Definition: The mind is the singularity which one identifies as constituting his essence and being.
If one doubts that the mind is of singularity then conceive it being of form, for no variation could occur in thought processes or projected material reality, i.e. mode of thought would be confined to single state. Note that this does not mean the mind is not form entirely, for it could be a form of a higher singularity but this shall not be addressed immediately.
We shall first address whether it is possible to doubt the existence of oneself, since our very mind is a singularity the material realm encompasses individual forms of objects known to the mind. Since these forms are of another singularity our mind must come to know of this singularity first, as it is possible for form to exist independent of singularity, and when our singularity encompasses that of material forms it is safe to say that at the very least our mind is formed from infinitely generalized thoughts of the material realm which we inhabit. Therefore it follows that at the very least the material reality is contained in the singularity of the mind.
However, to the keen thinker this is not the case, for assume it was - and it is well proven from previous statements that we can think of deeper metaphysical ideas and quantities such as natural numbers whose singularity is of a countable infinite. And since we proved this to be immaterial our mind must encompass some immaterial structure. Singularities can be said to be immaterial, and are hence greater than the material world; our mind must be immaterial in essence as to avoid contradiction of basic principles.
Furthermore, it is conceivable to ask from what structure our conception of infinity arisen For to understand infinite singularity from material form one must be acquainted with infinite forms, and this is clearly impossible. Our conception of infinity must have arisen from an immaterial state, boundless of time. Since our mind is singularity in itself, infinity must be embedded in its structure, now we have already passed illusion of material state and hence of time so physical cause and effect are not of essence here. But recalling our generalized definition of cause and effect we ask from what singularity our mind must have begetteth, for in this all our conception of infinity and of course all our very being must have arisen.
We are left with two fundamental paths both leading to drastically different conclusions. One being the acceptance of ones mind as initial substance and singularity, hence encompassing all existence and the highest infinite. Our mind would hence be God. The other being acceptance of state greater than our own, and with an infinity greater than another infinity one cannot stop but must make an infinite sequence of itself. I shall not discuss the implications of doing so now, but rather concentrate on the first proposition.
If we are the initial singularity then our form must be initial singularity and we would come to know of ourselves as substance from which all things arise. Since we must come to know of things before we come to know of ourselves this is not a logical proposition, to elaborate our very mind does not contain crystalline and vivid conceptions of all that does exist and this reality seems to be of a passing dream of which we have no control. The only knowledge it is safe to say that one truly knows a priori would be of infinity.But from this infinity which we have knowledge over we can construct infinite greater than the other, and form an infinite sequence of infinite sets each varying in greater dimension than the other. Notice that for a set to be countable its dimension of infinity remains the same, and for it to be uncountable it would increase by a factor of infinity. So if we made an infinite sequence of infinities known to us it must be of the same order, say countable. But if the infinities contained were of uncountable magnitude then the resulting set would be of uncountable magnitude of uncountable elements. This is assuredly greater than what we would have conceived of. For if not, then we would be simply renaming the elements and devaluing this state of existence by negating their essence. And hence it follows that there is knowledge greater than our own.
Gödel once wrote to an editor:
ReplyDelete‘It is easy to allege very weighty and striking arguments in favor of my views, but a complete
elucidation of the situation turned out to be more difficult than I had anticipated.’
In my opinion the arguments presented by Gödel in favor of platonism does not actually work, but i still think the questions about the status of mathematical reality are really interesting and it is somewhat a shame they got tied up in technicalities, when they should have been examined more thoroughly. For after all what does it mean to say that it is true that 1 +1 = 2? And what does this fact hinge on?
The best counterargument to the platonistic or realistic view is simply that it can’t hinge on some kind of mathematical reality since there exists no such actual thing.
On the other hand the realist persuading one to accept the realist view can simply say “it works”, for after all who needs a formal consistency proof for say Peano arithmetic when you can prove it like this:
1. Obviously all the propositions contained in the axioms are true (given their intended interpretation)
2. The mehod deriving theorems from the axioms are truth-preserving
3. A contradiction is always false
Since you cannot derive a false proposition you cannot derive a contradiction
Since you cannot derive a contradiction the system is consistent
But then again what does it mean to say that it’s true that “For every natural number n, S(n) is a natural number”? Is it just an arbitrary definition like “Emerald city buildings contain green tiles”? There seems to be some kind of difference but what kind?
I am in the process of writing a small essay on Skolem's paradox and my philosophical resolution to them. Hopefully this shall elucidate the difference between aspects of our perception and conception and thus the difference between a logical system we construct and the entirety of mathematics existing as a singularity. After this essay I will elaborate upon my theory of perception in a more abstract and rigorous fashion.
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