I don’t think so. To “justify what is true” seems like an odd phrase, but if you merely mean “demonstrate or show why it is true,” I suppose that’s all right. Whereas, when I justify my belief about X, I am explaining why I claim it to be correct. That can go well or badly without affecting the truth of the statement, or its correspondence (or lack of it) to X. The ordinary usage to refer to here would be, “I was fully justified in believing X, but as it turned out X wasn’t true.” Unless you think that’s incoherent? Some philosophers want “justify” to mean something very technical.
None of this is very important, I just wanted to be sure I hadn’t inadvertently misrepresented the question as being about truth rather than belief.
x=x is not assumed in the way an axiom is assumed; it could not be false. An axiom is a proposal that might be false, but is taken as being true; for example, that only one line parallel to another given line passes through a given point.
To see this, consider the negation of each. ~(x=x) is a contradiction, but assuming more that one line may be parallel to another given line and pass through a given point gives us non-Euclidean geometry.
it’s not uncommon for a group of different ideas hereabouts to be run together. These are, that x=x, Leibniz’s Law, and a few curious Aristotelian metaphysical notions of essence. Folk will slide between these three distinct notions so as to re-cast identity as essence. Better to keep them separated and have folk argue their case clearly.
x=x is a tautology. Leibniz’s Law tells us about the consequences of a=b. Essentialism presumes that a thing is a thing because of some mooted essential properties. These are three different proposals, two of which concern logic, the third, metaphysics. If you want to do the latter, at least recognise that it is not a point of logic.
For the Aristotelian-Thomistic view on this question, see my old post here. That two-part thesis from Laval is the best source I know of on this topic, although I have not studied the topic in great depth.
The better reply is found in @Sam26’s various threads on “On Certainty”. Any doubt rests on a background of certainty, even if in the language in which the doubt is expressed. We are already in a communal structure that takes some things as foundational; one can doubt anything, but not everything.
‘Dogma’, in the historical sense for Christianity, is truth revealed by an infallible source (viz., The Holy Deposit): it is not a belief that is assumed to be true. In modern times, we also use the term ‘dogma’ to mean that latter sense; but you equivocated them. In the OP, I was using ‘dogma’ in the modern sense (of an assumed truth); but you responded about religious dogmas which are not assumed truths.
It would be impossible for a finite faculty to give the totality of reasons for any justification; but it would be technically a valid chain of justification if the finite faculty of reason is traversing an infinite chain of valid reasons. You wouldn’t be able to critique this view to the point of successfully demonstrating an infinite chain of justification leads to unjustified beliefs exactly because you are not challenging the legitimacy of the justification itself: you are, rather, just commenting on the impossibility of a finite faculty traversing the whole infinite chain in time.
Your belief that ‘x=x cannot be false’ is what is in question here: not ‘x=x’. Either your belief here is assumed, justified with an infinite chain of reasons, or bottoms out at a justified reason. Which is it?
I’m sorry, but you aren’t contending with Agrippa’s Trilemma by claiming we cannot absolutely know anything: that’s simply irrelevant. This trilemma is talking about justification which does require absolute certainty.
As explained, x=x is a stipulation. As such it is not the sort of thing that can be false. To suppose it false or to ask it to be justified is to misunderstand the use of “=” or of “x”.
If an axiom is understood as a substantive presumption that might have turned out to be false, then x = x is not an axiom in that sense. Nor is it properly described as an assumption. Rather, it is constitutive of the symbolism itself: once “=” is introduced as the identity relation, and “x” as a variable, x = x is fixed by those conventions. It is not a claim that stands in need of evidence or justification, but part of what makes the symbolism function as it does.
I’m not sure you followed what was said in that post. I am certainly not claiming that “we cannot absolutely know anything”. We do know things. Quite a bit, actually.
But further: are you reading this post now? I don’t see how you could sensibly write a reply to this post without it being true that you read it, at least to some degree. It seems then that in order to reply to my post, you must grant some degree of truth to how things are - that there is a post to which you are replying.
Participation in life requires taking some things as granted. That includes doubt. To doubt something one must take other things as granted.
Thanks, that’s informative, though in fairness I didn’t equivocate them; I was doing my best to unequivocate them by asking into the (possible) difference. Another poster raised the “religious dogma” question, to which you responded.
x = x is a proposition. It would require some sort of clarification. Wikipedia, where I get most of my information from, has an entry on the laws of logic but it’s vague and unclear.