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.
- UTC=20170530T0315Z/version 2.0.0: Kmo finished converting the point-form outline into coherent sentences, and started a process of polishing. He reserved the right to make further tiny, nonsubstantive, purely cosmetic, changes over the coming 48 hours, as here-undocumented versions 2.0.1, 2.0.2, 2.0.3, ... .
- UTC=20170530T0148Z/version 1.0.0: Kmo, running a bit over an hour behind the schedule he thought he could achieve, at last uploaded a correctly readied point-form outline. He hoped to convert this outline into full-sentences prose in a series of uploads, finishing around UTC=20170530T0401Z.
[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 is 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 Toomas.Karmo@gmail.com.]
I must begin this week by correcting a fault which I allowed to creep into last week's writing. Last week I wrote of "concepts", and of "concept formation", and at one point also of "concept gestation". If one is to write at all of "concepts", then it would be better to write of "concept discovery".
For consider last week's examples - notably, the post-1900 topologically defined "concept" of limit and the post-1800 "concept" of energy. To write merely that early 20th-century mathematicians "formed" or "constructed" a topological "concept" of limit, or that the 19th-century physicists "formed" or "constructed" a "concept" of energy, is to make limits and energies look like things authored by humans. In fact, however, limits and energies would have been features of, respectively, abstract topological spaces and physical processes even had Homo sapiens never arisen. It would, for instance, still have been true that when two masses approach under mutual gravitation, the total energy of the two-body system is conserved (with the kinetic energy of the system rising, as the bodies accelerate, so as to offset the fall in the system's potential energy). Further, it there are intelligent extraterrestrial organisms, we can ask such questions as the following:
- Have they discovered limits in the generalized, abstract, set-theoretic realm of topology, or do their mathematical notations capture only numerical limits?
- Have they discovered the conservations governing potential energy and kinetic energy in a two-body gravitating system?
A further example illustrates this same general point about discovery, in at least an oblique way, and so I add it here as a possibly helpful parenthesis. The integer zero is not a thing "humanly constructed", but a human-independent thing. If there were no intelligent organisms in the cosmos, then zero would still have various properties - now among them the interesting property of enumerating the intelligent organisms in the cosmos.
There is, happily, some appreciation on the Web of this mind-independence. The page https://hsm.stackexchange.com/questions/402/discovery-of-zero, at any rate, has the following helpful language (in which a correct use is made of "discover", as opposed to the more Web-common "invent" - evidently with some reference to ancient India): I have read at many places that zero was discovered by Aryabhata but when [I] was discussing this with my mathematics teacher he told me that zero had already been discovered before Aryabhata [and so on].
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It was also a little unfortunate that I wrote last week of the "construction" of complex numbers as ordered pairs of reals. This, again, makes a human-independent thing appear human-dependent. "Construction" in mathematics is a mere metaphor, ultimately drawn from cabinetry or carpentry. All that I should have written last week is that if F is a field, then the collection of ordered pairs <a,b>, where a and b are F-elements, with a certain addition and a certain multiplication operation (and a certain additive inverse, "<0,0>", under the addition operation, and a certain multiplicative inverse, "<1,0>", under the multiplication operation) is itself a field. My point, correctly written out, would have been a purely conditional, i.e., a purely "if...then", point: IF there exists at least one field having the properties standardly ascribed to the real numbers, THEN there exists at least one field (here I would exhibit the just-mentioned set of ordered pairs) having the properties standardly ascribed to the complex numbers. Later on , to be sure, I wold have to speak categorically, in the spirit of my 1971 spring-semester Dalhousie University analysis professor, Max Edelstein: yes, there IS at least one field having the properties standardly ascribed to the real numbers. It would be necessary to exhibit, when thus waxing categorical, the field properties of some such thing as convergent infinite-sequences-of-rationals, citing at that moment appropriate field operations on such sequences. Here I am a bit vague. But Prof. Edelstein's ghost, or any living university real-analysis lecturer, would be able to fill in the gaps.
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Having commented in a corrective way on a couple of last week's modes of expression, I now move forward just a short distance in my multi-week writing project.
