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	<title>Comments on: Knowledge Entails Certainty</title>
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	<pubDate>Sat, 04 Sep 2010 20:51:30 +0000</pubDate>
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		<title>By: Jonathan</title>
		<link>http://jonathanichikawa.net/weblog/knowledge-entails-certainty/#comment-388</link>
		<dc:creator>Jonathan</dc:creator>
		<pubDate>Thu, 18 Mar 2010 14:54:41 +0000</pubDate>
		<guid isPermaLink="false">http://jonathanichikawa.net/?p=201#comment-388</guid>
		<description>An important part of the project, Jonathan, is to be contextualist about terms like 'perfectly' and 'absolutely', too. These are gradable adjectives. So I'm denying that these represent an invariantist maximum standard.

(Notice also that to describe the view as 'contextualist about circles' is to commit a use/mention error.)

I'm not going to agree with you about Lewis and evidence. There are lots of non-psychologistic bits of evidence that Lewis can happily recognize. You think the only evidence Lewis represents himself as having in favor of the claim that concessive knowledge attributions are untenable is that they sound bad. But how about this obvious fact: they are conjunctions of knowledge attributions with the epistemic possibility of the negation of the object of the knowledge attribution. That a sentence conjoins a claim of knowledge of p with the possibility of not-p is strong evidence that it is false.</description>
		<content:encoded><![CDATA[<p>An important part of the project, Jonathan, is to be contextualist about terms like &#8216;perfectly&#8217; and &#8216;absolutely&#8217;, too. These are gradable adjectives. So I&#8217;m denying that these represent an invariantist maximum standard.</p>
<p>(Notice also that to describe the view as &#8216;contextualist about circles&#8217; is to commit a use/mention error.)</p>
<p>I&#8217;m not going to agree with you about Lewis and evidence. There are lots of non-psychologistic bits of evidence that Lewis can happily recognize. You think the only evidence Lewis represents himself as having in favor of the claim that concessive knowledge attributions are untenable is that they sound bad. But how about this obvious fact: they are conjunctions of knowledge attributions with the epistemic possibility of the negation of the object of the knowledge attribution. That a sentence conjoins a claim of knowledge of p with the possibility of not-p is strong evidence that it is false.</p>
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		<title>By: Jonathan Weinberg</title>
		<link>http://jonathanichikawa.net/weblog/knowledge-entails-certainty/#comment-377</link>
		<dc:creator>Jonathan Weinberg</dc:creator>
		<pubDate>Tue, 16 Mar 2010 01:51:17 +0000</pubDate>
		<guid isPermaLink="false">http://jonathanichikawa.net/?p=201#comment-377</guid>
		<description>I don't really understand what you're saying about Unger; I mean, it's right that his view is very closely related in a lot of ways to the contextualist rival he constructs for it, so of course his discussions play an important role in later elaborations of contextualism.  But it's still the case (isn't it?) that the contextualist shouldn't want to tie the meaning of her contextualist term of choice to a construction in which all the contextually-sensitive parameters have been set to a _non_-contextually-sensitive maximum setting.  And words like "absolutely", "perfectly", etc. do exactly that -- they set that parameter of a gradable predicate to its maximum setting. Which is why it shouldn't make any sense, if you want to be a contextualist about circles, to say "all circles are perfectly round." 

Regarding Lewis, you say, "In the passages you cite, he isn’t explicitly making claims about evidence...."  I take that statement to be directly falsified by Lewis' reference to "the explananda phenomena", unless you have a very weird view on which our explananda are not part of our evidence (which seems required by taking inference to the best explanation to be a good, evidence-based form of inference.)  So evidence is very much an explicit part of the discussion.

Looking at the passages in question, he's clearly saying: the badness of "I know that p but I could be wrong" is part of our evidence; and he's also clearly representing himself as having no further evidence for that badness, beyond how he thinks the re-naive ear will hear it.

