All you've managed to do is to throw a tiny fishing net in the ocean in the hopes of catching frickin Cthulhu himself.

For instance when you have something like a car crash, we can model that with things like Finite Element Analysis. Lots of wacky mathematics in the movements right there. But isn't it evident that the mathematics is already "there" and things only make it apparent? For a car to accelerate, a whole range of mathematical values have to change. But not only that, all the formulas which control these values, they stay constant. But the values of the formulae which are indirectly derived from them, they change. All at once, 'instantaneously'. If X changes, then X^2 changes, sin(X) changes, etc. But something does not change, can anybody actually explain what THAT is?

But it always comes down to that age old question - Why are things the way they are, and not anything else? Why is 1=1 and 1+1=2 a truthful and eternal construct, what makes blueness blue and green-ness green?

Over the course of his writings, Leslie develops a Platonic ontology. As a Platonist, Leslie posits a background of logically possible abstract objects. This is the Abstract Background (see Leslie, 1970: secs. 6 & 7; 1978: 182, 191; 1993b: 72-73; 1997). The Indispensability Argument can be used to justify this Background (Colyvan, 2001). The Abstract Background exists with an absolute logical necessity: “an infinite realm of logical possibilities has of course to exist, eternally and unconditionally” (2012: 1).

The Abstract Background is ontologically plentiful. Following traditional Platonism, it is reasonable to say that the Background contains at least three types of abstract objects. The first type includes all Platonic ideals like truth, beauty, and goodness. The second type includes all consistently definable mathematical objects. For example, the Background includes the maximal iterative hierarchy of pure sets. And, if there are mathematical objects that are not sets, then it contains those objects too. The third type of abstract object includes all forms. Forms are represented by statements in logical languages. Among forms there are the propositions (forms with zero open places); the properties (forms with one open place); and the relations (forms with many open places).

[...]

Among the necessarily existing abstract objects, there are objective ideals like truth, beauty, and goodness. Plato said that goodness is creatively effective: an abstract goodness causes This Pattern rather than That Pattern to be instantiated.

Above all, where my mind is blasted is that these things seem to be unchanging objects in a reality which is always in a perpetual state of change. Other than mathematical objects, are there any other kind of "unchangeables" like so? These things appear perfect, whole, complete. Yet clearly looking around I abide in a universe which is only rendered complete, perfect, whole by its process of continous adapting unto itself.

To understand this, it helps to distinguish between two ways of viewing our external physical reality. One is the outside overview of a physicist studying its mathematical structure, like a bird surveying a landscape from high above; the other is the inside view of an observer living in the world described by the structure, like a frog living in the landscape surveyed by the bird.

One issue in relating these two perspectives involves time. A mathematical structure is by definition an abstract, immutable entity existing outside of space and time. If the history of our universe were a movie, the structure would correspond not to a single frame but to the entire DVD. So from the bird’s perspective, trajectories of objects moving in four-dimensional space-time resemble a tangle of spaghetti. Where the frog sees something moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. Where the frog sees the moon orbit the Earth, the bird sees two intertwined spaghetti strands. To the frog, the world is described by Newton’s laws of motion and gravitation. To the bird, the world is the geometry of the pasta.

1 = 1 because someone said 1 represented a single entity in numerology, the first whole number. On another planet the symbol 1 could mean soup, or 4 here on earth. Blue is blue and green is green because people said blue was blue and green was green and that is how it is taught. Just like math. Math unfortunately though a very logical and useful thought construct cannot prove its own existence by its own means. No system I no of can.

So mathematicians use "axioms", things we believe to be true, and that's what all of this is based on. In math they call them "self evident truths", but ultimately they are not and lapse in on each other in funny ways. In fact an axiom is about as logical as saying "you can do this, because it's just how it works".

Want to watch me break math in a fun way?

Back on topic:
Ultimately I find the conclusion incredibly weak. The conclusion that it is logical that mathematical objects are infinite and existed before a mind created them. That is the same as saying a word existed before a mind/body created it.

Φ 42. As to mathematical truths, we should be still less inclined to consider anyone a geometer who had got Euclid’s theorems by heart (auswendig) without knowing the proofs, without, if we may say so by way of contrast, getting them into his head (inwendig). Similarly, if anyone came to know by measuring many right-angled triangles that their sides are related in the way everybody knows, we should regard knowledge so obtained as unsatisfactory. All the same, while proof is essential in the case of mathematical knowledge, it still does not have the significance and nature of being a moment in the result itself; the proof is over when we get the result, and has disappeared. Qua result the theorem is, no doubt, one that is seen to be true. But this eventuality has nothing to do with its content, but only with its relation to the knowing subject. The process of mathematical proof does not belong to the object; it is a function that takes place outside the matter in hand. Thus, the nature of a right-angled triangle does not break itself up into factors in the manner set forth in the mathematical construction which is required to prove the proposition expressing the relation of its parts. The entire process of producing the result is an affair of knowledge which takes its own way of going about it. In philosophical knowledge, too, the way existence, qua existence, comes about (Werden) is different from that whereby the essence or inner nature of the fact comes into being. But philosophical knowledge, for one thing, contains both, while mathematical knowledge sets forth merely the way an existence comes about, i.e. the way the nature of the fact gets to be in the sphere of knowledge as such. For another thing, too, philosophical knowledge unites both these particular movements. The inward rising into being, the process of substance, is an unbroken transition into outwardness, into existence or being for another; and conversely, the coming of existence into being is withdrawal into the inner essence. The movement is the twofold process in which the whole comes to be, and is such that each at the same time posits the other, and each on that account has in it both as its two aspects. Together they make the whole, through their resolving each other, and making themselves into moments of the whole.

