Defenders of infinity are simply saying that mathematical platonism is a useful mental shortcut to provide decidability for you in the absence of understanding, the way religion is a useful mental shortcut for decidability for others in the absence of understanding.
Authority (decidability) in platonic mathematics and authority (decidability) in religion are provided by the same error: empty verbalisms.
If mathematical decidability is constrained to correspondence with reality, we do not need the concept of limits because limits are determined by that which we measure.
Yet as we use mathematics to create general theories of scale independence, we intentionally abandon scale dependence substituting arbitrarily definable *limits*. By applying mathematics of general rules under scale independence to some real world phenomenon, we merely substitute limit for precision necessary to achieve our ends (marginal indifference).
As we add the dimension of movement to our measurements we add time to our general rules, which like distance we define as a constant. (though it is not, per relativity).
As the universe consists entirely of curves, yet our deduction from measurements requires lines, and angles (geometry) with which we perform measurements of curves by the measurement of very small lines, we must define limits at which the marginal difference in the application of mathematics to a real world problem is below the margin of error in the prediction of any movement. (where we have reached the *limit* of the measurement necessary for correspondence.
While measurement requires both time, and a sequence of operations, and while mathematical deduction requires time and a sequence of operations, cantor removed time and a sequence of operations. So instead of operationally creating *positional names* (numbers) at different RATES, as do gears, and therefore creating sets larger or smaller than one another at different rates, he said, platonically that they created different ‘infinities’. Despite the fact that no infinity is existentially possible, just that at scale independence we use infinity to mean *limited only by context of correspondence: quantity, operations, and time.
This is just like using superman as an analogy for scale independence in the measurement of man. Literally, that’s all it is: supernaturalism.
All mathematical statements must be constructable (operationally possible), just as all mathematical assertions must be logically deducible. (and you can see this in proof tools being developed in mathematics).
Mathematics always was, and always will be, and only can be, the science of creating general rules of MEASUREMENT at scale independence. And the fact that math still, like logic was in the late 19th and all of the 20th century, lost in platonism is equivalent to government still being lost in religion.
The only reason math is challenging is that it is not taught to people *truthfully*, but platonically.
Otherwise the basis of math is very simple: this pebble corresponds to any constant category we can imagine, and each positional name we give to each additional pebble represents a ratio of the initial unit of measure: a pebble, and as such corresponds to reality.
Hence why I consider mathematical platonism, philosophical platonism, and supernatural religion crimes against humanity: the manufacture of ignorance in the masses in order to create privileged priesthoods of the few through mere obscurantist language.
Another authoritarian lie. Another priesthood.
Yet I understand. I understand that heavy investment in comforting shortcuts is indeed an investment and that the cost of relearning to speak truthfully is just as painful for mathematicians, as it is for philosophers, and theologists.
(Ps: oddly, my sister is sitting next to me working on common core standards designed to improve math skills)
=== Addendum by Frank ===
by Propertarian Frank
The exact same argument we use to stop believing in ghosts should have prevented Cantor’s infinities. But it didn’t.
(1) People familiar with Diagonal Argument and understand it is epistemic cancer.
(2) People familiar with advanced Platonist trickery like the Diagonal Argument and buy it even though they avoid falling for Platonism in other domains.
(3) People that are unfamiliar with advanced Platonist trickery, but intuitively understand truth is ultimately about actionable reality.
(4) People that are unfamiliar with advanced Platonist trickery, and believe in primitive forms of Platonism (theism, dualism).
Type (1) people will get testimonialism immediately.
Type (2) people could be persuaded. Trick is to prompt them to explain what differentiates the type of reasoning Cantor uses from the type of reasoning that tries to determine how many angels can dance simultaneously on the head of a pin. Induce cognitive dissonance by making explicit that wishful thinking is only possible when you use non-constructed names.
Type (3) people lack the information necessary to judge constructionism in philosophy of mathematics. Understanding Testimonialism requires a bare minimum of familiarity with philosophy of science. Absolute key concept is ‘decidability’. How does a type (3) person ascertain that he ‘gets’ operationalism? Through demonstration in something like the ‘line exercise’ from the other day. So, unfortunately, this type of person will miss the profundity and importance of operationalism. (Seeing the importance of operationalism was the reason I kept reading your corpus). We need to see concrete instances of a method failing so that we can eventually incorporate the solution to that failure into our epistemological method. Without the concretes, it’s impossible. Unfortunately, adding lessons on the Diagonal Argument, operationalism in psychology, instrumentalism and measurement in physics etc, would not be feasible methods for familiarizing the uninitiated. In other words, if you haven’t spent considerable time thinking about philosophy of science already, courses in Propertarianism will not convince you, because you lack the means of judging them.
Type (4) people are the hardest to persuade. You have to show them a domain in which Idealism fails, and prompt them to think about why they think it doesn’t fail in this other domain. If you can’t crush their Platonist belief in a certain domain (due to emotional blocks for instance), they can’t consistently apply operationalism. The fact that they haven’t already given up on simpler forms of Platonism indicates that they may have psychological blocks. Ergo, I think this type of person is the least amenable to learn Testimonialism through video lectures.