Fwiw, responding to your last parenthetical point: I can't think of any reason to _want_ to be a contextualist, if we have free license to just override the folk usages at will.  For Heaven's sake, if that's the methodological situation, then let's just all be traditional, boring, non-sensitivist, non-contextualist invariantists, and call it a day.  (That is, in fact, the theory of knowledge I would have if held at gunpoint and forced to have a theory of knowledge.)</description>
		<content:encoded><![CDATA[<p>I don&#8217;t really understand what you&#8217;re saying about Unger; I mean, it&#8217;s right that his view is very closely related in a lot of ways to the contextualist rival he constructs for it, so of course his discussions play an important role in later elaborations of contextualism.  But it&#8217;s still the case (isn&#8217;t it?) that the contextualist shouldn&#8217;t want to tie the meaning of her contextualist term of choice to a construction in which all the contextually-sensitive parameters have been set to a _non_-contextually-sensitive maximum setting.  And words like &#8220;absolutely&#8221;, &#8220;perfectly&#8221;, etc. do exactly that &#8212; they set that parameter of a gradable predicate to its maximum setting. Which is why it shouldn&#8217;t make any sense, if you want to be a contextualist about circles, to say &#8220;all circles are perfectly round.&#8221; </p>
<p>Regarding Lewis, you say, &#8220;In the passages you cite, he isn’t explicitly making claims about evidence&#8230;.&#8221;  I take that statement to be directly falsified by Lewis&#8217; reference to &#8220;the explananda phenomena&#8221;, unless you have a very weird view on which our explananda are not part of our evidence (which seems required by taking inference to the best explanation to be a good, evidence-based form of inference.)  So evidence is very much an explicit part of the discussion.</p>
<p>Looking at the passages in question, he&#8217;s clearly saying: the badness of &#8220;I know that p but I could be wrong&#8221; is part of our evidence; and he&#8217;s also clearly representing himself as having no further evidence for that badness, beyond how he thinks the re-naive ear will hear it.</p>
<p>Fwiw, responding to your last parenthetical point: I can&#8217;t think of any reason to _want_ to be a contextualist, if we have free license to just override the folk usages at will.  For Heaven&#8217;s sake, if that&#8217;s the methodological situation, then let&#8217;s just all be traditional, boring, non-sensitivist, non-contextualist invariantists, and call it a day.  (That is, in fact, the theory of knowledge I would have if held at gunpoint and forced to have a theory of knowledge.)</p>
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		<title>By: Jonathan</title>
		<link>http://jonathanichikawa.net/weblog/knowledge-entails-certainty/#comment-360</link>
		<dc:creator>Jonathan</dc:creator>
		<pubDate>Wed, 10 Mar 2010 22:08:01 +0000</pubDate>
		<guid isPermaLink="false">http://jonathanichikawa.net/?p=201#comment-360</guid>
		<description>Jonathan, obviously there's quite a lot here -- more than is really apt for this forum -- but let me just say a couple of things. First, I don't agree that Lewis's methodology is irreconcilable with my metaphilosophical outlook. In the passages you cite, he isn't explicitly making claims about evidence, and I don't see why we should interpret him as making implicit ones.

Just as a matter of contemporary history of epistemology, I don't think of Unger as (merely) defending a rival to contextualism. Rather, I think of Unger as an important precursor to contemporary contextualism -- that's certainly the way DeRose talks about it, and I think there's something to that.

Maybe you and I agree that my claims about knowledge and certainty are as plausible as Unger's about circles and perfect circles. I'd like that. I do take that data seriously, although I see that you don't agree with it. I agree that it might be interesting to see what the folk think. I suspect they're friendlier to the Unger line than you suggest. (But if I'm wrong about that, I'm not too worried. They're only the folk.)</description>
		<content:encoded><![CDATA[<p>Jonathan, obviously there&#8217;s quite a lot here &#8212; more than is really apt for this forum &#8212; but let me just say a couple of things. First, I don&#8217;t agree that Lewis&#8217;s methodology is irreconcilable with my metaphilosophical outlook. In the passages you cite, he isn&#8217;t explicitly making claims about evidence, and I don&#8217;t see why we should interpret him as making implicit ones.</p>
<p>Just as a matter of contemporary history of epistemology, I don&#8217;t think of Unger as (merely) defending a rival to contextualism. Rather, I think of Unger as an important precursor to contemporary contextualism &#8212; that&#8217;s certainly the way DeRose talks about it, and I think there&#8217;s something to that.</p>
<p>Maybe you and I agree that my claims about knowledge and certainty are as plausible as Unger&#8217;s about circles and perfect circles. I&#8217;d like that. I do take that data seriously, although I see that you don&#8217;t agree with it. I agree that it might be interesting to see what the folk think. I suspect they&#8217;re friendlier to the Unger line than you suggest. (But if I&#8217;m wrong about that, I&#8217;m not too worried. They&#8217;re only the folk.)</p>
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		<title>By: Jonathan Weinberg</title>
		<link>http://jonathanichikawa.net/weblog/knowledge-entails-certainty/#comment-358</link>
		<dc:creator>Jonathan Weinberg</dc:creator>
		<pubDate>Tue, 09 Mar 2010 21:46:02 +0000</pubDate>
		<guid isPermaLink="false">http://jonathanichikawa.net/?p=201#comment-358</guid>
		<description>A couple of things are a bit off here, it seems to me.

