Inductive reasoning is extremely important in the real world - it is the kernel of the scientific method, for example - but it never reaches certainty (except where it reduces to trivial deductive reasoning - eg hypothesis = all the balls in an urn are black, evidence = one white ball is taken out)
No, I am not "playing the game". I am participating in rational discussion where everyone (that matters) agrees on the reasoning that is valid.
The fact that you responded without becoming aware of what combinatorial means shows the root of your difficulty. The correct response was to look the word up. This process, executed habitually thousands of times, means all those involved in rational discussion speak the same language, the language of rational discourse about that topic.
Solving chess is a combinatorial problem because it is about a finite system. There are a finite number of positions. There are a finite number of strategies that determine play for one side. The question is whether there exists a strategy for one or other side that wins.
Handwaving is not sufficient to prove this. There are games where very simple reasoning suffices (such as it is easy to show the second player in generalised tictactoe cannot ever have a winning strategy). No-one has demonstrated this is true for chess (and I would bet my life it is not possible).
Good post !
I agree with most of it.
The final statements there can be qualified though -
Its not possible now to solve chess.
Is that proven? Is the fact that it isn't - 'proof' ?
Not exactly. For some - proof is just 'wanting to believe it or push it'.
Anyway - given strong enough hardware/software/programming combined with enough time (there might not be enough time if the global warming deniers and the nukes people and the anti-environmental people get their way - and they might)
then chess might someday be solved.
And @Elroch won't be able to 'bet his life' if he's not around by then ...
(probable) 
Proof is being systematically misrepresented as, more or less, something that the experts understand, interpret and recommend to lesser mortals. A proof has to be so according to criteria used by the experts. You have put yourselves forward as "leaders of the lesser mortals", into which category you place basically everyone, because you have no idea who is capable and who isn't, unless they produce a piece of paper, bought and paid for in one way or another. Therefore everyone has to believe what YOU want them to believe and if they dare to speak, say things that you approve of. The scientists are now the priests and the fact that they are humans with their own intellectual biasses doesn't come into it.
A real proof is a thorough systematic explication that can be reproduced by anyone who so wishes, and is laid out completely and in detail so that it may be examined for imprecise methodology and untenable conclusions.
YOU (and Ponz to a far lesser extent) are the one that uses self-proclaimed superior intelligence and greater understanding of chess, as well as the experience of GMs and top correspondence players, to hand a judgement that "we" all agree on. Dissenters must provide a much stronger proof to the contrary, but your belief is enough to make your opinion fact.