Great reply! The motivation for my post was accepting the underlying points about analysis that you seemed to be making, and then looking at your proof that ought ⇒ can and feeling as though you had, knowingly or unknowingly, smuggled in extra assumptions and assumed that the "ought+assumptions" you were now discussing still pointed back to the "ought" you were originally talking about. This made me concerned that either you or your readers would misapprehend what analysis meant, or seem to apprehend it in vacuo but fail to execute in practice.
It seems, based on your second footnote, that the issue wasn't a lack of clarity about whether the thing you were doing was analysis or not, but a lack of clarity and exposition on the page of the analysis you were doing in your head. This makes me think we are quite likely on the same page!
I think an essay on revealed preferences and belief-in-belief might be illuminating. This line of thinking is what I find most compelling about your approach. You can believe that you value religion more than anything in your life, but if you miss church to watch TV and you are aware that you could have gone to church, then you are in fact mistaken about your own values. Prima facie, at least, this is a strong case.
Framing ε-δ as one possible explication of the ordinary concept of continuity makes more sense to me than claiming that it is the one correct analysis of the term. In particular since there is an entire zoo of notions of continuity in math. In a possible world not too distant from this one, mathematicians might have settled on calling "continuity" what we call "uniform continuity", or on calling "continuity" what we call "Lipschitz continuity"; these mathematicians might call ε-δ continuity "pseudo-continuity", perhaps because it fails to preserve Cauchy Sequences or because pseudo-continuous functions cannot be uniquely extended to the closure of their domain etc...
And why should there only be one fruitful or important concept in the vicinity of the ordinary language concept "continuity"? I take the development of mathematics to in fact have shown that the ordinary language concept conflates a whole family of different notions, all of which are important in some sense (which mathematics makes precise); but none of which can really be called the one correct "analysis" of "continuity".
I think, following the Sellars, Brandom, and Wittgenstein lineage of word/concept analysis, one of the more interesting approaches to differences in uses of words that other people can track is just in the plurality of vocabularies for expressing the same thing. When it comes to differences in attitudes, perspectives, or contexts for those words, higher-order analysis really comes to shine in a way that those who endorse a univocal first order analysis fails to exhaust the intricacies of use. The treatment of words as types which have different functions then becomes a matter of tracking which function is at play keeps analysis consistent in a way that not only satisfies many intuitions about how words work, but seems to get things right in that philosophically relevant way.
I'm with you most of the way, except in your optimism at the end of the post that the concepts we discover in mathematics are at best contingently interesting/important, while philosophers try to analyze concepts whose significance is truly and utterly necessary. This feels closely related to the Kant/Hume contrast that came up in the other post; I'm much more inclined to see the concepts philosophers treat as depending in important ways on (contingent) human nature, rather than only on stuff that would be shared by all rational beings as such.
My bet is that if we ever meet intelligent aliens, their math will look at lot more like ours than their philosophy.
This is all correct given the premise that what matters is joints in nature, or "joints" in the thinking of any possible rational being, but a lot of people, including myself, think that a lot of key philosophical concepts don't carve any joints in the world, or bear a relationship to anything fundamental about existing as a being in a world. "Knowledge" for example, seems like a hodgepodge concept that serves multiple only partially overlapping roles. For an ethical anti-realist such as myself, "good" and "right" are likewise inventions rather than tracking something that matters apart from our own contradictory purposes and desires. I even strongly suspect "causation" might fall in this category. From this perspective, ideas like reflective equilibrium, minimal mutilation, and conceptual engineering make sense as processes in trying to decide a conceptual stance given historically and biologically shaped conceptual functions- they are methodologies for "getting one's house in order". It's a kind of conceptual anthropology, combined with a little bit of engineering.
I suspect that we're in agreement about these two kinds of methodology as possibly sensible enterprises. For example, I think it would be nuts to try to think about the structure of concepts in chemistry without thinking about how those concepts need to be to capture something important and pre-existing. Likewise, I suspect you would grant that at least some work in, say, the philosophy of disability is necessarily going to involve a bit of conceptual anthropology and trying to hammer out folk intuitions. It's just that we disagree on some core cases, especially the good and the right.
It is very irritating to me, by the way, that these debates happen all the time in philosophy, but are not organised very well. If you want to look up "coherentism versus foundationalism," you can very easily. If you want to read the literature about whether debates in philosophy are primarily about doing justice to the things in our head or the joints in the world, that fragments into dozens of different, often disjoint literatures.