First, while it may work for some things that philosophers do in this neighborhood, I don't think that  your deflationary line on intuitions is going to make sense of some sizeable chunks philosophical practice, and at the very least,  it fails to make any sense of _ Lewis_.  Go back and re-read the relevant bits of  "Elusive Knowledge", and it's just obvious that he, at least, doesn't have any further "considerations that do count in that direction" of his claims about the infallibility of knowledge.  It's just something he takes to be a psychologically powerful datum, and if someone disagrees with him about that, then he thinks that all they can do is agree to disagree.  First, his appeal is of a frankly psychological nature: "Yet fallibilism is the less intrusive madness [compared to skepticism]. It demands less frequent corrections of what we want to say. So, if forced to choose, I choose fallibilism. (And so say all of us.) We can get used to it, and some of us have done. No joy there - we know that people can get used to the most crazy philosophical sayings imaginable. If you are a contented fallibilist, I implore you to be honest, be naive, hear it afresh. 'He knows, yet he has not eliminated all possibilities of error.' Even if you've numbed your ears, doesn't this overt, explicit fallibilism still _sound_ wrong?" (And note, by the way, that he is precisely asking us to step _away_ from any ways in which our epistemological expertise may be informing our judgments here.)

If Lewis had other considerations to muster, he would have mustered them, or at least gestured towards where they might be mustered from (the historical record or empirical observation or a mathematical proof published elsewhere or whatever it might be).  And it's not surprising that he proceeds -- or, rather, doesn't even try to proceed -- in that manner, since indeed it's hard to see what further considerations there are to be mustered here at all.  We're at bedrock, he thinks.  E.g., he writes, 

"I started with a puzzle: how can it be, when his conclusion is so silly, that the sceptic's argument is so irresistible? My Rule of Attention, and the version of the proviso that made that Rule trivial, were built to explain how the sceptic manages to sway us - why his argument seems irresistible, howevertemporarily. If you continue to find it eminently resistible in all contexts, you have no need of any such explanation. We just disagree about the explanandum phenomenon."

That it can't make sense of this very famous paper is some indication that, despite your protests to the contrary, your proposal is substantially more revisionary than you're trying to make it out to be.  Now, if philosophers had, upon reading the paper,  tended to go, "wow, some interesting stuff here, but what in the world is Lewis doing with those weird psychological premises? You can't go about making serious philosophical arguments that way," etc., then that would go some distance in your favor.  But that's not at all the reception the paper has garnered, however.  The baldly psychological aspects of what he's doing have gone unremarked, because they are part &amp; parcel of the mainstream practice. 

Turning to the  Unger stuff, I think it's important to keep in mind that he is just plain wrong about the linguistic data here.  If someone says, say,  that southern Illinois is flat, and Unger says, "aha!  but it really does have lots of ups and downs and peaks and valleys and roughnesses ... I mean, just compare it to, say, this piece of paper here.  Isn't this piece of paper much, much flatter?" , then the first person is likely to agree to that comparative judgment.  But if Unger presses them, "aha, so don't you want to say that southern Illinois isn't _really_ flat?  It's not _perfectly_ flat, right?", then they are likely to respond with some combination of (i) "whoa, you think southern Illinois isn't really flat?  dude, try driving through it sometime"; (ii) "well, right, so it's not _perfectly_ flat.  no one would think it is.  but it's still _flat_.  Really, really flat, in fact"; and (iii) rolling their eyes and looking to renew their earlier commitment not to talk to philosophers, who so often have wasted their time with tin-eared  sillinesses.  Pretty much no one is going to say, "gosh, maybe southern Illinois isn't really flat!"  It's just not going to happen.  More generally, there's just nothing amiss with utterances like, "Sure, it's got some little  bumps here and there, but it's flat" said of, say, a football field.   It doesn't seem to So that whole premise of the discussion is basically off.  

