How to we protect any choice when it ultimately has an aribtrary foundation?
By choosing to treat non-foundational issues in a single unified way that is distinct from how we treat foundational issues, we keep our thought more ordered and localize whatever problems there might be to our axioms.
“Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily from sensory experience.”
I see no need to assume such a doctrine. If it turned out to be false (say, if we were programmed from birth with many innate truths), we could still do science. It’s also worth noting that the logically knowable truths are far greater in number than the empirically knowable ones.
By choosing to treat non-foundational issues in a single unified way that is distinct from how we treat foundational issues, we keep our thought more ordered and localize whatever problems there might be to our axioms.
That just says they are different. They have to be, because we can pin non-foundational issues to foundationail issues, but we can’t pin foundational issues to foundational issues. However a difference is not the difference* -- the differnce tha would show that any arbitrariness of foundations affects what is founded on them
If [empiricism] turned out to be false (say, if we were programmed from birth with many innate truths), we could still do science
I suppose there could be a weak empiricism that just fills out the gaps in apriopri reasoning. However,
it is doubtful that apriori reasoning can supply truth at all. See below.
It’s also worth noting that the logically knowable truths are far greater in number than the empirically knowable ones.
So long as you are willing to accept valid derivations from arbitrary premises as actually true. One can derive
all sorts of things from the cheesiness of the Moon..
Sure. p → p is a logical truth. p → (p → p) is also a logical truth. So too p → (p → (p → p)). You can iterate this procedure to build arbitrarily long assertions. Likewise for mathematical equations. I don’t think that what we ordinarily mean by ‘empirical facts’ can be generated so easily. The empirical facts are a vanishingly small subset of the things we can know.
If that sort of thing is acceptable, can’t I also generate new empirical truths by for example just concatenating existing truths together? Say “The moon orbits the Earth, and George Washington was the first President”? That seems to be very close to what you are doing. Worse, I can use counterfactuals in a similar fashion, so “If homeopathy works then the moon is made out of green cheese” becomes an empirical truth?
There’s an argument here that these statements I’m using are mixes of empirical and logical truth, and if one buys into that then it seems like you are correct.
Say “The moon orbits the Earth, and George Washington was the first President”?
That still will only get you as many truths as there are combinations of empirical facts. A better method is to use disjunction: Since ‘The moon orbits the Earth’ is true ‘The moon orbits the Earth or is a hamster’ is true; hence ‘Either the moon orbits the earth or is a hamster, or the moon is a hamster’ is also true. And so on. Here we do get infinite strings, if we want them. But at this point it’s not clear to me that these new truths are ‘empirical facts.’ If so, then the class of empirical truths is indeed comparable in size to the class of logical truths.
And just how ‘empirical’ are counterfactuals? I don’t know. I try to avoid them when possible. There be dragons.
‘Rule 338(b) of the English Language: Sentences stop being grammatical when the number of morphemes equals ω₁. Seriously. Don’t do that shit. It’s obnoxious.’
They’re all just valid. You haven’t got to sound yet.
The empirical facts are a vanishingly small subset of the things we can know
OK, I see what you mean better now. For one single empirical fact (sound premise) on can generate
an infinite number of sound logical sentences, which basically say the same thing in ever more complicated
ways. If p is true, (p & T) is true as are (p & T &T..). Many people have the instict that these are trivial “cambridge” truths
and don;t add up to konwing an extra countable infinity of facts every time you learn one empirical fact.
It would be intersting to think about how that pans out in terns of the JTB theory.
They’re all just valid. You haven’t got to sound yet.
‘Valid’ and ‘sound’ are predicated of arguments. ‘p → p’ and the other sentences I listed are sentences, not arguments. Sentences are true or false, not valid or invalid, nor sound or unsound.
Many people have the instict that these are trivial “cambridge” truths and don;t add up to konwing an extra countable infinity of facts every time you learn one empirical fact.
Perhaps, but it will be a pretty huge project to explain ‘know’ in a way that clearly distinguishes the ‘fake’ knowledge from the real stuff.
By choosing to treat non-foundational issues in a single unified way that is distinct from how we treat foundational issues, we keep our thought more ordered and localize whatever problems there might be to our axioms.
I see no need to assume such a doctrine. If it turned out to be false (say, if we were programmed from birth with many innate truths), we could still do science. It’s also worth noting that the logically knowable truths are far greater in number than the empirically knowable ones.
That just says they are different. They have to be, because we can pin non-foundational issues to foundationail issues, but we can’t pin foundational issues to foundational issues. However a difference is not the difference* -- the differnce tha would show that any arbitrariness of foundations affects what is founded on them
I suppose there could be a weak empiricism that just fills out the gaps in apriopri reasoning. However, it is doubtful that apriori reasoning can supply truth at all. See below.
So long as you are willing to accept valid derivations from arbitrary premises as actually true. One can derive all sorts of things from the cheesiness of the Moon..
Can you explain what makes you conclude this inequality? It isn’t obvious to me.
Sure. p → p is a logical truth. p → (p → p) is also a logical truth. So too p → (p → (p → p)). You can iterate this procedure to build arbitrarily long assertions. Likewise for mathematical equations. I don’t think that what we ordinarily mean by ‘empirical facts’ can be generated so easily. The empirical facts are a vanishingly small subset of the things we can know.
If that sort of thing is acceptable, can’t I also generate new empirical truths by for example just concatenating existing truths together? Say “The moon orbits the Earth, and George Washington was the first President”? That seems to be very close to what you are doing. Worse, I can use counterfactuals in a similar fashion, so “If homeopathy works then the moon is made out of green cheese” becomes an empirical truth?
There’s an argument here that these statements I’m using are mixes of empirical and logical truth, and if one buys into that then it seems like you are correct.
That still will only get you as many truths as there are combinations of empirical facts. A better method is to use disjunction: Since ‘The moon orbits the Earth’ is true ‘The moon orbits the Earth or is a hamster’ is true; hence ‘Either the moon orbits the earth or is a hamster, or the moon is a hamster’ is also true. And so on. Here we do get infinite strings, if we want them. But at this point it’s not clear to me that these new truths are ‘empirical facts.’ If so, then the class of empirical truths is indeed comparable in size to the class of logical truths.
And just how ‘empirical’ are counterfactuals? I don’t know. I try to avoid them when possible. There be dragons.
You could also concatenate truths with themselves. ‘The moon orbits the Earth, and the moon orbits the Earth, and the moon orbits the Earth....’
Not in English, I’d say. But you do get an infinite set of finite strings of arbitrary length.
‘Rule 338(b) of the English Language: Sentences stop being grammatical when the number of morphemes equals ω₁. Seriously. Don’t do that shit. It’s obnoxious.’
I’m convinced. Thanks.
Check this out.
They’re all just valid. You haven’t got to sound yet.
OK, I see what you mean better now. For one single empirical fact (sound premise) on can generate an infinite number of sound logical sentences, which basically say the same thing in ever more complicated ways. If p is true, (p & T) is true as are (p & T &T..). Many people have the instict that these are trivial “cambridge” truths and don;t add up to konwing an extra countable infinity of facts every time you learn one empirical fact.
It would be intersting to think about how that pans out in terns of the JTB theory.
‘Valid’ and ‘sound’ are predicated of arguments. ‘p → p’ and the other sentences I listed are sentences, not arguments. Sentences are true or false, not valid or invalid, nor sound or unsound.
Perhaps, but it will be a pretty huge project to explain ‘know’ in a way that clearly distinguishes the ‘fake’ knowledge from the real stuff.