Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact (e.g. entropy), rather they are used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof
Formalisms measure regularities of nature. — ucarr
This is how I read your statement.
No they don't. As I wrote: formalisms ARE USED to measure or describe the regularities of nature (e.g. arithmetic IS USED to count apples in a barrel). — 180 Proof
This is your argument supporting your claim I mis-read your claim.
You seem to be implying that
guidelines for best arrangement of signs (syntax) for the sake of effective communication are exclusively generalizations.
You propound your implied characterization by pointing out how your statement presents the critical verb "measurement" in the passive voice, whereas my statement presents it in the active voice. This emphasis on the passive voice is your effort at distancing formalisms from
regularities of nature_matters of concrete fact.
Obviously, by definition of formalism, there is a chain-link of narration linking the meaning of formalisms (axiomatic or otherwise) with how they're applied directly by their agents to things in nature. The degree of elaboration of the components of the narration (and the narrative "distance" accreted) never breaks the chain-link of narration connecting the formalisms to their objects.
sine qua non | ˌsinā ˌkwä ˈnōn, ˌsinē ˌkwä ˈnän |
noun
an essential condition; a thing that is absolutely necessary: grammar and usage are the sine qua non of language teaching and learning.
ORIGIN
Latin, literally ‘(cause) without which not’.
The Apple Dictionary
In my understanding, axiomatic system = sine qua non. If something is essential to a following thing that is the consequence of the first thing, then the first thing refers beyond itself specifically to the following thing.
There appears to be an idea floating through the zeitgeist of the scientific age that generalizations, i.e., abstractions, run parallel to the concrete and specific creations of nature. In my understanding, a generalization is a thinking process that utilizes cognitive compression of multiple applications of the generalization. This cognitive process produces the axiomatic system.
Although the cognitively compressed idea, while occupying its compressed state as an abstraction, seems not to be directly tied to any one of the many objects of its meaning, this in fact is a falsehood.
Claiming formalisms do not refer beyond themselves parallels claiming the distinction between a verb in the active voice and a verb in the passive voice has no connection to the grammar specifying a distinction between the two voices.
Formalisms measure regularities of nature. — ucarr
No they don't. As I wrote: formalisms ARE USED to measure or describe the regularities of nature (e.g. arithmetic IS USED to count apples in a barrel). — 180 Proof
.
Your above quote makes it clear beyond doubt you're using the distinction of the passive voice of the verb from the active voice of the verb to defend your denial of the following:
Formalisms measure regularities of nature. You say (above) regularities of nature are concrete matters of fact. Since formalisms measure regularities of nature, and regularities of nature are concrete matters of fact, formalisms measure concrete matters of fact. — ucarr
So, our debate over formalisms referring to things beyond themselves comes into focus here as a specific argument point you make in which you do the very thing you deny the possibility of doing: basing your defensive argument upon a grammatical formalism: English verbs have both an active and a passive voice, such that, per your argument, the grammatical formalism about the voice distinction,
when it refers to that distinction in application, defends against :
Since formalisms measure regularities of nature, and regularities of nature are concrete matters of fact, formalisms measure concrete matters of fact. — ucarr
The premise behind your defensive argument is the following: formalisms (English verbs have both passive and active voice) do refer to concrete matters of fact, with the purported supporting fact in this instance being: "Because I wrote my claim with the verb in the passive voice, my claim 'formalisms do not refer beyond themselves to concrete matters' stands."
As you assume (in contradiction to what you say), formalisms do refer to things beyond themselves. So, by your own assumption (and debate maneuver), your claim to the contrary is false.