This is probably very good fodder for some x-phi treatment, btw; I found a tiny bit of data informally reported here: http://www.gap5.de/proceedings/pdf/157-168_blome-tillmann.pdf   Couldn't find anything else that seemed to have taken a real look at Unger's outrageous claims, though. 

Even setting that aside, although claims like "all circles are perfect circles" are the stock-in-trade of the standard Ungerian line, they are meant to support a _rival_ to the contextualist line -- it's the line of the invariantist skeptic!  So if you're making a case for contextualist certaintism, you don't want to go that way.  The parallel claim would be "all knowledge requires perfect certainty", and you don't want that.  On the picture you're trying to paint, you want something like, simply, "all knowledge requires certainty", plus a story about how the contextually-determined certainty threshhold gets driven higher once it is pointed out that one is currently operating short of some still-higher possible such threshhold.  Generally speaking, the contextualist in these debates wants to hook up to gradable terms, maybe even ones that are absolutizable,  but they don't want to hook up their target term to the _absolutized_ form of any such term.  Flat enough is flat enough, and need not be perfectly flat, for the contextualist.

Now, it should be noted that  Lewis himself does do this a bit differently.  He does seem to embrace the absolutized form, only to un-embrace it; he  jumps all the way out to it -- and then walks it all back a ways, with his "psst!"s.  This is another area where the infallibilist may have resources that the certaintist might not.   The infallibilist can try to use the Lewisian machinery of "properly ignoring", because she can point out, in her theory, those possibilities that are to be properly ignored, and of course he has lots of rules on offer to guide such ignorings.  Certainty doesn't seem to have the right structure for that.   You're just certain to a greater or lesser degree, end of story.   There's nothing like the infallibilist's possibilities for any such walking-back machinery to get a hold of, when dealing with certainty.</description>
		<content:encoded><![CDATA[<p>A couple of things are a bit off here, it seems to me.</p>
<p>First, while it may work for some things that philosophers do in this neighborhood, I don&#8217;t think that  your deflationary line on intuitions is going to make sense of some sizeable chunks philosophical practice, and at the very least,  it fails to make any sense of _ Lewis_.  Go back and re-read the relevant bits of  &#8220;Elusive Knowledge&#8221;, and it&#8217;s just obvious that he, at least, doesn&#8217;t have any further &#8220;considerations that do count in that direction&#8221; of his claims about the infallibility of knowledge.  It&#8217;s just something he takes to be a psychologically powerful datum, and if someone disagrees with him about that, then he thinks that all they can do is agree to disagree.  First, his appeal is of a frankly psychological nature: &#8220;Yet fallibilism is the less intrusive madness [compared to skepticism]. It demands less frequent corrections of what we want to say. So, if forced to choose, I choose fallibilism. (And so say all of us.) We can get used to it, and some of us have done. No joy there - we know that people can get used to the most crazy philosophical sayings imaginable. If you are a contented fallibilist, I implore you to be honest, be naive, hear it afresh. &#8216;He knows, yet he has not eliminated all possibilities of error.&#8217; Even if you&#8217;ve numbed your ears, doesn&#8217;t this overt, explicit fallibilism still _sound_ wrong?&#8221; (And note, by the way, that he is precisely asking us to step _away_ from any ways in which our epistemological expertise may be informing our judgments here.)</p>
<p>If Lewis had other considerations to muster, he would have mustered them, or at least gestured towards where they might be mustered from (the historical record or empirical observation or a mathematical proof published elsewhere or whatever it might be).  And it&#8217;s not surprising that he proceeds &#8212; or, rather, doesn&#8217;t even try to proceed &#8212; in that manner, since indeed it&#8217;s hard to see what further considerations there are to be mustered here at all.  We&#8217;re at bedrock, he thinks.  E.g., he writes, </p>
<p>&#8220;I started with a puzzle: how can it be, when his conclusion is so silly, that the sceptic&#8217;s argument is so irresistible? My Rule of Attention, and the version of the proviso that made that Rule trivial, were built to explain how the sceptic manages to sway us - why his argument seems irresistible, howevertemporarily. If you continue to find it eminently resistible in all contexts, you have no need of any such explanation. We just disagree about the explanandum phenomenon.&#8221;</p>
<p>That it can&#8217;t make sense of this very famous paper is some indication that, despite your protests to the contrary, your proposal is substantially more revisionary than you&#8217;re trying to make it out to be.  Now, if philosophers had, upon reading the paper,  tended to go, &#8220;wow, some interesting stuff here, but what in the world is Lewis doing with those weird psychological premises? You can&#8217;t go about making serious philosophical arguments that way,&#8221; etc., then that would go some distance in your favor.  But that&#8217;s not at all the reception the paper has garnered, however.  The baldly psychological aspects of what he&#8217;s doing have gone unremarked, because they are part &amp; parcel of the mainstream practice. </p>