Imagine that when walking in town one day, you feel a throbbing pain when you are at the intersection of First Avenue and A Street. Imagine further that as you proceed up First Avenue, the throbbing pain subsides, only to be replaced by a steady nausea when you reach First Avenue and B Street - with this nausea itself subsiding as you leave the intersection behind, on your way up First Avenue to C Street. Imagine, further, that everyone with whom you discuss the topography of First Avenue reports a pain and a nausea similar to yours, localized to that same pair of intersections.
Maybe everyone's reports are consilient as a matter of sheer coincidence - as when fifty tossed dimes all, astonishingly, land heads-up. (Person A, as it were, had an attack of indigestion from bad pickles upon approaching First and B, and Person B coincidentally had an attack of indigestion at this same intersection from a bout of flu, and so on.) But it would be reasonable to suspect that, far from coincidences being in play, there is something at that pair of intersections which is making everyone feel pain in the one place and nausea at the other. If (if, I stress) the suspicion of common causes is true, then it would be a reasonable use of language to say, "There is a throbbing Pain at the intersection of First Avenue and A Street, and a steady Sick at the intersection of First Avenue and B Street." Although such a use of language would depart from English idiom, it would be coherent: i.e., would possess a well-grasped meaning.
Later on, inquiries could be mounted, to determine what the Pain and the Sick are. Two broad kinds of outcome are possible.
(I) The inquiries may have an outcome favourable from the standpoint of existing natural science. It might turn out that, e.g., everyone is made to be in pain by some concealed loudspeakers, vibrating powerfully at some subsonic frequencies cunningly selected for resonance with the bones of the Homo sapiens middle ear, and that the nausea is induced in everyone by the same colourless gas, venting from some cunningly concealed nozzle. In that case, people would say, "Well, the Pain is a subsonic atmospheric vibration, and the Sick is a gas possessing such-and-such a molecular formula."
(II) The inquiries may lead to no outcome favourable from the standpoint of existing natural science. In that case, people will be like astrophysicists grappling with Dark Matter and Dark Energy: they will aver that there are some easily human-perceptible things on First Avenue (assemblages of non-baryonic matter, perhaps?) whose nature is as yet mysterious.
Two possible sub-cases now present themselves.
(II.a) Perhaps the Pain and the Sick will prove frustratingly thin in their phenomenology - never moving around, for instance, and never in other ways changing, and so not lending themselves to any very pleasing mathematics.
(II.b) Perhaps, on the other hand, close observation will disclose a more or less rich phenomenology - with the Pain, perhaps, migrating up First Avenue at certain times of the month, and upon reaching B Street either passing unimpeded through the Sick or else pushing the Sick along with it. - In this "II.b" sub-case, people will be able to write out "laws" regarding the behaviour of the Sick and the Pain, and these "laws:" might ultimately prove to be just as detailed, and just as amenable to exact mathematical formulation, as the laws governing the movements of electrons and protons in electric and magnetic fields. With laws to hand, it will eventually be suggested that the Sick and the Pain are as well understood as the electron and proton themselves, even while in a sense belonging, perhaps, "to a different Kingdom of Matter, with which ordinary baryonic matter has few points of contact outside the physiology of Homo sapiens observers".
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It is now necessary to consider (A) a philosophical problem in the notion of one thing making another happen (a "problem regarding causation") and immediately thereafter to consider (B) a formally parallel philosophical problem, in the notion of someone's experiencing something (a "problem of Other Minds").
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(A) Consider an example from some dead Department of Philosophy authority, Darren Gloom or Dagwood Spume or something, from Edinburgh or Glasgow or Culloden or Skye or somewhere. Mindful of my "Igominy and Humiligation Precept" from the blog posting of 2017-05-22 or 2017-05-23, I refrain from bogging down in admittedly juicy History-of-Post-Mediaeval-Philosophy minutiae - refraining, even, from the explicit naming of names. I merely call the long-dead author, who might be imagined resplendent in bonnet and tartans, "Philosopher DEFGH".
As I recall it, DEFGH said that it is only in a special, subtle, etiolated snse that one event "makes" another happen. He developed his radical idea with an example involving billiard balls. It is an idea which I, trying to make all relevant things explicit, must in my writing project explicitly reject.
If Ball X rolls up against stationary Ball Y, Ball Y in turn starts rolling. Now, asks Philosopher DEFGH, what is meant by saying that Ball X's moving "makes" Ball Y move? DEFGH's answer is that people project the idea of "making", rather as they might project the idea of bad-tasting.
