In light of Jesse's critique I sharpened a few requirements for T.
The first question is how do we justify the existence of T? The second question is why is it unique in existing?
The strategy for justifying the existence of T is: a reinterpretation of possibility, and a notion of relational existence.
We do not use the possible-worlds semantics for possibility. A possibility’s is ontology is not given by “possible” worlds semantics. In what ways does a possibility exist? It might be the case that the existential status of a possibility has some third truth-value u instead of t or f. This might be made plausible with an example form quantum mechanics. It is not the case that either x-spin is up or else x-spin is down for some electron in a superposition. We know this because Y-spin up is possible. So the existence of the possibility of y-spin up is not reducible to the worlds in which the x-spin is up and the worlds in which the x-spin is down. This way the possibility of the existence of T is not reducible to those worlds in which it exists together with those worlds in which it does not exist (recall we wanted to avoid the latter).
The second move is to say some things exist in a relative way. The number two exists relative to the number three. T exists relative to its own logical inevitability.
The second question is why would just T exist and not every possible thing? We want to argue that T is the theory most likely to exist out of all mathematical theories.
Brian Tenneson suggests that what exists is the maximal structure P (more later...).
I'm just thinking of what that maximal structure is predicated on in terms of its existence. It boils down to axioms. Axioms can't be justified. Axioms that state something exist don't justify that those somethings exist.
ReplyDeleteHowever, I think it is a reasonable axiom to state that something exists.
If you look at the axioms I invoke in that essay I linked to, they are axioms about this something that exists. They may be harder to accept after the primary assumption that something exists. Yet what's also hard to accept (imo) is not accepting any other axioms. Suppose we only accept one axiom: Something exists, but no further axioms. Then we will never be able to say anything about that something. On the other hand, the axioms we accept could easily lead us down the wrong path towards understanding this elusive yet dramatically immanent Something.
Those axioms dictate the shape of that something. If the axioms are changed, the shape of that something changes.
A TOE could be defined to be a complete description of this Something (ie, reality). If we assume that this something is not predicated on humans to exist (which might require a leap of faith), then it follows that reality is (at least isomorphic to) a mathematical structure.
If one further hypothesizes that that mathematical structure must be maximal in a structural sense, then I think it's possible to prove that it exists from first principles.
Its uniqueness is not something I've thought much about.
Is there any way to get past making an assumption that something exists?
ReplyDeleteWhat constitutes evidence is in a sense arbitrarily defined. You have a definition of existence in mind and I have a definition of "totality" and of "all" in mind when I say that "the totality of all that exists" exists. That would constitute enough evidence in certain contexts that something exists, though it seems circular.
ReplyDeleteThat totality is quite flexible though. If we're in a matrix or imagined by a brain in a vat, for examples, then that totality is quite different *yet there is still that totality*.
Or if we attribute meanings to words, then at least we can say that words exist.
Even if I am dreaming, there is this thing I call "I" which is something that exists.
It depends on what constitutes evidence of existence. And that varies among contexts (mathematical, scientific, perceptual, imagined/imaginary, objects of thought, legal, etc.).
Even if this is an illusion, that would entail that an illusion exists, and would be something.
Yes then even the illusion exists.
ReplyDeleteI am concerned with the question of whether we have to "assume" something exists, or if it might be derivable in some way.
What do you think it might be derivable from, what sort of thing would it be derivable from, that isn't assumed?
ReplyDeleteI tried to make a case for a particular line of reasoning in the posts (starting with the first one on this blog.)
ReplyDeleteFirst, we are to make no assumptions whatever. But then (so the argument goes) the existence of something is a possibility, as we do not assume nothingness is more "logically inevitable". Consider the existence of a possibility of some theory T.
That possibility exists.
Then, one posits that existence is a kind of relational thing, so that a theory might exist in relation to itself.
Combining these, it would be argued that it might be enough for the theory to bootstrap itself into actual existence...
So where did the possibility for the existence of the possibility of such a theory come from? Perhaps one could do something like assigning a third truth value to "the possibility exists that ...". Then argue that this is sufficient for the relational existence of some theory that refers to itself.
I tried to motivate this with a (possible) example from quantum mechanics. Consider an electron in a superposition of x-spin down and x-spin up. Then there exists a possibility that the electron is in the the state y-spin up. But the existence of this possibility is not reducible to possible worlds in which x-spin is up together with possible worlds in which x-spin is down (since the electron can not have simultaneous sharp values for x-spin and y-spin).
...so the existence of a possibility is a new ontological category (maybe?)
So, are you buying any of this? Please let me know.
Then what one wants is the (hopefully unique) theoy that is "most likely" to exist. What makes one theory more likely to exist than another? To start with, one could say that a theory that expresses its own existence is more likely to exist than one that does not... (Actually, I am assuming it is not possible for a theory to prove the theory itself does not exist--if so then proving existence in a theory would be irrelevent to questions of actual existence.) Then maybe there is a hierarchy of theories...
Which theory should it be? The idea is that it mut be the theory that expresses that its own existence is logically inevitable (which I guess gets translated to the theory exists in all possible worlds).
Then, if our universe was that theory, then the existence of our universe would be logically inevitable.
So, what do you think?