Φ 43. In mathematical knowledge the insight required is an external function so far as the subject-matter dealt with is concerned. It follows that the actual fact is thereby altered. The means taken, construction and proof, contain, no doubt, true propositions; but all the same we are bound to say that the content is false. The triangle in the above example is taken to pieces, and its parts made into other figures to which the construction in the triangle gives rise. It is only at the end that we find again reinstated the triangle we are really concerned with; it was lost sight of in the course of the construction, and was present merely in fragments, that belonged to other wholes. Thus we find negativity of content coming in here too, a negativity which would have to be called falsity, just as much as in the case of the movement of the notion where thoughts that are taken to be fixed pass away and disappear.

Φ 44. The real defect of this kind of knowledge, however, affects its process of knowing as much as its material. As to that process, in the first place we do not see any necessity in the construction. The necessity does not arise from the nature of the theorem: it is imposed; and the injunction to draw just these lines, an infinite number of others being equally possible, is blindly acquiesced in, without our knowing anything further, except that, as we fondly believe, this will serve our purpose in producing the proof. Later on this design then comes out too, and is therefore merely external in character, just because it is only after the proof is found that it comes to be known. In the same way, again, the proof takes a direction that begins anywhere we like, without our knowing as yet what relation this beginning has to the result to be brought out. In its course, it takes up certain specific elements and relations and lets others alone, without its being directly obvious what necessity there is in the matter. An external purpose controls this process.

Φ 45. The evidence peculiar to this defective way of knowing – an evidence on the strength of which mathematics plumes itself and proudly struts before philosophy – rests solely on the poverty of its purpose and the defectiveness of its material, and is on that account of a kind that philosophy must scorn to have anything to do with. Its purpose or principle is quantity. This is precisely the relationship that is non-essential, alien to the character of the notion. The process of knowledge goes on, therefore, on the surface, does not affect the concrete fact itself, does not touch its inner nature or Notion, and is hence not a conceptual way of comprehending. The material which provides mathematics with these welcome treasures of truth consists of space and numerical units (das Eins). Space is that kind of existence wherein the concrete notion inscribes the diversity it contains, as in an empty, lifeless element in which its differences likewise subsist in passive, lifeless form. What is concretely actual is not something spatial, such as is treated of in mathematics. With unrealities like the things mathematics takes account of, neither concrete sensuous perception nor philosophy has anything to do. In an unreal element of that sort we find, then, only unreal truth, fixed lifeless propositions. We can call a halt at any of them; the next begins of itself de novo, without the first having led up to the one that follows, and without any necessary connection having in this way arisen from the nature of the subject-matter itself. So, too – and herein consists the formal character of mathematical evidence because of that principle and the element where it applies, knowledge advances along the lines of bare equality, of abstract identity. For what is lifeless, not being self-moved, does not bring about distinction within its essential nature; does not attain to essential opposition or unlikeness; and hence involves no transition of one opposite element into its other, no qualitative, immanent movement, no self-movement, It is quantity, a form of difference that does not touch the essential nature, which alone mathematics deals with. It abstracts from the fact that it is the notion which separates space into its dimensions, and determines the connections between them and in them. It does not consider, for example, the relation of line to surface, and when it compares the diameter of a circle with its circumference, it runs up against their incommensurability, i.e. a relation in terms of the notion, an infinite element, that escapes mathematical determination.

Φ 46. Immanent or so-called pure mathematics, again, does not oppose time qua time to space, as a second subject-matter for consideration. Applied mathematics, no doubt, treats of time, as also of motion, and other concrete things as well; but it picks up from experience synthetic propositions – i.e. statements of their relations, which are determined by their conceptual nature – and merely applies its formulae to those propositions assumed to start with. That the so-called proofs of propositions like that concerning the equilibrium of the lever, the relation of space and time in gravitation, etc., which applied mathematics frequently gives, should be taken and given as proofs, is itself merely a proof of how great the need is for knowledge to have a process of proof, seeing that, even where proof is not to be had, knowledge yet puts a value on the mere semblance of it, and gets thereby a certain sense of satisfaction. A criticism of those proofs would be as instructive as it would be significant, if the criticism could strip mathematics of this artificial finery, and bring out its limitations, and thence show the necessity for another type of knowledge.

As to time, which, it is to be presumed, would, by way of the counterpart to space, constitute the object-matter of the other division of pure mathematics, this is the notion itself in the form of existence. The principle of quantity, of difference which is not determined by the notion, and the principle of equality, of abstract, lifeless unity, are incapable of dealing with that sheer restlessness of life and its absolute and inherent process of differentiation. It is therefore only in an arrested, paralysed form, only in the form of the quantitative unit, that this essentially negative activity becomes the second object-matter of this way of knowing, which, itself an external operation, degrades what is self-moving to the level of mere matter, in order thus to get an indifferent, external, lifeless content.

Every mathematician will tell you their proofs are not "reality" nor are the concepts. They are tools, made in ones mind, to try to explain our surroundings or potential surroundings(at least in an applied perspective). Much like a description of an event.

It is a truth universally acknowledged that almost all mathematicians are Platonists, at least when they are actually doing mathematics rather than philosophizing about it. As Hardy [8, §22] said, “I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply the notes of our observations.”

Was a lot of fun thinking about this . Thanks for the thought inspiration primordium and other posters.

So Cthulhu is the 'IT' we're after...

Great vid...I'm off to dig out my Lovecraft papers and do some re-reads...