I think that the scientific rather than platonic explanations are more truthful and less “magical” (and less ridiculous honestly).
So try this: We can act in four dimensions of the physical universe, measure in four dimensions of the physical universe, and model four dimensions of the physical universe with mathematics. However, we can use the same techniques to model purely logical relationships, as we do to model physical relationships. It requires quite a bit of skill to keep track of what you’re doing, but when we are modeling very complex things, like waves, magnetism, forces, economic phenomenon, we can perform very complex calculations – not because these spaces exist, but because we can use the techniques we developed in the more simple physical spaces consisting of a small number of dimensions of change, to solve problems with many many, dimensions of change. It’s not that complicated really. It just sounds complicated because of the old fashioned (archaic) language we use to describe what we’re doing.
Understanding advanced mathematics of economics and physics for ordinary people.
The Mengerian revolution, which we call the Marginalist revolution, occurred when the people of the period applied calculus ( the mathematics of “relative motion”) to what had been largely a combination of accounting and algebra.
20th century economics can be seen largely as an attempt to apply the mathematics of relative motion (constant change) from mathematics of constant categories that we use in perfectly constant axiomatic systems, and the relatively constant mathematics of physical systems, to the mathematics of inconstant categories that we find in economics – because things on the market have a multitude of subsequent yet interdependent uses that are determined by ever changing preferences, demands, availability, and shocks.
Physics is a much harder problem than axiomatic mathematics. Economics is a much harder problem than mathematical physics, and before we head down this road (which I have been thinking about a long time) Sentience (the next dimension of complexity) is a much harder problem than economics.
And there have been questions in the 20th century whether mathematics as we understand it can solve the hard problem of economics. But this is, as usual, a problem of misunderstanding the very simple nature of mathematics as the study of constant relations. Most human use of mathematics consists of the study of trivial constant relations such as quantities of objects, physical measurements. Or changes in state over time. Or relative motion in time. And this constitutes the four dimensions we can conceive of when discussing real world physical phenomenon. So in our simplistic view of mathematics, we think in terms of small numbers of causal relations. But, it does not reflect the number of POSSIBLE causal relations. In other words, we change from the position of observing change in state by things humans can observe and act upon, to a causal density higher than humans can observe and act upon, to a causal density such that every act of measurement distorts what humans can observe and act upon, by distorting the causality.
One of our discoveries in mathematical physics, is that as things move along a trajectory, they are affected by high causal density, and change through many different states during that time period. Such that causal density is so high that it is very hard to reduce change in state of many dimensions of constant relations to a trivial value: meaning a measurement or state that we can predict. Instead we fine a range of output constant relations, which we call probabilistic. So that instead of a say, a point as a measurement, we fined a line, or a triangle, or a multi dimensional geometry that the resulting state will fit within.
However, we can, with some work identify what we might call sums or aggregates (which are simple sets of relationships) but what higher mathematicians refer to as patterns, ‘symmetries’ or ‘geometries’. And these patterns refer to a set of constant relations in ‘space’ (on a coordinate system of sorts) that seem to emerge regardless of differences in the causes that produce them.
These patterns, symmetries, or geometries reflect a set of constant relationships that are the product of inconstant causal operations. And when you refer to a ‘number’, a pattern, a symmetry, or a geometry, or what is called a non-euclidian geometry, we are merely talking about the number of dimensions of constant relations we are talking about, and using ‘space’ as the analogy that the human mind is able to grasp.
Unfortunately, mathematics has not ‘reformed’ itself into operational language as have the physical sciences – and remains like the social sciences and philosophy a bastion of archaic language. But we can reduce this archaic language into meaningful operational terms as nothing more than sets of constant relations between measurements, consisting of a dimension per measurement, which we represent as a field (flat), euclidian geometry (possible geometry), or post Euclidian geometry (physically impossible but logically useful) geometry of constant relations.