<p>Turning to the  Unger stuff, I think it&#8217;s important to keep in mind that he is just plain wrong about the linguistic data here.  If someone says, say,  that southern Illinois is flat, and Unger says, &#8220;aha!  but it really does have lots of ups and downs and peaks and valleys and roughnesses &#8230; I mean, just compare it to, say, this piece of paper here.  Isn&#8217;t this piece of paper much, much flatter?&#8221; , then the first person is likely to agree to that comparative judgment.  But if Unger presses them, &#8220;aha, so don&#8217;t you want to say that southern Illinois isn&#8217;t _really_ flat?  It&#8217;s not _perfectly_ flat, right?&#8221;, then they are likely to respond with some combination of (i) &#8220;whoa, you think southern Illinois isn&#8217;t really flat?  dude, try driving through it sometime&#8221;; (ii) &#8220;well, right, so it&#8217;s not _perfectly_ flat.  no one would think it is.  but it&#8217;s still _flat_.  Really, really flat, in fact&#8221;; and (iii) rolling their eyes and looking to renew their earlier commitment not to talk to philosophers, who so often have wasted their time with tin-eared  sillinesses.  Pretty much no one is going to say, &#8220;gosh, maybe southern Illinois isn&#8217;t really flat!&#8221;  It&#8217;s just not going to happen.  More generally, there&#8217;s just nothing amiss with utterances like, &#8220;Sure, it&#8217;s got some little  bumps here and there, but it&#8217;s flat&#8221; said of, say, a football field.   It doesn&#8217;t seem to So that whole premise of the discussion is basically off.  </p>
<p>This is probably very good fodder for some x-phi treatment, btw; I found a tiny bit of data informally reported here: <a href="http://www.gap5.de/proceedings/pdf/157-168_blome-tillmann.pdf" rel="nofollow">http://www.gap5.de/proceedings/pdf/157-168_blome-tillmann.pdf</a>   Couldn&#8217;t find anything else that seemed to have taken a real look at Unger&#8217;s outrageous claims, though. </p>
<p>Even setting that aside, although claims like &#8220;all circles are perfect circles&#8221; are the stock-in-trade of the standard Ungerian line, they are meant to support a _rival_ to the contextualist line &#8212; it&#8217;s the line of the invariantist skeptic!  So if you&#8217;re making a case for contextualist certaintism, you don&#8217;t want to go that way.  The parallel claim would be &#8220;all knowledge requires perfect certainty&#8221;, and you don&#8217;t want that.  On the picture you&#8217;re trying to paint, you want something like, simply, &#8220;all knowledge requires certainty&#8221;, plus a story about how the contextually-determined certainty threshhold gets driven higher once it is pointed out that one is currently operating short of some still-higher possible such threshhold.  Generally speaking, the contextualist in these debates wants to hook up to gradable terms, maybe even ones that are absolutizable,  but they don&#8217;t want to hook up their target term to the _absolutized_ form of any such term.  Flat enough is flat enough, and need not be perfectly flat, for the contextualist.</p>
<p>Now, it should be noted that  Lewis himself does do this a bit differently.  He does seem to embrace the absolutized form, only to un-embrace it; he  jumps all the way out to it &#8212; and then walks it all back a ways, with his &#8220;psst!&#8221;s.  This is another area where the infallibilist may have resources that the certaintist might not.   The infallibilist can try to use the Lewisian machinery of &#8220;properly ignoring&#8221;, because she can point out, in her theory, those possibilities that are to be properly ignored, and of course he has lots of rules on offer to guide such ignorings.  Certainty doesn&#8217;t seem to have the right structure for that.   You&#8217;re just certain to a greater or lesser degree, end of story.   There&#8217;s nothing like the infallibilist&#8217;s possibilities for any such walking-back machinery to get a hold of, when dealing with certainty.</p>
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		<title>By: Jonathan</title>
		<link>http://jonathanichikawa.net/weblog/knowledge-entails-certainty/#comment-346</link>
		<dc:creator>Jonathan</dc:creator>
		<pubDate>Wed, 03 Mar 2010 19:31:33 +0000</pubDate>
		<guid isPermaLink="false">http://jonathanichikawa.net/?p=201#comment-346</guid>
		<description>Jonathan, I'm not convinced that I'm making a particularly revisionary claim when I say that intuitions don't comprise a very important part of one's evidence. I know that there are a few people who have written on the methodology of philosophy who sign up to that claim -- I think they're wrong -- but I don't see that there's any kind of widespread commitment to a practice that is by my lights erroneous. And I certainly don't see why you think the passage you've quoted in my post commits to such a practice. Are you supposing that when I said that uncertain knowledge was 'counterintuitive', I meant that thing I said to comprise the central evidence counting against uncertain knowledge? I didn't; that was a rhetorical move, designed to remind the reader of the considerations that do count in that direction. (Compare the use of such sentences as "we all agree that p" -- they don't state evidence; they remind us that there is a compelling case for p.)