It will be generally acknowledged that strawberries taste bad with mustard. But all that is objectively present in that famous Charlie Chaplin scene is the unfortunate presence, at a summit-meeting diplomatic buffet, of strawberries daubed with mustard. (This is the diplomatic buffet at which His Excellency Herr Adenoid Hynkel, the "Fooey" of "Tomania", and his fellow dictator, Signor Benzino Napoloni of "Bacteria", descend into a food fight, as at https://www.youtube.com/watch?v=dLyd7v0RwNI - a 2017-04-07 upload of YouTube user "TheChaplinFilms", to a length of 4:36.) The "bad-tastingness" is something Herr Hynkel, Signor Napoloni, and we as spectators project onto that distressing Reichskanzlei scene. We make our projection from, so to speak, within our only-too-human breast.
Imagine that accompanying us - who are normal in our culinary preferences - is a person of deviant constitution, for whom mustard is specially agreeable with strawberries, and for whom hot dogs are distinctively acceptable once smothered in cream. We may dispute with our seemingly eccentric colleague, urging that Herr Hynkel's and Signor Napoloni's discomfort at the Chancellery is a fully appropriate reaction to something that "tastes bad". When our colleague urges the putatively eccentric contrary position, saying that it is strawberries under cream that "taste bad", and strawberries under mustard that "taste good", what are we to reply? We can say nothing at all, beyond recalling the old Roman adage "There's no disputing over taste" (de gustibus non disputandum). The disagreement between us and our colleague is, then, not an agreement over facts.
So, says Philosopher DEFGH (admittedly not with this merry Chaplinesque illustrative analogy) for causation. For DEFGH, it is not an objective fact that the motion of Ball X "makes" Ball Y move. Rather, having seen billiard balls collide on many past occasions, people have in their only-too-human breast a subjective feeling of anticipation, focused on Ball Y, as they behold Ball X approach. The feeling is akin to our subjective feeling of discomfort as we juxtapose the respectively contemplated flavours of strawberries and of mustard.
Now to be very explicit: my own upcoming discussion of perception and agency, over the coming weeks, will be presupposing a position on causation not in agreement with, but instead at variance with, DEFGH's. I must spell out my own position on causation tonight, as a necessary preliminary to my anticipated work over the upcoming weeks.
Imagine that accompanying us - who are normal in our culinary preferences - is a person of deviant constitution, for whom mustard is specially agreeable with strawberries, and for whom hot dogs are distinctively acceptable once smothered in cream. We may dispute with our seemingly eccentric colleague, urging that Herr Hynkel's and Signor Napoloni's discomfort at the Chancellery is a fully appropriate reaction to something that "tastes bad". When our colleague urges the putatively eccentric contrary position, saying that it is strawberries under cream that "taste bad", and strawberries under mustard that "taste good", what are we to reply? We can say nothing at all, beyond recalling the old Roman adage "There's no disputing over taste" (de gustibus non disputandum). The disagreement between us and our colleague is, then, not an agreement over facts.
So, says Philosopher DEFGH (admittedly not with this merry Chaplinesque illustrative analogy) for causation. For DEFGH, it is not an objective fact that the motion of Ball X "makes" Ball Y move. Rather, having seen billiard balls collide on many past occasions, people have in their only-too-human breast a subjective feeling of anticipation, focused on Ball Y, as they behold Ball X approach. The feeling is akin to our subjective feeling of discomfort as we juxtapose the respectively contemplated flavours of strawberries and of mustard.
Now to be very explicit: my own upcoming discussion of perception and agency, over the coming weeks, will be presupposing a position on causation not in agreement with, but instead at variance with, DEFGH's. I must spell out my own position on causation tonight, as a necessary preliminary to my anticipated work over the upcoming weeks.
****
Consider again, then, DEFGH's billiard table. The question on which I dissent from from DEFGH is a question about meanings: what is meant by saying that one event "makes" another occur? Ball X moves, and a click is heard as it makes contact with Ball Y, and then Ball Y is seen to move. On considering meanings, we find (say I, pointing out a fact about meanings overlooked by DEFGH) that language makes logical space for two contrary, even though observationally indistinguishable, scenarios. (a) First, there is the common-sense scenario, that it is the movement of Ball X that makes Ball Y move. (b) Second, there is the scenario on which Ball Y would have moved even if Ball X had remained stationary. On the meaning attaching to "make", "cause", and the like, these are two different, mutually exclusive, suppositions, incapable of being jointly true.
