What is truth?

I think what Godel showed is that there are always going to be truths out there that our current mathematical models don't cover so that the future is yet unwritten. For example, the inside of a black hole isn't described by maths since it simply breaks down and contradicts itself which, I think, is nature's way of telling us how dumb we are.

They would eventually and maybe that's what WILL happen in the end. 

Well, I know Roger Penrise thinks there's more to mathematics than computability in the sense that you need consciousness to understand what is going on, rather than a rule-based model that is limited by it's own parameters.In fact, we may need a new physics in order to account for the deeper mysteries of mathematics which incorporates consciousness.

His contention is that computers, no matter how powerful and fast, still do not understand what they are processing.

I don't know the answer, but I have one perspective.

There are words which I think map to multiple concepts called, and not all of them are necessarily related at a deeper level. These are called "pluralistic".

As an example, this is a recent pluralistic view of information. I think that "truth" may be a similar. For example:

• There is an inner/subjective/conscious experience which is always real or true, even if it is an illusion (the illusion is real, just as a dream is). We experience the truth, in some sense.
• There is also truth which requires a verification method and is inter-subjective, but usually verification does not hold (Popper says this, for example, with the concept of falsifiability). Even science itself evolves, e.g. the mechanistic views or so-called clock-universe isn't our truth anymore. According Kuhn and other philosophers, science evolve through changes in paradigms. (PS: I think Popper did define truth as "Correspondence of a statement with the facts", in this interview, taken from Tarski, at some point.)
• There is also the truth of a formal system, which you mentioned.
• There is also truth in the sense that it must be computable.
• There is also a sense of truth of any system which survives for enough time understands the environment in which it lives, and has then some truth about how the world works. And we also see their limitations. And there may be such limitations for the kinds of truths humans can find. Some truths that may be reachable only by other natural or artificial cognitive systems. This is related to Noam Chomsky and The New Mysterianism, but goes back to a view of the world by Newton and others.
• There is also, the notion of truth by William James' pragmatism, along the lines of "that which is useful". A similar but somewhat opposing view is encapsulated in "All models are wrong, but some are useful".

Overall, I get the sense that there are different concepts of truth, all of them meaningful. (But speaking of Truth, I may be wrong.)

lostmyway said:

my question is, how can we know that mathematics really describes reality and that reality may simply be a construct that human beings invent on order to stay alive?

I remember asking this question when I started my degree in Applied Physics and the answer is that any rules that we use in mathematics must be rigorously tested and proven using the basic laws of mathematics.

Physics however is all about observing and working out what rules apply to a system (eg gravity) and then testing these laws repeatedly and being open to updating them when new evidence comes to light through research.

Typically changes are a refinement of the rules that make it more comprehensive or allows for additional factors that the original rule did not incorporate, but this typically leads to a lot of peer reviewing and the scientific community really puting it through its paces to make sure it really is the right thing to use until a better model comes along.

Scientific Method is the backbone to all of this and it is as rigorous a system as we have been able to develop to avoid subjective views from taking hold. It is this that is the most effective shield against such foolishness as flat earth theory.

Of course some like to invoke claims like "god made it this way to test you" when it comes to things like the fossil record proving that dinosaurs existed but their claims cannot be proven by definition. Terribly convenient that.

So in essence any system worth its salt allows for revision and adaptation as new proof emerges and even then it is only valid until the next revision and the next etc.

There are times when I wonder if the Gods, gave us these questions as a sort of soother or dummy, something to keep us occupied whilst they go and have some Gods time?

I've often wondered if we all woke up tomorrow and had forgotten all about Newtonian maths and physics would all our bridges and things fall down.