Who first invented calculus - Newton or Leibniz?
in [Logic]
|
Prev: Model != World?
Next: If Gauss Put His FFT On His Web Page It Wouldn't Have Had To Be Rediscovered In WWII
From: John Stafford on 5 Jan 2010 14:09 In article <d780e1ad-fd18-4a44-a183-9b4c408bcee1(a)m25g2000yqc.googlegroups.com>, M Purcell <sacscale1(a)aol.com> wrote: > On Jan 5, 10:13�am, John Stafford <n...(a)droffats.net> wrote: > > We may be hung on a technicality here. I agree that the vast majority of > > mathematics is inductive, but during the formulation of a thesis the > > mathematician might use induction to create a case to test for a proof, > > or as I hope I once wrote, once induction is complete then one moves to > > deductive reasoning. > > The argument: > > Statement S(1) is true. > Statement S(n) implies Statement S(n+1). > Therefore, S(n) is true for all n. For natural numbers. Inductive in mathematics involves proofs. Not so in philosophy where it is about inductive _reasoning_. > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could > > find! I can explain but it might split the subject. > > Haven't seem the movie but it is my understanding that kind of > deduction is more a process of elimination, trying to find premises to > fit the conclusion. He used _abductive_ reasoning. Arg! I think I just blew-up my speel checker. Really, abductive.
From: M Purcell on 5 Jan 2010 15:02 On Jan 5, 11:09 am, John Stafford <n...(a)droffats.net> wrote: > In article > <d780e1ad-fd18-4a44-a183-9b4c408bc...(a)m25g2000yqc.googlegroups.com>, > M Purcell <sacsca...(a)aol.com> wrote: > > > On Jan 5, 10:13 am, John Stafford <n...(a)droffats.net> wrote: > > > We may be hung on a technicality here. I agree that the vast majority of > > > mathematics is inductive, but during the formulation of a thesis the > > > mathematician might use induction to create a case to test for a proof, > > > or as I hope I once wrote, once induction is complete then one moves to > > > deductive reasoning. > > > The argument: > > > Statement S(1) is true. > > Statement S(n) implies Statement S(n+1). > > Therefore, S(n) is true for all n. > > For natural numbers. Inductive in mathematics involves proofs. Not so in > philosophy where it is about inductive _reasoning_. Indeed, anything for which natual numbers can not be assigned. > > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could > > > find! I can explain but it might split the subject. > > > Haven't seem the movie but it is my understanding that kind of > > deduction is more a process of elimination, trying to find premises to > > fit the conclusion. > > He used _abductive_ reasoning. Arg! I think I just blew-up my speel > checker. Really, abductive. The truth of improbability, actually I was just reading than Holmes used modus ponens, an inferential deduction.
From: John Stafford on 5 Jan 2010 15:31 In article <715cf711-3b9e-4d89-96c1-9fc08c708643(a)h9g2000yqa.googlegroups.com>, M Purcell <sacscale1(a)aol.com> wrote: > On Jan 5, 11:09�am, John Stafford <n...(a)droffats.net> wrote: > > > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could > > > > find! I can explain but it might split the subject. > > > > > Haven't seem the movie but it is my understanding that kind of > > > deduction is more a process of elimination, trying to find premises to > > > fit the conclusion. > > > > He used _abductive_ reasoning. Arg! I think I just blew-up my speel > > checker. Really, abductive. > > The truth of improbability, actually I was just reading than Holmes > used modus ponens, an inferential deduction. modus ponens? Oh, thought that mons pubis.
From: Androcles on 5 Jan 2010 13:56 "John Stafford" <nhoj(a)droffats.net> wrote in message news:nhoj-A74572.12130305012010(a)news.supernews.com... > In article > <80022c43-5c39-46ea-ab95-6ed4e668e906(a)q4g2000yqm.googlegroups.com>, > M Purcell <sacscale1(a)aol.com> wrote: > >> On Jan 4, 7:36 pm, John Stafford <n...(a)droffats.ten> wrote: >> > It matters not. The Calculus was not philosophically rationalized until >> > quite recently. Regardless, it was perfectly useful until then, and >> > remains useful today. >> >> How was calculus recently philosophically rationalized? > > By recent, I mean after most philosophers were over dithering on the > meaning of infinitesimals. The philosophers could not 'rationalize' the > process, it seemed unnatural (another problem for the philosophers), but > somehow calculus all worked very well regardless of objections. The > first rationalization was when the Calculus turned to limits instead. I > think it was the late 1800's. More recently, the 1960s's, Abraham > Robinson returned to the interpretation of infinitesimal numbers apart > from the philosophical, to mathematical theory - a stunning bit of > reasoning, IMHO. > Given f'(x) = [f(x+h)-f(x)]/h, it naturally follows that h is the smallest number greater than zero and cannot be divided. This statement deeply upset Bonehead Green who insisted h was divisible by 2 simply by writing h/2. Yet at the other end of the scale he'd be perfectly happy to turn an 8 on its side and call it infinity. > I'm at a bit of a loss for precise description of the history - I no > longer work at the university library (real bummer, but better pay here.) > > >> > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts >> > out. >> >> I hope you realize mathematical induction is deductive. > > We may be hung on a technicality here. I agree that the vast majority of > mathematics is inductive, but during the formulation of a thesis the > mathematician might use induction to create a case to test for a proof, > or as I hope I once wrote, once induction is complete then one moves to > deductive reasoning. > >> >> > Back to the subnect, it was found that Leibniz's approach was more >> > useful, fewer hacks, more direct. Leibniz wins. >> >> Leibniz also published first, Newton's delay is suspect. > > I'm not as familiar with that history as I should be. Thanks for the > nudge. > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could > find! I can explain but it might split the subject.
From: bvcvideo on 5 Jan 2010 16:55
strictly untrue; Kepler et al were using the program of [Cardinal] Nicholas of Cusa; of course, since you are apparently British, you've probably been indoctrinated with the secular church of Newton, and/or the Harry Potter PS curriculum of the "Venetian Party" of England. also, I keep on referring to the 2.5-page article in *Math.Mag.* (MAA.org), that proves the isometry of inductive & deductive proofs, also giving a formula to convert from one to the other. the Royal Society attack on Leibniz was political; he was actively being considered to be the PM, by Queen Anne. (deny that, if you care to .-) > With Gawd getting in the way it's small wonder the Xtian Romans > produced no mathematicians of the earlier Greek calibre. :-)- Hide quoted text - thus: doctor Einstein's essay seems quite confuzed about the electromegnetic properties of matter, but that was a while before our standard textbookoid concepts were put out from the Texas Schoolbook Suppository. thus: he is giving a lot of credit to Lorentz, who may be more responsible, after all, for the time-space crack-up than doctor Minkowski; can you say, Most useless formalism of Century 20.1? however, the real problem is your persistent use -- with whomever else from the past & future -- of the the concept of vacuum, as Pascal first thought of it, which is really, strictly relative or active (as in, That giant sucking sound, you hear, when you're trying to read this ****). > http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html --Brit's hate Shakespeare, Why? http://wlym.com/campaigner/8011.pdf --Madame Rice is a Riceist, How? http://larouchepub.com/other/2009/3650rice_racist.html --The Riemannian Space of the Nucleus, What? http://www.21stcenturysciencetech.com/Articles_2009/Relativistic_Moon... --In perpetuity clause in healthcare bill, Where? |