It’s not clear to me how your reply is relevant. But by your own criteria, in what sense do these areas consist of ‘knowledge’ if there are no obvious axioms?
In the sense that they are taught in classrooms, cited in encyclopedias and so on. Take empirical knowledge. It may be based on vague intuitions, but it isn’t based on formal axioms.
Do you mean knowledge in a sense that I would accept?
I have no idea what you would accept.
It sure seems to me that, in practice, every area of knowledge simply accepts many claims as axioms because it’s impossible to reason at all without assuming something. For example, every area assumes that people exist, that the relevant object(s) of study exist, that people can gather evidence somehow of the objects of study, that the universe is not arbitrary and capricious ‘magic’, etc.
I have been drawing a distinction between necessary presuppositions (“intuitions”) and arbitrary premises (“axioms). The wholesale embrace of derivation from arbitrary axioms as fully-fledged truth leads to the undesirable outcome of an epistemological explosion..every proposition becomes proveable and disproveable.
Trying to manage without even the most basic intuition is desirable, but, as far as we can tell, impossible.
However, the ineradicability of some intuitions doesn’t make the wholesale embrace of arbitrary axioms a good idea! If we cannot manage without intuitions, we can avoid the worst of the problems by minimising their use, particularly in real-world contexts, but that is damage containment, not a full solution,
What I’ve yet to glean from your comments is how ‘absolute truth’ is any different than ‘green sound’. They’re both short phrases but neither seems to refer to anything.
If “depends on axioms” has a meaning, “does not depend on axioms” has a meaning. Whether truth indpendent of axioms is obtainable is another question.
hat exactly causes the ‘world to be turned upside down’ for these people? That, because they think all truth is ‘absolute truth’ and that they’re now convinced that the latter doesn’t exist that therefore nothing is true? If they think nothing is true would that also include the belief or claim that ‘absolute truth does not exist’?
Only if the law of the excluded middle remain robustly true, which it doesn’t...
So.. do you owe me that money? Arbitrary axioms are relatively safe in mathematics, because it is abstract..they are pretty disastrous when applied to the real world.
Your entire argument seems like an attempt at a ‘sophisticated’ justification of radical skepticism. So I’m not sure how I can possibly accept or decline either of those axioms. On what grounds would I do so or not do so?
The argument is supposed to work as a reductio ad absurdum. You are supposed to disbelieve the conclusion that you owe me money, and therefore reject the assumption that “truths about the real world can be derived from arbitrary axioms”.
And notice the amount of work being done by “arbitrary” here.
There is a thing ‘you’. There is a thing ‘me’. That there are things ‘the natural numbers’. There are things ‘dollars’ quantified using ‘natural numbers’. That the things ‘you’ and ‘me’ could possibly be related such that one of us ‘owes’ the other some number of ‘dollars’. x. …
There is some sort of evidence of argument for all of those, so they are neither arbitrary nor axiomatic, strictly speaking.
Mathematics does not “completelly” sidestep the Munchausen Trillema, because completely sidestrepping it would not involve a compromise nature of truth!
Okay, everything completely sidesteps the Münchhausen trilemma because it’s not actually a trilemma, because there is no absolute perfect truth of which anyone is capable of knowing.
That amounts to saying that the MT is true because it is false. That there is no absolute truth, no entirely satisfactory means of justification is the conclusion of the MT, so adopting it as a premise is hardly to argue against MT.
You seem to think that in the absence of absolute truth , relative truth is 1) unavoidable and 2) unproblematic.
But 1) doesn’t follow, because there is a third option, scepticism.
and 2) doesn’t follow, because of epistemological explosion. We always do have background intuitions , and one of them is that the set of true propositions isn’t a huge, incoherent , self-contradictory morass.
We can avoid the worst of (2) by minimising the use of intuition, but because that is not a full solution, we also need to adopt a degree of scepticism in recognition of the fact.
Or, nothing involves a “compromise nature of truth” – because there’s only one ‘truth’, it’s built on evidence, and it’s all bootstrapped by evolution and history.
if the arbitrary axioms are handed to us by evolution, they are still arbitrary in the ways that matter. So your rightly scare quoted ‘truth’ isn’t known to be true, and the MT still applies.
The Münchhausen trilemma has been around for awhile and yet truth is just as true as ever.
In the sense that they are taught in classrooms, cited in encyclopedias and so on. Take empirical knowledge. It may be based on vague intuitions, but it isn’t based on formal axioms.
I have no idea what you would accept.
I have been drawing a distinction between necessary presuppositions (“intuitions”) and arbitrary premises (“axioms). The wholesale embrace of derivation from arbitrary axioms as fully-fledged truth leads to the undesirable outcome of an epistemological explosion..every proposition becomes proveable and disproveable.
Trying to manage without even the most basic intuition is desirable, but, as far as we can tell, impossible.
However, the ineradicability of some intuitions doesn’t make the wholesale embrace of arbitrary axioms a good idea! If we cannot manage without intuitions, we can avoid the worst of the problems by minimising their use, particularly in real-world contexts, but that is damage containment, not a full solution,
If “depends on axioms” has a meaning, “does not depend on axioms” has a meaning. Whether truth indpendent of axioms is obtainable is another question.
Only if the law of the excluded middle remain robustly true, which it doesn’t...
The argument is supposed to work as a reductio ad absurdum. You are supposed to disbelieve the conclusion that you owe me money, and therefore reject the assumption that “truths about the real world can be derived from arbitrary axioms”.
And notice the amount of work being done by “arbitrary” here.
There is some sort of evidence of argument for all of those, so they are neither arbitrary nor axiomatic, strictly speaking.
That amounts to saying that the MT is true because it is false. That there is no absolute truth, no entirely satisfactory means of justification is the conclusion of the MT, so adopting it as a premise is hardly to argue against MT.
You seem to think that in the absence of absolute truth , relative truth is 1) unavoidable and 2) unproblematic.
But 1) doesn’t follow, because there is a third option, scepticism.
and 2) doesn’t follow, because of epistemological explosion. We always do have background intuitions , and one of them is that the set of true propositions isn’t a huge, incoherent , self-contradictory morass.
We can avoid the worst of (2) by minimising the use of intuition, but because that is not a full solution, we also need to adopt a degree of scepticism in recognition of the fact.
if the arbitrary axioms are handed to us by evolution, they are still arbitrary in the ways that matter. So your rightly scare quoted ‘truth’ isn’t known to be true, and the MT still applies.
How do you know?