The former. Some axioms will be applicable to reality and some will not, but the rules of inference work in either case.
And if some axioms are applicable to reality, then the whole edifice is supported? You mean, maths is like a rigid structure, where if one part supported, that in turn supports the other parts? That would be the case if you could logically infer axioms B and C from axiom A. But that is exactly how axioms don’t work. A set of axioms is a minimal set of assumptions: if one of your axioms is derivable from the others, it shouldn’t be in the set.
Maths doesn’t need empirical support to work as maths, since it isn’t physics, and adding empirical support
doesn’t show “it works” in any exhaustive way, only that some bits of it are applicable to physical reality,
In both cases, we have evidence that these rules of inference actually work, which is not the case by default.
Whatever “actually works” means. If a true mathematical statement is one that is derived by standard rules of inference from standard axioms, then it could hardly fail to “work”, in that sense. OTOH, it can still fail to apply
to reality, and so fail to work in that sense. (You really need to taboo “work”). But in the second case, evidence is only supporting the idea that some maths works, in the second sense. You make things rather easy by defining works to mean sometimes works...
Even if we supposed that we had a system for moral reasoning which, like math, could extrapolate the consequences of axioms to their necessary conclusions (which I would argue we don’t actually have, humans are simply not good enough at natural language reasoning to pull that off with any sort of reliability,) how would we determine if any of those moral axioms apply to the real world, the way some mathematical axioms observably do?
The job of morality is to guide action, not to passively reflect facts, so the question is irrelevant.
Whatever “actually works” means. If a true mathematical statement is one that is derived by standard rules of inference from standard axioms, then it could hardly fail to “work”, in that sense.
The “standard rules of inference” could very easily simply be nonsense. Sets of rules do not help produce meaningful information by default. Out of the set of all methods of inference that could hypothetically exist, the vast majority do not produce information that is either true or consistent.
The job of morality is to guide action, not to passively reflect facts, so the question is irrelevant.
So let’s suppose that we live in a universe in which it is objectively true that there are no objective moral standards. In your view, would this be a relevant fact about morality?
The “standard rules of inference” could very easily simply be nonsense.
In what sense? Are there alternative rules that are also truth preserving? Is truth-preservation hard to establish?
Sets of rules do not help produce meaningful information by default.
I wouldn’t say they produceinformation at all. Truth isn’t meaning, preservation isn’t production, truth preservation therefore isn’t meaning production.
Out of the set of all methods of inference that could hypothetically exist, the vast majority do not produce information that is either true or consistent.
We are supposed to have already chosen a set of rules that is truth-preserving.: ie, if you treat truth as a sort of numerical value, wihout any metaphysics behind it, that is assigned by fiat to your axioms, then you can show that it is preserved by using truth tables and the like (although there as some circularities there). Do you doubt that? Or is your concern showing that axioms are somehow “really” true, about something other than themselves?
So let’s suppose that we live in a universe in which it is objectively true that there are no objective moral standards. In your view, would this be a relevant fact about morality?
It’s more metaethical. You cant use “there are not moral truths” to guide your actions at the object level..
In what sense? Are there alternative rules that are also truth preserving? Is truth-preservation hard to establish?
If you count empiricism as a set of alternative rules which are truth preserving, then yes. If you’re talking about other non-empirical sets of rules, I would at least tentatively say no; formal logic is a branch of math, and natural language logic really doesn’t meet the same standards.
I wouldn’t say they produceinformation at all. Truth isn’t meaning, preservation isn’t production, truth preservation therefore isn’t meaning production.
In that case, what if anything would you describe as the production of information?
We are supposed to have already chosen a set of rules that is truth-preserving.: ie, if you treat truth as a sort of numerical value, wihout any metaphysics behind it, that is assigned by fiat to your axioms, then you can show that it is preserved by using truth tables and the like (although there as some circularities there). Do you doubt that? Or is your concern showing that axioms are somehow “really” true, about something other than themselves?
What set of rules “we are supposed to have already chosen” are you referring to?
Based on some of your statements about morality so far, I suspect I would argue that you are extrapolating from axioms that are not true in real life, much as some mathematical axioms seem to apply to the real world, while other ones do not.
It’s more metaethical. You cant use “there are not moral truths” to guide your actions at the object level..
Sure you can. Whether you should is an entirely separate value judgment.
If empiricism just means gathering observations, stamp collecting style, then i dont see where the truth preservation comes in. I can see where truth preservation comes into making predictions from evidence you already have, but that seems to use logical inference.
If you draw a line around an entity, then there will be information crossing that line, which is new, unpredictable, and “produced” as far as that entity is concerned.
I meant we are supposed to have already chosen a set of truth preserving mathematical and logical rules.
