A lot say that with every next step we make in science comes always a set of new questions. I think this means there's an infinite number of questions we can ask about the natural laws. And that means that nature is not governed by a limited set of laws we could write down and call the final theory.
So does it mean that if the new-questions is correct, does it mean there's an infinite number of natural laws that we can never capture all? Am I missing something?
You might find what Aristotle said about this question in his Physics over two millenia ago; he begins first by identifying contraries as principles if nature (ie as laws of nature), in Greek arche:
(188a19 - 189a10)
All thinkers then agree in making the contraries principles; both those who describe the All as one and unmoved (for even Parmenides treats hold and cold as principles under the name earth and fire) and those who use the rare and dense. The same is true of Democritus also, of his plenum and void; both of which he says exist, the one as being, and the other as non-being. Again, he speaks of differences of position, shape and order; and these are genera, of which the species are contraries; of position, above and below, before and behind; of shape, angular and angle-less, roundness and straightness.
He describes principles discursively as:
for first principles must not be derived from each other, nor from anything else; while everything must be derived from them.
And then
but these condition are fulfilled by the primary contraries; which are not derived from anything because they are primary; nor from each other because they are contraries.
His presupposes that
in nature, nothing acts on or is acted upon by any other thing at random, nor can anything come from anything else
And so
Eveything that comes to be by a natural process is either a contrary or a product of contraries.
He then asks, as you do:
(188a11-189b19)
the next question is whether the principles are two, three or more in number.
And
one they cannot be, for there cannot be one contrary
He offers no argument for, at least at this point of the text; and then
nor can they be in-numerable [ie infinite in number] because if so Being would be unknowable.
Hence he presupposes that Being must be of such a nature that it must be knowable; and also
granted then, that there is a finite number, it is plausible to suppose them more than two in number; for it is difficult to see how density should be of such a nature as to act on rarity, or rarity on density; the same is true of any other contrary ... both act on a third thing different from either.
Interestingly he clarifies the notion of a principle further in terms of his logic
what is a principle ought not to be the predicate of any subject; if it were, there would be a principle of the supposed principle; for the subject is principle, and prior, presumably, to anything predicated of it.
He then adds
All, however agree in this, that they differentiate their one by means of contraries such as density and rarity, or more and less; which may be generalised, as already been said, into excess and defect; indeed, this doctrine (that the one and excess and defect are the principle of things) would appear to be of old standing ... for the early thinkers made the two the active principle, and the one the passive; whereas some of the more recent maintain the reverse.
(Interestingly he does not say how old this theory is; after all, in his time, Parmenides was around two generations ago, so not much more than a century from his writing this); so he concludes:
to suppose then that the elements are three in number would seem, from these and similar considerations, a plausible view ... it is clear then that the number of elements is neither one nor more than two or three; but whether it is two or three is, as I have said, a question of considerable difficulty.
This is asked in a very ambiguous manner, for one there are many possible definitions of natural law you could formulate each with subtle differences that can affect the final picture(also depending on our initial assumptions we could end up begging the question).
I'll answer this question as best as I can: we do not know the answer, and it seems unlikely we ever will and unlikely if we can even know whether we can know. I can be wrong though, Im not ascertaining this as truth (such would be a fun little contradiction :) ).
Suppose there is a final theory T that is couched in a logic L_1. But in order to say T is valid we have to justify that the logical system L_1 holds for T but for that justification we would need another logical system that justifies it with elements not in L_1( to avoid circular reasoning). Call this logical system L_2. But then L_2 needs to be justified by L_3 without circularity. And L_3 needs L_4 and so on Ad Infinitum. So it seems impossible to say if we can know whether T is the final theory.
Notice T still might be true and have finite number of laws. Also these logics do not need to be formal rigorous logics.
Also there are problems that we have been "stuck on" virtually since they were asked:
Hume's Problem of Induction being one. If we say "who cares, it just works" then we're implicitly using induction to justify induction. It seems safe to say that any non-inductive logic would be deductive. But if there is a deductive logic that gives us induction then induction is an extensive of dedictive logic which has its own problems and paradoxes. And since induction is absolutely crucial to deriving laws it seems we cannot come to any certain method to justify them.
So it seems there would be infinite questions that come about but they could be the result of infinite number of intrepretations of possibly the same ulti.ate reality which we are unable to see as connected due to the issues listed above.
