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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?

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    Two points, one is that the people who are saying that we will never find a theory of everything might be wrong, we could be zoning in on a theory of everything (M theory?) and the claim that "we will never find one" is their inductive opinion on the subject, not an objective fact. Two, just because (if) there are an infinite amount of laws doesn't mean we can't have one "rule" that explains them all. Look at an axiom schema, it is one "rule" that explains how to make an infinite list of axioms, we could have infinite laws but still one schema. – Not_Here Aug 13 '17 at 8:03
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    Actually three, it doesn't necessarily mean that we will always run into new questions, some people think we might get to a point where we can no longer answer the actual question. String theory is often criticized for being untestable, because the amount of energy and precision needed is on the planck scale so we may never be able to actually verify any of its predictions. In this case we might actually have a final theory of everything, but we cannot test it to see if it is empirically sound, so the final questions are not infinite, just unanswerable. – Not_Here Aug 13 '17 at 8:06
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    Over the past 35 years or so, professional philosophers of science have moved away from the idea that scientific progress requires approaching a single universal set of natural laws. I think most philosophers of science today are pluralists: a variety of scientific fields study a variety of objects/phenomena, using a variety methods, and producing a variety of different kinds of representations (many of which are not laws and most of which aren't easily reconciled across fields). Stanford Encyclopedia entry here. – Dan Hicks Aug 13 '17 at 11:53
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    Gadamer: truth exceeds method. If we are wise enough to make it to the future, there will be more truth for us there. – Gordon Aug 13 '17 at 13:52
  • It can also mean that nature is not law governed altogether, only some of its aspects are. This is the view of Nancy Cartwright's Dappled World:"When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in their own diverse ways... laws are very special productions of nature, requiring very special arrangements for their generation". – Conifold Aug 13 '17 at 20:14
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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.

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    Thanks. My opinion of Democritus has just gone up. I think Peirce might have agreed that three is the magic number for necessary principles. The question speculates that science can be reduced to a small number of laws, but first principles are the business of metaphysics, By the time we get to physics first principle have been left far behind and we are stuck with a long list of non-reductive laws. . – PeterJ Sep 14 '17 at 15:42
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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.

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