Great reply! The motivation for my post was accepting the underlying points about analysis that you seemed to be making, and then looking at your proof that ought ⇒ can and feeling as though you had, knowingly or unknowingly, smuggled in extra assumptions and assumed that the "ought+assumptions" you were now discussing still pointed back to the "ought" you were originally talking about. This made me concerned that either you or your readers would misapprehend what analysis meant, or seem to apprehend it in vacuo but fail to execute in practice.
It seems, based on your second footnote, that the issue wasn't a lack of clarity about whether the thing you were doing was analysis or not, but a lack of clarity and exposition on the page of the analysis you were doing in your head. This makes me think we are quite likely on the same page!
I think an essay on revealed preferences and belief-in-belief might be illuminating. This line of thinking is what I find most compelling about your approach. You can believe that you value religion more than anything in your life, but if you miss church to watch TV and you are aware that you could have gone to church, then you are in fact mistaken about your own values. Prima facie, at least, this is a strong case.
Heya! Perhaps Carnap on explication might be of interest to you? (See e.g. section 1 here: https://plato.stanford.edu/entries/carnap/methodology.html)
Framing ε-δ as one possible explication of the ordinary concept of continuity makes more sense to me than claiming that it is the one correct analysis of the term. In particular since there is an entire zoo of notions of continuity in math. In a possible world not too distant from this one, mathematicians might have settled on calling "continuity" what we call "uniform continuity", or on calling "continuity" what we call "Lipschitz continuity"; these mathematicians might call ε-δ continuity "pseudo-continuity", perhaps because it fails to preserve Cauchy Sequences or because pseudo-continuous functions cannot be uniquely extended to the closure of their domain etc...
And why should there only be one fruitful or important concept in the vicinity of the ordinary language concept "continuity"? I take the development of mathematics to in fact have shown that the ordinary language concept conflates a whole family of different notions, all of which are important in some sense (which mathematics makes precise); but none of which can really be called the one correct "analysis" of "continuity".
I think, following the Sellars, Brandom, and Wittgenstein lineage of word/concept analysis, one of the more interesting approaches to differences in uses of words that other people can track is just in the plurality of vocabularies for expressing the same thing. When it comes to differences in attitudes, perspectives, or contexts for those words, higher-order analysis really comes to shine in a way that those who endorse a univocal first order analysis fails to exhaust the intricacies of use. The treatment of words as types which have different functions then becomes a matter of tracking which function is at play keeps analysis consistent in a way that not only satisfies many intuitions about how words work, but seems to get things right in that philosophically relevant way.
I'm with you most of the way, except in your optimism at the end of the post that the concepts we discover in mathematics are at best contingently interesting/important, while philosophers try to analyze concepts whose significance is truly and utterly necessary. This feels closely related to the Kant/Hume contrast that came up in the other post; I'm much more inclined to see the concepts philosophers treat as depending in important ways on (contingent) human nature, rather than only on stuff that would be shared by all rational beings as such.
My bet is that if we ever meet intelligent aliens, their math will look at lot more like ours than their philosophy.
This is all correct given the premise that what matters is joints in nature, or "joints" in the thinking of any possible rational being, but a lot of people, including myself, think that a lot of key philosophical concepts don't carve any joints in the world, or bear a relationship to anything fundamental about existing as a being in a world. "Knowledge" for example, seems like a hodgepodge concept that serves multiple only partially overlapping roles. For an ethical anti-realist such as myself, "good" and "right" are likewise inventions rather than tracking something that matters apart from our own contradictory purposes and desires. I even strongly suspect "causation" might fall in this category. From this perspective, ideas like reflective equilibrium, minimal mutilation, and conceptual engineering make sense as processes in trying to decide a conceptual stance given historically and biologically shaped conceptual functions- they are methodologies for "getting one's house in order". It's a kind of conceptual anthropology, combined with a little bit of engineering.
I suspect that we're in agreement about these two kinds of methodology as possibly sensible enterprises. For example, I think it would be nuts to try to think about the structure of concepts in chemistry without thinking about how those concepts need to be to capture something important and pre-existing. Likewise, I suspect you would grant that at least some work in, say, the philosophy of disability is necessarily going to involve a bit of conceptual anthropology and trying to hammer out folk intuitions. It's just that we disagree on some core cases, especially the good and the right.
It is very irritating to me, by the way, that these debates happen all the time in philosophy, but are not organised very well. If you want to look up "coherentism versus foundationalism," you can very easily. If you want to read the literature about whether debates in philosophy are primarily about doing justice to the things in our head or the joints in the world, that fragments into dozens of different, often disjoint literatures.