And more importantly, once we can identify these patterns, symmetries, or geometries that arise from complex causal density consisting of seemingly unrelated causal operations, we have found a constant by which to measure that which is causally dense but consequentially constant.
So think of the current need for reform in economics to refer to and require a transition from the measurement of numeric (trivial) values, to the analysis of (non-trivial) consequent geometries.
These constant states (geometries) constitute the aggregate operations in economies. The unintended but constant consequences of causally dense actions.
Think of it like using fingers to make a shadow puppet. If you put a lot of people together between the light and the shadow, you can form the same pattern in the shadow despite very different combinations of fingers, hands, and arms. But because of the limits of the human anatomy, there are certain patterns more likely to emerge than others.
Now imagine we do that in three dimensions. Now (if you can) four, and so on. At some point we can’t imagine these things. Because we have moved beyond what is possible to that which is only analogous to the possible: a set of constant relations in multiple dimensions.
So economics then can evolve from the study of inputs and outputs without intermediary state which allows prediction, to the study of the consequence of inputs and the range of possible outputs that will likely produce predictability.
in other words, it is possible to define constant relations in economics.
And of course it is possible to define constant relations in sentience.
The same is true for the operations possible by mankind. There are many possible, but there are only so many that produce a condition of natural law: reciprocity.
Like I’ve said. Math isn’t complicated if you undrestand that it’s nothing more than saying “this stone represents one of our sheep”. And in doing so produce a constant relation. all we do is increase the quantity of constant relations we must measure. And from them deduce what we do not know, but is necessary because of those constant relations.
Math is simple. That’s why it works for just about everything: we can define a correspondence with anything.
The Propertarian Institute
The foundations of mathematics are so simple. Seriously. The fact that they even phrase the question as such is hysterical. The reason mathematics is so powerful a tool is precisely because its foundations are so trivial. Like discourse on property in ethics and law it is a word game because no one establishes sufficient limits under which the general term obscures a change in state.
Math very simple. Correspondence (what remains and what does not), Types, operations, grammar, syntax. Generally we use mathematics for the purpose of scale independence. in other words, we remove the property of scale from the set of correspondences. But we might also pass from physical dimensions to logical dimensions (there are only so many possible physical dimensions). So now we leave dimensional correspondence. In mathematics we remove time correspondence by default, and only add it in when we specifically want to make use of it. In sets we remove temporal and causal correspondence … at least in most cases. So we can add and remove many different correspondences, and work only with reciprocal (self referencing) correspondence (constant relations). But there is nothing magic here at all except for the fields (results) that can be produced by these different definitions as we use them to describe the consequences of using different values in different orders.
But if you say “I want to study the parsimony, limits, and full accounting, of this set of types using this set of operations, with the common grammar and syntax” that is pretty much what someone means when they say ‘foundations’. Most of the time. Sometimes they have no clue.
There is nothing much more difficult here in the ‘foundations’ so to speak. What’s hard in mathematics is holding operations, grammar and syntax constant, what happens as we use different correspondences (dimensions), types, and values in combination with others and yet others, to produce these various kinds of patterns that represent phenomenon that we want to describe. And what mathematicians find beautiful is that there is a bizaare set of regularities (that they call symmetries or some variation thereof), that emerge once you becomes skilled in these models, just like some games become predictable if you see a certain pattern.
But really, math is interesting because by describing regular patterns that produce complex phenomenon, we are able to describe things very accurately that we cannot ‘see’ without math to help us find it.
Its seems mystical. It isn’t. Its just the adult version of mommy saying ‘boo’ to the toddler and the joy he gets from the stimulation. There is nothing magical here. it’s creative, and interesting, but it’s just engineering with cheaper tools at lower risk: paper, pencil, and time.
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.
Mar 22, 2017 11:08am
I THINK THIS MIGHT BE HARD FOR YOU BUT ….
(mathematics and truth) (very important) (hot gates pls read)
The answer is quite simple: you just demonstrated proof of operational construction and named that series of actions.