It is like the old Department of Philosophy remark about time. The remark is familiar enough from the seminar room at last week's imagined school, the Tallahassee Swampwater Junior Training College. On considering meanings, we find that language makes logical space for two contrary, and yet observationally indistinguishable, scenarios regarding the past. (a) First, there is the common-sense scenario, on which the cosmos is much more than two seconds old, and on which people's mundane memories and historical records are for the most part accurate. On this scenario, for instance, the memories one might possess of having seen it rain half an hour ago, and of having had breakfast twelve hours ago, are accurate. Further, the thing in this evening's yard, purporting to be a footprint made on damp soil during the rain, really is such a footprint. (b) Second, there is a radically contrary scenario, on which the cosmos is a mere two seconds old, with everyone's purported "memories" and purported "historical records" painfully recent creations-ex-nihilo The meanings attaching to phrases like "half an hour ago", "twelve hours ago", and the like is such that these two scenarios really are distinct - even though (as everyone at the Tallahassee Swampwater Junior Training College rightly insists) no mere observation can establish the one scenario to be true and the other false.
Indeed, in a still more banal way, it is like the two competing Furniture Hypotheses. (a) First, there is the common-sense scenario, on which articles of furniture continue existing when we are not inspecting them. (b) Second, there is a radically contrary scenario, on which tables and chairs and sofas and the like pop in and out of existence - with, e.g., my parlour currently (when I sit at a computer in another room) quite empty, but with its two wicker chairs and mirror-topped coffee table obligingly springing into existence as soon as I peep through the parlour door. The meanings attaching to phrases like "wicker chair" and "mirror-topped coffee table" are such that these two scenarios really are distinct - even though no mere observation can establish the one scenario to be true and the other false.
Analogously, say I, in rebuttal of linguistic analyst DEFGH, language makes logical space for two contrary, and yet observationally indistinguishable, scenarios in the general field of causation. (a) First, there is the common-sense scenario, on which various events in the cosmos make various other events happen. (b) Second, there is a radially contrary scenario, on which for every event E2 supposedly caused by some event E1, E2 would have happened even if E1 had failed to happen. On this second scenario, the whole cosmos is, as it were, "one big coincidence after another".
It is, to be sure, a hard question with what right we believe the former of the Tallahassee Swampwater pair of cosmic-history scenarios while rejecting the contrary scenario, or with what right we believe the common-sense scenario regarding wicker chairs and mirror-topped coffee tables while rejecting the contrary scenario. Likewise, it is a hard question with what right we believe the former of my pair of scenarios regarding the causal connectedness of the cosmos while rejecting the radically contrary scenario. How to answer the hard question I do not know. My contention here is merely that the hard questions have content, and that therefore DEFGH is mistaken in his analysis of "cause", "make", and similar language.
It is, to be sure, a hard question with what right we believe the former of the Tallahassee Swampwater pair of cosmic-history scenarios while rejecting the contrary scenario, or with what right we believe the common-sense scenario regarding wicker chairs and mirror-topped coffee tables while rejecting the contrary scenario. Likewise, it is a hard question with what right we believe the former of my pair of scenarios regarding the causal connectedness of the cosmos while rejecting the radically contrary scenario. How to answer the hard question I do not know. My contention here is merely that the hard questions have content, and that therefore DEFGH is mistaken in his analysis of "cause", "make", and similar language.
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It is a point perhaps not sufficiently stressed by philosophy writers (DEFGH among them, as I dimly recall?) that the considerations raised by DEFGH for causation have formal parallels in the "Problem of Other Minds". Indeed as the position I shall be spelling out here over coming weeks requires a particular view of causation at variance with the DEFGH theory-of-causation, so too does my upcoming exposition require a particular, contrary-to-(the-inner-spirit-of?)-DEFGH, view of "Other Minds". I leave it to the reader, by way of homework, to develop the parallels over the coming week. I hope to start next week, i.e. to start in the upload scheduled for the 4-hour interval UTC=20170606T0001Z/20170606T0401Z, by writing out a specimen solution for this (small, straightforward) assignment.
[This is the end of the current blog posting.]
[This is the end of the current blog posting.]
