Pattern-chaser wrote: ↑August 7th, 2022, 12:14 pm
GE Morton wrote: ↑August 5th, 2022, 12:28 pm
The axioms and postulates of every theory are unjustified assumptions --- which means that no justification for them is given
within the theory; they're accepted as true
a priori. But that doesn't mean they
have no justification.
Pattern-chaser wrote: ↑August 6th, 2022, 7:12 am
Er, yes, it does. If we had a justification for these assertions, we would use it. But, thanks to Herr Gödel, we know that any logical system is — must be — incomplete, and these assertions simply reflect that. Nevertheless, they remain unjustified.
GE Morton wrote: ↑August 6th, 2022, 12:18 pm
Sorry, but that leads to a
reductio ad absurdum, namely, an infinite regress. Hence no argument could ever reach a conclusion.
All theories begin from some premises assumed to be true and self-evident.
No, all theories begin from premises assumed to be true. But they are not considered or declared to be "self-evident".
We're just quibbling here about the use of that phrase. Consul (above) posted an SEP link reviewing debates in the philosophy literature as to its meaning. The author quote Lockes's definition: "Locke says that a self-evident proposition is one that 'carries its own light and evidence with it, and needs no other proof: he that understands the terms, assents to it for its own sake.'” Others have adopted that definition, but the author also cites objections, which hold that mere understanding of a proposition surely can't be evidence of its truth, or provide a reason for believing it.
The only propositions which "carry . . . evidence within it" of their truth are
tautologies, e.g., "All bachelors are unmarried." Someone who disputes this needs to explain just how any other sort of evidence is "carried" within a proposition.
They are honestly declared as "axioms" or as "assumptions", making it clear that these are things we believe to be true, but which might not actually be true, because we have no conclusive proof to offer or present.
Yes, the axioms of a theory might not have been true. But the evidence that they are true is so pervasive and consistent that there is no room for doubt about it --- we simply
cannot doubt them (just try to doubt that the sun rises in the East and sets in the West --- and don't confuse doubting that it does with imagining it being otherwise).
The term "self-evident" is unfortunate, because the words themselves suggest something like Locke's definition. But that is not the understanding most theoreticians have in mind when they choose the axioms for their theories. What they mean by it is "obvious, beyond reasonable doubt, compelled by the available evidence."
Correct. Perhaps this is because there is no "necessity" for "self-evident" premises in theories or arguments?
Of course there is. Unless the theory proceeds from premises whose truth is not in question there can be no confidence in the conclusion.
GE Morton wrote: ↑August 5th, 2022, 12:28 pm
Common experience doesn't justify "The sun rises in the East and sets in the West"? What, in your view, WOULD justify it?
If it is offered as a certain conclusion, then nothing could justify it.
Huh? Observations and experience can't justify synthetic propositions? We can never be sure that any of them are true or false?
Yes, I'm as aware of such definitions as you are. I assert that such definitions continue a long-standing misunderstanding. They might be OK in everyday parlance/life, but such things are unacceptable in science or in philosophy.
Ah, but they're ubiquitous in both science and philosophy. For example, one axiom of General Relativity is the Equivalence Principle:
https://www.britannica.com/science/equi ... -principle
That principle certainly can be imagined not to hold, but the evidence that it does is beyond doubt. So it's taken as self-evident, in the dictionary sense.