How do we call a collection of axioms radical sceptic would have to accept as being true in order for a statement to be true?

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Let's suppose that I want to write or say a statement to which I want to add meaning. Also let's suppose that this statement is only true if we say so or we deduce it from axioms. Also let's suppose that no implicit premises count in a deduction. Everything has to be explicit. Now.. how do we call a collection of axioms necessary for a statement which has a meaning to be true? In the real life people say things without explicitly saying on which grounds they argue a particular statement. What part of philosophy deals with the thinking about what is necessary to be true in order for a particular statement with added meaning to be true?

To give a example: if I say that 2+2=4, I would have to write explicitly everything that I suppose is true in order for this statement to be true. I would have to say for example that I suppose that it is true that I can be true and that knowledge is possible. In plain english, I want to have absolutely no room for a speculation in this statement. It seems to me that even in mathematics we don't explicitly say everything that we have to assume to be true in order for a statement to be true.

TKN

Posted 2019-09-20T08:29:34.197

Reputation: 355

Not clear... 2+2=4 is a theorem of arithmetic. It is proved form the axioms of arithmetic. What is needed in order to prove it ? The said axiom and the rules of deductive logic.

– Mauro ALLEGRANZA – 2019-09-20T08:54:45.283

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We do not say everything because we can not, it does not depend only on what can be said. Even if we specify axioms and rules of arithmetic in excruciating detail it would still not be enough because we also need the ability to follow those rules. And even if we prescribe the rules for such an ability, we'd need another ability to follow those. This is known as Ryle's regress. Wittgenstein's rule-following paradox is closely related.

– Conifold – 2019-09-20T09:45:14.523

No answers