any sort of religious-holistic POV?
This is presumably a reaction to my
It seems to me that philosophy without science, which is to say, philosophy that does not observe the real world, nor test it's conclusions against the real world, is a vanity and a striving against the wind.
I think you're reading more into what I wrote than what I intended. I was not arguing that the only philosophy worth doing is science, but instead of against the position that science isn't important. Whereas I see it as grounding the larger philosophical enterprise in the real world, and so as serving a crucial role in a much larger conversation.
I suppose my point ultimately is this. Let's suppose that our theological musings lead us to the firm conclusion that earth is fixed and flat. Something has to adjust, and it's not going to be the world.
jh,
Did Gödel have a cat? Or are you thinking of Schrödinger?
It's unfortunate that you don't know Gödel's work, because I believe it would shed light on things that you care about. After all, you care about Aquinas, and ultimately the incompleteness theorem says something about the intrinsic limitations of Aquinas's rational philosophical method.
--Google uses some set theory in their search engine secret-sauce, Ive read. So it does seem to have applications--for technological capitalism at least. Probably the military as well. Similarly for formal logic. Thus, the analytical formalization--and reduction of language to syntax, really-- does serve Mammon in a sense. Im not opposed to it exactly, nor consider say a Quine a nazi (as some postmods do). It's more a matter of...how it is used. Even the Counterforce might need some UNIX skills. St Francis the hacker
--as the sentence indicates, I said Modus Ponens is an argument form (or rule of inference, as they say now). So the issue is whether a conclusion is valid--follows from premises, whether thats a syllogism or complex prenex statement with quantifiers and predicates. Even with Lewis Carrollian premises, one can have valid arguments. That was the point--for sound and valid deduction, premises must be true and conclusion valid. Sort of undergraduate-y but many even academics philosophers don't seem to get it.
i awoke this morning and i thought
not goedel but rodinger no growdinger no showdinger no shroedinger yeah that's it he had the cat
i feel i am not epistemologically privy to the rhetoric of mathematical imagination
i''m glad someone does
maybe i could try to write a song about set theory logic imaginary numbers and the vaporous locus of truth presumed by those who study such things
i stick with is
i don't often go to how man
i stick with is
quality impresses me
numeration is tedious
at best
plus and minus
constantly
one and 2
zero and 1
hey number poetry
can be fun
jh
J,
Google uses some set theory in their search engine secret-sauce, Ive read.
Not set theory. It's actually graph theory restated as linear algebra. Imagine the internet as a complete graph whose nodes are web pages, and where each arc represents the probability that the target page will be visited immediately after the source page.
If we put a probability distribution on the set of nodes, we can then ask what the distribution will be after everyone takes one step. This can be formalized as a stochastic matrix, i.e., a matrix where every entry is non-negative and each column sums to one, acting on a probability vector. Perron-Frobenius says that such matrixes have a principal eigenvector that consists of non-negative real components. The interpretation of such an eigenvector is that it is a stationary distribution on the set of pages -- the probability that a long random walk will end at that page.
And that, modulo some difficult but fairly standard information retrieval indexing and retrieval, and a bit of web spidering, is Google.
As for the logic bit, I reiterate: we're agreeing, and the basic structure of the discussion has been that we've each become progressively more careful in our use of language.
but...actually the google search is still boolean, and boolean at least is basic or naive set theory--combine..."google executives" with AND "oppressors" and then--via probability function (probably related to what you say--the 'n-grams" ,that pop up on google) you get an new--set of oppressive google execs. But there is some advanced set theory jazz ala Stanford U as well (dont have time for the search). Stanford alums (likethe google boys) want to win, baybe.
I still consider Wittgenstein (ie, the Tractatus) sort of a bridge between the analytical and ..holistic/continental sorts of thinker--like Frege he viewed logical form in nearly..spiritual sense--the "great mirror". Though the pious might not care for him--maybe St Ludwig's in the hell-lake of ice too.
J,
The boolean ops are what are subsumed in "standard information retrieval." What makes Google searches interesting isn't that they can find a bazzilion hits for
"google executives" AND "oppressors", it's that they can present the results of this search in an interesting order -- i.e., by getting the heaviest weighted pages to you first.
Before there was Google, there was Alta Vista and it's ilk, and to try to winnow down from a bazzilion pages (presented in arbitrary order) to the one page that matters, you'd have to provide more and more restrictive search terms. This had a high coefficient of suckage.
AFIAK, there's no "advanced set theory." It's not as if there aren't apostles of Lofti Zedah out there, it's just that this isn't what makes Google tick. Set theory is more a Berkeley thing than a Stanford thing, anyway.
--its essentially boolean with some trimmings, ie a probability function (seen in the graphs...bell curve anyone), which puts the more relevant info. first . Billionaires via...Boole! Maybe the Google execs should pay some royalities to the family trust or something.
--Brin and Page are Steinford U alums--and there are some ST guys there.
J,
Brin and Page are Steinford U alums--and there are some ST guys there.
Who. 'tis a serious question. The only full-bore logicians I can see on the math websites are Solomon Fefferman, and he's emeritus (and has been since '04, per his CV), and Grigori Mints, whose primary appointment is in philosophy.
My experience is that logicians are thin on the ground, and it's a rare math department that has more than one, and when it has more than one, they're generally in a fairly similar area. Berkeley is a rare exception, since they manage to cover computability theory (Slaman, Harrington), set theory (Addison, Silver, Steele, Wooden), with room left over for a model theorist (Scanlon). Of course, they all talk to one another and get in one another's work.
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