Monday, 26 June 2017

Toomas Karmo (Part F): Philosophy of Perception, Action, and "Subjectivity"

Quality assessment:

On the 5-point scale current in Estonia, and surely in nearby nations, and familiar to observers of the academic arrangements of the late, unlamented, Union of Soviet Socialist Republics (applying the easy and lax standards Kmo deploys in his grubby imaginary "Aleksandr Stepanovitsh Popovi nimeline sangarliku raadio instituut" (the "Alexandr Stepanovitch Popov Institute of Heroic Radio") and his  grubby imaginary "Nikolai Ivanovitsh Lobatshevski nimeline sotsalitsliku matemaatika instituut" (the "Nicolai Ivanovich Lobachevsky Institute of Socialist Mathematics") - where, on the lax and easy grading philosophy of the twin Institutes, 1/5 is "epic fail", 2/5 is "failure not so disastrous as to be epic", 3/5 is "mediocre pass", 4/5 is "good", and 5/5 is "excellent"): 4/5. Justification: There was enough time to write out the  necessary points to reasonable length.

Revision history:

All times in these blog "revision histories" are stated in UTC (Universal Coordinated Time/ Temps Uniersel Coordoné,  a precisification of the old GMT, or "Greenwich Mean Time"), in the ISO-prescribed YYYYMMDDThhmmZ timestamping format. UTC currently leads Toronto civil time by 4 hours and currently lags Tallinn civil time by 3 hours.

20170627T0001Z/version 1.0.0: Kmo uploaded a not-quite polished version. His writing incorporated two recycled paragraphs from an earlier posting, as documented in the revision history for the "Part D" posting of this present philosophy-of-perception-and-action essay (2017-06-05/2017-06-06). He reserved the right to make tiny, nonsubstantive, purely cosmetic tweaks over the coming 48 hours, as here-undocumented versions 1.0.1, 1.0.2, 1.0.3, ... .]

[CAUTION: A bug in the blogger server-side software has in some past weeks shown a propensity to insert inappropriate whitespace at some points in some of my posted essays. If a screen seems to end in empty space, keep scrolling down. The end of the posting is not reached until the usual blogger "Posted by Toomas (Tom) Karmo at" appears. - The blogger software has also shown a propensity to generate HTML that gets formatted in different ways on different client-side browsers, perhaps with some browsers not correctly reading in the entirety of the "Cascading Style Sheets"  (CSS) which on all ordinary Web servers control the browser placement of margins, sidebars, and the like. If you suspect CSS problems in your particular browser, be patient: it is probable that while some content has been shoved into some odd place (for instance, down to the bottom of your browser, where it ought to appear in the right-hand margin), all the server content has been pushed down into your browser in some place or other. - Finally, there may be blogger vagaries, outside my control, in font sizing or interlinear spacing. - Anyone inclined to help with trouble-shooting, or to offer other kinds of technical advice, is welcome to write me via]

In this sixth ("Part F") installment of what might ultimately prove a 10- or 15- or 20-installment essay on the analytical philosophy of perception and action, I am still finishing off some preliminaries. In my third installment ("Part C", from 2017-05-29 or 2017-05-30), I wrote that I am presupposing a position on causation contrary to the position of a possible philosopher DEFGH (*"Darren Gloom" or "Dagwood Spume"). In my fourth installment ("Part D", from 2017-06-05 or 2017-06-06, I wrote that I am presupposing a position on other minds contrary to the position of a possible philosopher HGFED.

It might at this point be objected: Fine, then. In ordinary speech, "cause" and its cognates carry a meaning incompatible with the semantics proposed by DEFGH, and "aware" and its cognates carry a meaning incompatible with the semantics proposed by HGFED. But this is a mere sociological fact, regarding contingent linguistic habits in Homo sapiens. A deeper question remains unaddressed by such sociological observations. Deeper is the question what meanings ought to be attached to "cause" (and cognates), and to "aware" (and cognates). Could it be that common language tries in a confused and obfuscatory way to use meanings to which it lacks entitlement - even as the pre-Victorian physicists used a meaning to which they lacked entitlement when they  in their obfuscation wrote of heat as "Caloric Fluid"?