Reality consists of the following actionable and conceivable dimensions:
1 – point, (identity, or correspondence)
2 – line (unit, quantity, set, or scale defined by relation between points)
3 – area (defined by constant relations)
4 – geometry (existence, defied by existentially possible spatial relations)
5 – change (time (memory), defined by state relations)
6 – pure, constant, relations. (forces (ideas))
7 – externality (lie groups etc) (external consequences of constant relations)
8 – reality (or totality) (full causal density)
We can speak in descriptions including (at least):
1 – operational (true) names
2 – mathematics (ratios)
3 – logic (sets)
4 – physics (operations)
5 – Law (reciprocity)
6 – History (memory)
7 – Literature (allegory (possible))
8 – Literature of pure relations ( impossible )
8a – Mythology (supernormal allegory)
8b – Moral Literature (philosophy – super rational allegory)
8c – Pseudoscientific Literature (super-scientific / pseudoscience literature)
8c – Religious Literature (conflationary super natural allegory)
8d – Occult Literature (post -rational experiential allegory )
We can testify to the truth of our speech only when we have performed due diligence to remove:
1 – ignorance,
2 – error,
3 – bias,
4 – wishful thinking,
5 – suggestion,
6 – obscurantism,
7 – fictionalism, and
8 – deceit.
So of the tests:
1 – categorical consistency (equivalent of point)
2 – internal consistency (equivalent of line)
3 – external correspondence (equivalent shape/object)
4 – operational possibility (what you just described) (equivalent of change [operations])
6 – limits, parsimony, and full accounting. (equivalent of proof)
You have demonstrated test number 4. Only.
Those operations existed or can exist. That you engaged in conflation (or deception) because you have given allegorical (fictional) names to a sequence of operations does not. Because you reintroduced falsehood by analogy.
You can imagine a something with the properties of a unicorn, you can speak of the same, draw the same, sculpt the same … but until you can breed one (and even then we must question), and we can test it, the unicorn does not exist ***in any condition that we can test in all dimensions necessary for you to testify it exists***
This is just one of the differences between TRUTH (dimensional consistency (constant relations)), and some subset of the properties of reality (DIMENSIONAL CONSISTENCY).
Mathematics allows us to describe constant relations between constant categories (correspondence) by means of self-reference we call ‘ratios’ to some constant unit (one). The more deterministic (constant) the relations the more descriptive mathematics, the higher causal density that influences changes in state, the more information and calculation is necessary for the description of candidate consequences, and eventually we must move from the description of end states to the description of intermediary states that because of causal density place limits on the ranges of possible end states.
In other words, in oder to construct theories (descriptions) of general rules of constant relations, we SUBTRACT properties of reality from our descriptions until we include nothing but identity(category), quantity, and ratio, and constrain ourselves to operations that maintain the ratios between the subject (identity).
Mathematics has evolved but retained (since the greeks at least) the ‘magical’ (fictional, supernormal fiction, we call platonism) as a means of obscuring a mathematician’s lack of understanding of just why ‘this magic works’. When in reality, mathematics is trivially simple, because it rests on nothing more than correspondence (identity), quantity, ratio, and operations that maintain those ratios, and incrementally adding or removing dimensions, to describe relations across the spectrum between points(identities, objects, categories) and pure relations at scales we do not yet possess the instrumentation or memory or ability to calculate at such vast scales – except through intermediary phenomenon.
As such, operationally speaking, the discipline of mathematics consists (Truthfully) of the science (theories of), general rules of constant relations at scale independence, in arbitrarily selected dimensions. In other words. Mathematics consists of the study of measurement.
it is understandable why we do not grasp the first principles of the universe – they are unobservable directly except at great cost. It is not understandable why we do not grasp the first principles of mathematics: because measurement is a very simple thing, and dimensions are very simple things.