Could you give an example of how to use “there are no moral truths” to guide your actions?
If empiricism just means gathering observations, stamp collecting style, then i dont see where the truth preservation comes in. I can see where truth preservation comes into making predictions from evidence you already have, but that seems to use logical inference.
Could you taboo “truth preservation?”
Could you give an example of how to use “there are no moral truths” to guide your actions?
“Nothing is objectively right or wrong, therefore I will do whatever I feel like as long as I can get away with it.”
You or I might not consider this to be good moral behavior, but for a person who believed both that moral rules are only worth following if they’re objective, and that objective moral rules do not exist, it would be a reasonable conclusion to draw.
Atheism is, of course, a belief. It’s a belief that there are not any gods.
The belief that there are no objective moral rules only guides your actions to the extent that it may relieve you of constraints that you might have had if you thought there were any. But whether any other moral code is “better” than this would simply come down to a matter of value judgment.
And if some axioms are applicable to reality, then the whole edifice is supported? You mean, maths is like a rigid structure, where if one part supported, that in turn supports the other parts? That would be the case if you could logically infer axioms B and C from axiom A. But that is exactly how axioms don’t work. A set of axioms is a minimal set of assumptions: if one of your axioms is derivable from the others, it shouldn’t be in the set.
Maths doesn’t need empirical support to work as maths, since it isn’t physics, and adding empirical support doesn’t show “it works” in any exhaustive way, only that some bits of it are applicable to physical reality,
Whatever “actually works” means. If a true mathematical statement is one that is derived by standard rules of inference from standard axioms, then it could hardly fail to “work”, in that sense. OTOH, it can still fail to apply to reality, and so fail to work in that sense. (You really need to taboo “work”). But in the second case, evidence is only supporting the idea that some maths works, in the second sense. You make things rather easy by defining works to mean sometimes works...
The job of morality is to guide action, not to passively reflect facts, so the question is irrelevant.
The “standard rules of inference” could very easily simply be nonsense. Sets of rules do not help produce meaningful information by default. Out of the set of all methods of inference that could hypothetically exist, the vast majority do not produce information that is either true or consistent.
So let’s suppose that we live in a universe in which it is objectively true that there are no objective moral standards. In your view, would this be a relevant fact about morality?
In what sense? Are there alternative rules that are also truth preserving? Is truth-preservation hard to establish?
I wouldn’t say they produceinformation at all. Truth isn’t meaning, preservation isn’t production, truth preservation therefore isn’t meaning production.
We are supposed to have already chosen a set of rules that is truth-preserving.: ie, if you treat truth as a sort of numerical value, wihout any metaphysics behind it, that is assigned by fiat to your axioms, then you can show that it is preserved by using truth tables and the like (although there as some circularities there). Do you doubt that? Or is your concern showing that axioms are somehow “really” true, about something other than themselves?
It’s more metaethical. You cant use “there are not moral truths” to guide your actions at the object level..
If you count empiricism as a set of alternative rules which are truth preserving, then yes. If you’re talking about other non-empirical sets of rules, I would at least tentatively say no; formal logic is a branch of math, and natural language logic really doesn’t meet the same standards.
In that case, what if anything would you describe as the production of information?
What set of rules “we are supposed to have already chosen” are you referring to? Based on some of your statements about morality so far, I suspect I would argue that you are extrapolating from axioms that are not true in real life, much as some mathematical axioms seem to apply to the real world, while other ones do not.
Sure you can. Whether you should is an entirely separate value judgment.
If empiricism just means gathering observations, stamp collecting style, then i dont see where the truth preservation comes in. I can see where truth preservation comes into making predictions from evidence you already have, but that seems to use logical inference.
If you draw a line around an entity, then there will be information crossing that line, which is new, unpredictable, and “produced” as far as that entity is concerned.
I meant we are supposed to have already chosen a set of truth preserving mathematical and logical rules.
Could you give an example of how to use “there are no moral truths” to guide your actions?
Could you taboo “truth preservation?”
“Nothing is objectively right or wrong, therefore I will do whatever I feel like as long as I can get away with it.”
You or I might not consider this to be good moral behavior, but for a person who believed both that moral rules are only worth following if they’re objective, and that objective moral rules do not exist, it would be a reasonable conclusion to draw.
Who the problem with truthpreservation? It’s a technical term, and i gave a link
Your notion of using metaethical nihilism to guide action is analogous to treating atheism as a belief. Your actions would be unguided.
Atheism is, of course, a belief. It’s a belief that there are not any gods.
The belief that there are no objective moral rules only guides your actions to the extent that it may relieve you of constraints that you might have had if you thought there were any. But whether any other moral code is “better” than this would simply come down to a matter of value judgment.