@Cyracuz,
Cyracuz wrote:
Quote:I don't agree with either of you.
Facts are 'states of affairs', situations, happenings.
Factual truth is that truth which describes a state of affairs, and is decided in virtue of 'the facts' by a correspondence theory.
I agree with you in that, all truths are not just 'factual truths' but also include 'logical truths' tautologies...mathematics.
I do not disagree with this.
There are either facts or premises that reveal the truth of statements of the kind you mention here. But premises are not self evident. They have to be chosen, don't they?
There are no facts (situations) which reveal the logical truth of any proposition.
Facts show their presence by existence alone.
That is, situations (states of affairs) exist or not.
Situations do not posses the property of truth or falsity.
Premises that reveal tautologous truth are not self-evident (whatever self-evident could mean).
The premises of logic/mathematics, ie. the axioms and rules of inference, are
tautologies in use.
For example, Modus Ponens is derived from the tautology: (p & (p -> q)) -> q,
..we can state this theorem as..
p
p -> q
therefore,
q.
The choice of (axioms/rules of inference) is not arbitrary, as you say here.
There must be some special 'rules' that decide the suitability of a chosen axiom or rule of inference.
I don't know how axioms or rules of inference are decided, do you?
I understand that J. Lukasiewicz has shown that one primitive operator and one axiom and one rule of inference is all that is required for Propositional Logic.
See: Quine, Methods of Logic, 1982, page 87.