That mathematicians still speak in fictional language, just as do theists and just as do the majority of philosophers (pseudo science, pseudo-rationalism, pseudo-mythology) is merely evidence of retention of ancient fictionalism (platonism). And the fact that we must have these discussions demonstrates the equivalent of faith in platonic models, is equal to faith in theological models – merely lacking the anthropomorphism.
Ergo, infinities are a fictionalism. Multiple infinities are a fictionalism. Both fictionalism describe conditions where time and actions (operations) have been removed as is common in the discipline of measurement (mathematics). Operationally, numbers (operationally constructed positional names, must be existentially produced as are movements of gears attached in ratio. And as such certain sets of numbers (outputs) are produced faster (like seconds or minutes vs hours) than other sets of numbers (outputs), and the reverse: some slower. But we simply ignore this fact and instead of saying no matter what limits we apply, the size of the current set of x will always be larger than the current set of y, we say the infinities are of different sizes? No. the intermediary sets produce members at different rates, and the term ‘infinity’ merely refers to ‘unknown limit’ or ‘limit that must be supplies by correspondence with reality upon application.
Practice math as science, or practice it as supernatural religion. I can make correspondent statements referring to god, I can make correspondent statements referring to ‘infinities’ or any other form of mathematical platonism, but in the end, when I do that, I merely make excuses for my inability to testify to causality: TRUTH.
Ergo, like I said, I am pretty well versed in the philosophy of mathematics, and I am perhaps most versed in the philosophy of science of anyone living. And I am pretty confident that mathematicians are no different from scripturalists and platonists: using arcane language and internal consistency to justify a failure to grasp causality: that the only reason internal consistency correspondence to reality is because at least in the physics of the universe if not the actions of man, determinism reigns. In other words, mathematicians in most senses have no idea why what they do, allows them to do what they do.
And at least physicists admit it.
And lawyers before juries have no choice.
Our “Objectives” (intentions) are irrelevant in court. You do not have any right, permission, or ability to determine harm to others. Others determine if you have caused harm to them. And the jury, the judge, and the law are used to determine if in fact your words and deeds cause harm to others. As a prosecutor in court, trying you on whether you speak truthfully, you are guilty of making excuses for the harm you have done by false representation of the discipline of measurement. 😉 you might claim no harm, but then the opposition would say that your retention of fictionalism imposes a cost on every student which is multiplied by every possible action that they could have taken involving any judgement requiring measurement. If we can prevent other kinds of fraud in the market for goods, services, and testimony, why cannot we fill the gap, and prevent fraud in the market for information? 😉
In other words, in crime, neither your intentions nor your opinion matter. Defacto, you’re imposing costs on the commons.
The question is only whether the outcome of your actions imposes costs. Once that question is settled, you are liable for restitution regardless of intent.
Now, since the cost of the practice of supernaturalism, super-normalism (platonism), pseudo-rationalism, and pseudoscience, are only substantial when in the commons, whatever you think in your head is your choice. However once yo speak it in public you are just as liable for that damage as you are liable for yelling fire in the theater. There is no fire in the theatre, and there is no imaginary existence.
Infinity is the name we give to unknown limits that must be provided by context.
YES, MATHEMATICS IS TAUGHT AS FICTION: “LET US TEACH EVERYONE A VERY INTERESTING AND IMPORTANT LESSON VIA MR JOHN BLACK.”
—“Mathematical fictionalism is more tenable than mathematical platonism.”—Melvin Davila Martinez
“There are no such things as abstract objects?
Prove it.” — John Black
The verb ‘to-be’ = ‘exists’. (is, are, was, were, be, being, been) It is the most ‘irregular’ verb in the english language. Irregular means ‘fungible’. In other words, it is the least precise verb in the english language. It allows us to ‘cheat’, and save both thinking and words, and to claim authority rather than subjectivity, by circumventing the process of constructing the existence of the referent.
The cat is black = i see a cat, and the cat looks like the color black to me.
The first is both a verbal shortcut, a testimony of one’s honesty, and an appeal to authority by a definitive statement, which can only POSSIBLY be a subjective statement.