On allegedly abductive knowledge: this is a bit afield, and really ought to be discussed more thoroughly elsewhere, but the basic line I'm interested in is closer to your trivial interpretation than to your inane one -- but not, I think, in a way that renders it genuinely trivial. I do think that lots of the stuff that most people think is abductive knowledge is genuine knowledge, but I deny that it's abductive. Not merely because E=K -- my view's a bit stronger than that. E = K says that for all knowledge, there is evidence that entails it; I claim that all knowledge is BASED on entailing evidence. Since not all knowledge is self-evident, I make a stronger and less trivial claim. Basically, I think that there's lots of tacit knowledge of bridging premises, and that this tacit knowledge plays an important role in inference.

On circles and perfect circles: as Unger cogently observed, pointing out that something isn't a perfect circle is a pretty good way of convincing people that it's not really a circle at all. So the conditional you say is obviously false is -- wait for it -- intuitive. You're pointing out that it looks like it has crazy consequences, like the consequence that the side of a hockey puck isn't a circle. That's like saying that infallibilism leads to skepticism. The solution to both worries is contextualism.</description>
		<content:encoded><![CDATA[<p>Jonathan, I&#8217;m not convinced that I&#8217;m making a particularly revisionary claim when I say that intuitions don&#8217;t comprise a very important part of one&#8217;s evidence. I know that there are a few people who have written on the methodology of philosophy who sign up to that claim &#8212; I think they&#8217;re wrong &#8212; but I don&#8217;t see that there&#8217;s any kind of widespread commitment to a practice that is by my lights erroneous. And I certainly don&#8217;t see why you think the passage you&#8217;ve quoted in my post commits to such a practice. Are you supposing that when I said that uncertain knowledge was &#8216;counterintuitive&#8217;, I meant that thing I said to comprise the central evidence counting against uncertain knowledge? I didn&#8217;t; that was a rhetorical move, designed to remind the reader of the considerations that do count in that direction. (Compare the use of such sentences as &#8220;we all agree that p&#8221; &#8212; they don&#8217;t state evidence; they remind us that there is a compelling case for p.)</p>
<p>On allegedly abductive knowledge: this is a bit afield, and really ought to be discussed more thoroughly elsewhere, but the basic line I&#8217;m interested in is closer to your trivial interpretation than to your inane one &#8212; but not, I think, in a way that renders it genuinely trivial. I do think that lots of the stuff that most people think is abductive knowledge is genuine knowledge, but I deny that it&#8217;s abductive. Not merely because E=K &#8212; my view&#8217;s a bit stronger than that. E = K says that for all knowledge, there is evidence that entails it; I claim that all knowledge is BASED on entailing evidence. Since not all knowledge is self-evident, I make a stronger and less trivial claim. Basically, I think that there&#8217;s lots of tacit knowledge of bridging premises, and that this tacit knowledge plays an important role in inference.</p>
<p>On circles and perfect circles: as Unger cogently observed, pointing out that something isn&#8217;t a perfect circle is a pretty good way of convincing people that it&#8217;s not really a circle at all. So the conditional you say is obviously false is &#8212; wait for it &#8212; intuitive. You&#8217;re pointing out that it looks like it has crazy consequences, like the consequence that the side of a hockey puck isn&#8217;t a circle. That&#8217;s like saying that infallibilism leads to skepticism. The solution to both worries is contextualism.</p>
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