A mathematical parallel helps reinforce this parallel from physics. The question of underlying entitlement is analogous to questions which (so I vaguely gather) have been posed by a particular school or grouping in the philosophy of mathematics. In the case of mathematics, I shall have now to depart in a small way from my Igominy and Humiligation Precept, openly naming three names. The workers in question are the "intuitionists", in the Netherlands, along with a Russian "ultra-finitist". (I have not to any significant extent read in these authors.) In the Netherlands was a movement led by Luitzen Egbertus Jan Brouwer (1881-1966) and Arend Heyting (1899-1980). In Russia (with later a period of American exile) was Alexander Sergeyevich Esenin-Volpin (more formally Александр Сергеевич Есенин-Вольпин; 1924-2016).

The revisionist philosophers of mathematics represent themselves as rejecting a traditionally "Platonic" conception of mathematics. The general flavour of their position is illustrated by an anecdote regarding A.S. Essenin-Volpin. The story goes somewhat as follows (I embellish slightly, for clarity: 

A mathematician of a traditionalist disposition - (call her, or him, "Professeur Platonique") fond of the "actually infinite set, of cardinality aleph-null, which is the positive integers" - asks Essenin-Volpin, "Does reality contain such an entity as the integer 1?" Essenin-Volpin replies, after some short time interval Delta-t (we might imagine this being 125 or 250 or 500 milliseconds, or so): Yes. 

"And does reality contain such an entity as the integer 2?" Essenin-Volpin pauses just a little longer, in fact 2*2 = 4 times as long as Delta-t, before saying "Yes."

"And does reality contain such an entity as the integer 3?" Essenin-Volpin pauses a little longer still, in fact 2*2*2 = 8 times as long as Delta-t, before saying "Yes."  

And does reality contain such an entity as the integer 4? Essenin-Volpin pauses rather perceptibly, in fact for an interval 2*2*2*2 = 16 times as long as Delta-t, before saying "Yes." 

The general flavour of their position can also be conveyed by remarking that some of them formalized what was and was not admissible in their prescribed day-to-day mathematical practice. (Here I write "some" to signal the fact that Brouwer, in contrast with Heyting, eschewed formal metamathematics.) I gather that you were not allowed to assert that for every mathematical proposition p, either p or not-p. In fact, as I (dimly) understand it, you were only allowed to assert "either p or not-p" in cases in which you somehow could show that either a proof of p could be written or a proof of the impossibility of ever proving p could be written. (Here, I presume, the potentially troublesome conception of "writing a proof" itself got duly formalized.) 

In general, we have no guarantee that (given, I presume, a reasonable formalization of the informal locution "writing a proof") for every mathematical proposition p, either we can write a proof of p or we can write a proof of the impossibility of writing a proof of p

One real-life example - I have, even in my ignorance, to do my best to construct a real-life example - might be the series representation of Euler's number e = 2.71828182845904523536028747135... . This number is the base of the natural logarithms. It is notorious, like pi, for being not merely irrational as the square root of 2 is irrational, but for additionally lacking any finite algebraic representation such as "the unique positive real number x such that x*x = 2". 

In classical mathematics, as I presume rejected by the revisionists, e is the limit of the series  1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 + ...  - more tidily, of the series 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + ... . No finite initial segment (no "partial sum") from the series equals e. Nevertheless, from a classical-mathematics perspective, for any positive real number epsilon, no matter how excruciatingly small, there exists some (perhaps dauntingly large) number N such that the sum of the first N terms in the series (the "N-term partial sum") falls short of e by some quantity even smaller than epsilon. 

Let, now, p be the following proposition: For some sum-of-the-first-N-terms approximation "falls-Nshort" of e from the just-mentioned finite series, falls-Nshort contains, somewhere in its ordinary decimal expansion, the pre-2006 Toronto phone number of the author of this blog (namely 4169716955). 