The same applies to the use of the word ‘number’ which is an irregular NOUN – that like the most irregular VERB ‘to be’, allows us to ‘cheat’, and save thinking and words, by circumventing the process of constructing the existence of the referent. the natural numbers refer to a set of names for quantities of anything we choose to categorize.
But everything else we call a ‘number’ is, like the verb ‘to-be’ a pretense, since a number, including fractional representation using numbers, refers to the name of a quantity, whereas all other referents are the result of operations: FUNCTIONS, not numbers.
So let us scientifically test this statement:
“There are no such things as abstract objects.”
…. which translates to ….
“There [exist] no such [referents] as [non-existent] [referents]”
To which the answer is:
“There exist constant relations between constant relations.”
which is a tautology. In other words, its meaningless.
Why? Because what is a measurement? A measurement is a unitary quantity of constant relations. And what is a number? the name of a constant relation of quantities.
Do constant relations exist? Yes, we call this ‘determinism’ in the scientific ( not philosophical) sense: that the universe operates by a set of constant relations we call ‘laws’ that we must only discover. If the universe did not operate by constant relations thought would be impossible, since that is the function of memory: to identify constant relations, and test inconstant relations.
So do constant relations exist? Yes. We name those constant relations by the use of names that we call numbers, and functions that we reduce to the symbolic equivalent of numbers.
But all that ‘exists’ are constant relations. Mathematics currently consists of a large set of verbal myths and parables by which we reduce complex sequences of consistent operations upon a unitary measure of constant relations.
In other words, when we say Christianity or Aristotelianism, we give a name to a complex set of undefined operations. When we speak in much of mathematical language we do the same.
Why? Because the human mind uses mathematics as a symbolic store of constant relations beyond which our perceptions are able to discern, and beyond which our short term memories are capable of holding. So we speak in the language of manipulating the symbols and begin to treat those symbols as existential rather than as names for the set of constant relations and constant operations that they refer to.
ANY TESTIMONIAL STATEMENT (ANY STATEMENT IN WHICH YOU CLAIM TO CONSTRUCT A TRUTH PROPOSITION) THAT CONTAINS THE VERB TO BE, MUST BE TESTED AS A POTENTIAL ACT OF FRAUD, BECAUSE EACH SUCH STATEMENT IS A FRAUD CANDIDATE, SINCE ANY TESTIMONIAL STATEMENT CAN BE STATED WITHOUT THE VERB TO BE WITH GREATER DEFENSE AGAINST CONFLATION, SUBSTITUTION, SUGGESTION, AND DECEIT.
Almost all philosophical questions that we normally find irresolvable are dependent upon the use of the verb to be to create appeal to authority through the use of confusion and incommensurability by acts of polymorphism by the use of conflation, substitution, suggestion, loading (moral distraction) and deceit (counter-factual loading).
In other words MATHEMATICAL FICTIONALISM truthfully and scientifically describes the ‘story’ or ‘mythology’ of mathematics. When we speak in the names of heroes, and refer to myths and legends, and use these parables as methods of decidability in the face of a kaleidic universe, we are ‘calculating’ using symbolic referents and operations. Just as when we claim that the square root of two exists, when it cannot, since we refer to a constant relation that cannot be reduced to a constant relation without a context to provide the information supplied by context: what mathematicians call ‘limits’ or ‘decidability’ or ‘the axiom of choice’.
Mathematics is to Programming, what Rationalism is to Empiricism: a smaller set of properties. Mathematics functions as a language for the expression of constant relations greater than the constant relations we can express by other means.
Mathematics is spoken in terms of mythology, but computer science is not. This is what separates the imaginary and mythological, from the existential, and computable.
Programming tests mathematics. Because functions exist, because operations exist. Everything else refers to some complex set of constant relations we give a name to: a function: a sequence of existentially possible operations.
QUOD ERAT DEMONSTRANDUM
Thus endeth the lesson.
The Propertarian Institute