Friday, February 15, 2019

two sentences, the dogma of semantic uniformity & alchemy (or how not to use the method of shouting to close a window)


But those infinities are perhaps not inevitable...
I regard Peirce's hypostatization as name magic,
Wittgenstein's alchemy.
Ian Hacking




Two sentences:
"There are at least three perfect numbers greater than 17."
"There are at least three large cities older than New York."
- from Ian Hacking's Why is there Philosophy of Mathematics at all (Cambridge, 2014, p. 216-17);

From the dogma of semantic uniformity: 
Both sentences are to be analysed in the same way [also from Hacking's Why is there Philosophy of Mathematics, p. 217, but Hacking doesn't subscribe to the dogma, he derides it]. 

What is semantic uniformity, standard semantics, denotational semantics? Something that is at odds with a minimal insightful understanding of mathematics. Something that is at odds with a minimal insightful understanding of "natural languages" (and moreover, who said that languages such as English not to speak Portuguese or Polish and even Hungarian are supposed to be natural?!): 
"Nobody who takes Wittgenstein seriously is likely to agree to denotational [or referential] semantics applied to mathematics," Hacking's Why is there Philosophy of Mathematics, p. 218 [and even more important: "As his philosophy evolved, Wittgenstein absolutely rebelled against the uniformity-of- semantics premise"] [aside on Sir Peter Frederick Strawson: "expressions have meanings, while we use some expressions to refer," "Strawson's lesson, that words do not refer, but that speakers use words to refer, seems to have been largely forgotten," Hacking, p. 219];

Brewing the alchemy [but that against semantic uniformity & in favour of Python Gored Naturalism]: 


- what is 17?
- what is New York?
- what is a perfect number?
- what is a large city?
- what are numbers?
- what are cities?
- what is an object?
- what is an entity?
...
→ there are things, real things (although not all things are like that) which we are acquainted with and with which we don't have causal relations [for example, some mathematical stuff &/or phenomena related to non-locality];

"... it is very much a philosopher's view that the only objects there are are physical or material objects, or regions of space-time, or whatever it is that philosophers tell us... to maintain that there aren't any numbers at all because numbers are abstract and not physical objects seems like a demented way to show respect for physics, which of course everyone admires," George Boolos, as quoted by Hacking, Why is there Philosophy of Mathematics at all.

"We are of divine species," Dedekind as quoted by Hacking, Why is there Philosophy of Mathematics at all.

***More on the dogma of semantic uniformity, or an expatiation on how to accommodate Python Gored Naturalism with Styles of Scientific Reasoning & Pedestrian Reality: "... when facing this possibility of using the notion of styles of thinking to address so diversified kinds of human undertakings, a special point must be considered. Hacking is not saying that in order to point to truth or falsehood every proposition depends on some kind of style of thinking. He “rejects any uniform all-purpose semantics,” and the “idea that a uniform theory of truth or of meaning should apply across the board to an entire language”... In contrast to sentences that would depend on styles of thinking in order to point to truth or falsehood, Hacking refers to “the boring utterances that crop up in almost any language, and which make radical translation relatively easy.” He refers to “propositions that have a sense for almost all human beings,” and to the “boring domains of ‘observations’ that we share with all people as people.” As an example of such an observation, Hacking suggests the proposition “my skin is warm”... It is possible to sustain that even the most apparently obvious propositions are in any case theory-laden. But the conflation of Hacking’s distinction between more and less sophisticated kinds of propositions would imply a very implausible oversimplification of the way real people use language. Under normal viewing conditions, no one would even think much less utter a proposition such as this table is brown, so obvious people take to be its meaning... Someone could perfectly say, however, this chair is made of Brazilian rosewood, and this would make sense exactly for denoting some kind of expertise. We can understand the first sentence as not depending on any specific style whatsoever, and capable of being understood straightforwardly by most people just by the use of the most elementary discursive and perceptual abilities. The second sentence demands the use of other skills, which do not have to be styles of thinking, but only a slightly more elaborated and technical use of elementary discursive and perceptual abilities. Finally, another sentence could be added in order to extend the comparison: the heat which has the refrangibility of the red rays is occasioned by the light of those rays... This latter sentence demands the use of styles of thinking, because it mentions concepts and types of objects (refrangibility, rays) which would not even exist for people unless they are engaged in certain specific and complex practices by which these concepts and objects are made possible... Ultimately, the problem with saying that everything is theory-laden [this is the core of Hacking's criticism of theory-laden armchair infatuation] is that this position undermines elementary distinctions that constitute human discursive practices—elementary distinctions such as between on the one hand saying, telling, giving an account of something, and on the other hand doing something. A person might just say to another that he or she feels cold and wants the window to be closed, but unless one goes over there and effectively interacts with the window the cold will not merely disappear just by saying close the window no matter how loudly you shout. Perhaps the cold goes away if you are Brian de Palma’s Carrie (1976), but what makes Carrie a Carrie either in movies or in real life (supposing there might be such a thing) is that her thought and talk are imbued with a special sui generis power that is faraway more effective than ordinary people’s thought and talk (and even limbs). You would still need distinctions between thinking, saying, and doing in order to make any sense of Carrie. Differences between things such as mental states, sentences, and external objects are all constitutive and germane to what is here called styles of thinking. Without such elementary distinctions, there is not much to be done with a sentence such as the heat which has the refrangibility of the red rays is occasioned by the light of those rays," Alessandro Zir, Luso-Brazilian Encounters of the Sixteenth-Century (Fairleigh Dickinson University Press, 2011, p. 6-7). 

Getting Wolfgang Pauli & the naive Portuguese, as a plus: 


"Generally speaking scientists are no Carries, though there might have been a few registered but far less noxious cases such as Wolfgang Pauli and the Pauli effect," Alessandro Zir, The Sixteenth-Century Corpus of the Portuguese Colonizers of Brazil (Dalhousie, PhD thesis) [the paragraph of this sentence (which refers also to Ludwik Fleck) unfortunately wasn't incorporated in the book Luso-Brazilian Encounters published in 2011 by FDU Press, which doesn't necessarily rank as a fatal blow to Pauli's scholarship supposing it exists].

"Sérgio Buarque de Holanda remarks that the Portuguese were naive realist people. Their realism would come exactly from their credulity, which would be, as he defines it, “a radical gentleness and passivity in face of reality” that “does not deny Nature infinite possibilities” and the supernatural... If this is correct, the Portuguese would be people capable of recognizing the most strange things in nature, without having to deny all the humdrum propositions that make sense to most people, including people having no sensibility whatsoever to apparitions of monsters and the devil. Besides seeing devils and monsters, the Portuguese would not have any difficulty and do not invoke anything spiritual in order to answer a simple question such as are you cold? They also never use the method of shouting in order to close windows," Alessandro Zir, Luso-Brazilian Encounters of the Sixteenth-Century (Fairleigh Dickinson University Press, 2011, p. 6-7).