If p is true, we might be able to prove it true, say by running a computer, and computing the 100,000-term approximation falls-100,000short of e, and expressing that approximation as some decimal, and taking lots of computer printout. It can be shown - at any rate, I have in my ignorance to say, in the framework of classical, pre-Brouwer, mathematics - that the computer result will be either a decimal expansion tidily ending in repeated 0, as for 1/25 = 0.0400000000..., or a decimal expansion tidily repeating with something other than mere "0000...", as in the case of 1/11 = 0.0909090909... So for any N, we can satisfy ourselves that we have grasped the result for N by taking some finite (perhaps prolix) printout, and finding the eventual, inevitable, onset-of-boredom stage beyond which things just repeat. We will have proved the truth of p once we have found, upon combing through some (suitably prolix, and yet finite) printout from the decimal representation of falls100,000short, the string 4169716955. We will have proved the truth of p if we find, for example,  2.7182818284590452353602874713 ... [and three thousand further unhelpful digits] 841697169559 [and ten thousand further digits in this particular prolix pile of printout - and yet, in our joy, we need not bother inspecting that further ten thousand]. 

But what if we search for a proof that p and fail? We can only perform a finite number of searches, even though each individual search, that is to say each falls-Nshort, for some N in the set {1, 2, 3, ... }, need only be printed out to some finite number of pages. It may well be that there is no way of proving that all possible searches for a proof that p are doomed to fail. The index N at any rate is - alas - unbounded. 

To reiterate: (1) according to this revisionist movement in the philosophy of mathematics, if we lack a proof that p, and also lack a proof that all possible attempts at a proof that p will fail, we cannot assert that either p or not p; and (2) I have tried tonight to supply a plausible candidate "p". 


It has already proved advisable to violate the guiding Igominy and Humiligation Precept from 2017-05-22 or 2017-05-23 ("Part B") by mentioning Brouwer, Heyting, and Essenin-Volpin. Now it is advisable for me to violate it again by citing, albeit tersely, the work of Catholic British logician-philosopher Prof. Sir Michael Dummett (1925-2011). 

Dummett, terming the just-described movement "anti-realism in the philosophy of mathematics", asserts anti-realism in mathematics to have potential parallels in other areas of philosophy. Dummett would say that DEFGH is working toward articulating "anti-realism" (not in the philosophy of mathematics, but) in the "philosophy of causation". Dummett would say that HGFED is working toward articulating "anti-realism" (not in the philosophy of mathematics, but) in the "philosophy of other minds". 

I for my part would rephrase this a little, representing Dummett as posing questions of entitlement. Our actual linguistic practice concerning causation and Other Minds, which I have tried to analyze over my last three postings by looking at such things as support-for-counterfactuals, is at variance with the practice of my hypothesized investigators DEFGH and HGFED. Dummett's question (on my formulation) is this: Is our actual linguistic practice legitimate - is it a linguistic practice to which we are entitled? Could it be that it is in some sense incoherent (confused), like the old 18th-century physical-science language of "Caloric Fluid"? 

Here I come to the limits of what I can do. I am like one of those 1950s Oxford linguistic philosophers who analyzed current semantic practice without pressing downward to Dummett's underlying question of entitlement. (I recall that one of the Surface Swimmers was called Jane Austin, or Jock Austen, or something. I recall the name of another coming up as the first in a trio of dropped names in that wonderful play a mathematician wrote and staged at Monash University in Melbourne, in 1978. (I became for our playwright a subtly mendacious café waiter from Knossos, sporting a Cretan accent - "See my passport, BIRTHPLACE: Knossos.") A melancholy guitarist in this café (at the "Paradox Hotel") professes his disdain for "a drama shared with all Creation", declaiming his countervailing preference for "Philosophical Investigation": Sometimes I while/ Away my time with Ryle;/ Next I incline/ To Wittgenstein/ Or even Quine. One must imagine the lines spoken while the so-sad guitar emits a plink and a plonk. - I like to think that the actor in this particular role had been selected in part for his marked air of melancholy, in part also for his robustly Australian phonemes.)

Tonight I simply have to put on record my assumption that yes, we are entitled to our current practice, both as regards causation and as regards the existence of other minds. Surface-skimming? Yes, alas. Let this admission constitute the hoisting of a formal "superficiality flag", within the meaning of the Debian Precept as promulgated on 2017-05-22 or 2017-05-23, in "Part B" of this essay.]

[This is the end of the current blog posting, as "Part F" of the philosophy-of-perception-and-action essay. It is hoped to upload "Part G" at some point in the coming four weeks, perhaps as early as next week or the week following.] 

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