Knowledge and Certainty

...I will reduce to the essential here and go straight to the point...
...in the example you gave on the context dependent propositions like "I have to hands" and so on, I disagree with W understanding upon the matter not because what he says is n´t true at all but because it is greatly exaggerated its importance on what knowledge actually is...what it means is that if we regard functions and systems of functions instead of "things" which classically portray non dynamic entity´s immediately one can see that such propositions not only make sense but that they are in fact informative upon actual dynamic state of affairs of integrated sets of functions which have an actual algorithmic behaviour going on...that is, "hands" as algorithmic systems, do exist, do have a roll, and do matter !!!

But that is in the context of hands. But what of weather phenomena, wars, economies etc... Your example of hands do not make a difference if there were 1000 people with hands and 1 person having 11 fingers. The percentage of the outlier would be minimal compared to say 1000 people with average incomes and 1 person who was Bill Gates. The outlier percentage would then be tipped in the scale of the 1 person. How we read uncertainty depends on the values themselves and the type of things we are hypothesising.

Knowledge is fallible, certainty is infallible knowledge.

Example:
Hypothesis, theory, and perhaps physical laws may be subject to falsification.
Theorems and axioms may not be subject to falsification.

Axioms are true by definition, but only by definition. They are presuppositions, not findings.

Truth and knowledge are provisional, never infallibles. Beliefs are always presented as certitudes, religious beliefs as eternal verities.

Yes, I agree.

However, do you agree that axioms are necessary true presuppositions, being the basis of formal systems?

There are two definitions of certainty:
-Perfect knowledge that has total security from error, or
-The mental state of being without doubt.

Is it possible satisfy the first definion from a circular premise, or your "findings"?

Example:
All the that I know are mortal =/= If all men are mortal

Yes, axioms are necessarily true--as formal or presupposed truths. They are formal but not empirical truths.
I like your distinction between objective certainty and subjective certainty. But unless we become gods our knowledge will never be perfect and our absence of doubt no more than a feeling.

In my opinion, the problem with formal systems is that they're not formal at all. Systems are in themselves highly complex and far more random than we are often lead to believe.

Do you have an example for an a priori, synthetic predicate?

Can the theorem '2 + 2 = 4' be refuted?

Defining formal systems: Inference of syntatic constructs.

Einstein is suggested to have eleven times glial cell density of the 'average' human, yet his formulations are consistent to all human cognitive faculties.

I have never observed any human interpret a 0=1 universe.

But why KIND of truth is the tautology? Isn't "2+2" just another way of saying "4"?

By the way, doesn't the Buddhist principle "Form equals emptiness and emptiness equals form" sound equivalent to "0=1 and 1=0"?

Very well.

Axioms may not be necessarily true in quantum mechanics, hence there is uncertainty, theoretical constructs, such as wave-particle dualism are now applied.

The universe may in fact be equal to zero, or perhaps nothingness (empty set), which has been argued by quantum mechanical ineterpretations.

I argue that contradictions exist, cosmologically, therefore the theorem '2 + 2 = 4' is deduced to Peano's axioms of natural numbers.

The origin of the universe may be a necessary contradiction, be it ex nihilo, or infinite regress.

Thanks, someday I hope to understand that.

Speak to some people in a psyche ward and make sense of their 'knowledge'.

No but like JL said, it can be changed around to mean the same thing.

Neither have I, most humans I know interpret the universe conceptually not mathematically, but then again, I'm no logician, physicist or cosmologist.