Footnotes to Plato from the foothills of the Superstition Mountains
1) What I know cannot be otherwise: if I know that p, then p cannot be false.
Therefore
2) If I know that a man is walking, then 'a man is walking' cannot be false.
Therefore
3) If I know that a man is walking, then it is necessarily true that a man is walking.
Extra credit: explain the meaning of 'specious.'
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Merry Xmas Bill!
The argument appears to be specious in the sense of being misleading as opposed to plausible (even though both these meanings of “specious” exist, so it makes it an antagonym like “cleave”).
In order to be sound, the premises of the argument must be true. But (1) isn’t true. I can know that p but p isn’t true (unless knowing is understood to be identical with true belief which is not a standard meaning of “know”).
Merry Xmas, Dmitri.
You are right that the premises of a sound argument must all be true, and you are right that (1) is not true. But you haven’t given the reason why (1) is not true.
There is no false knowledge. Therefore, if I know that p, then p is true. But it does not follow from my knowing that p that p is necessarily true. For most of the propositions that I know are merely contingently true. ‘A man is walking,’ if true, might not have been true: if Johnny is walking at time t, he might not have been walking at t: he might have been sitting or in some other posture inconsistent with walking. Johnny Walker is not walking at every time in the actual world, and, a fortiori, not at every time in every possible world in which he exists.
Note the difference between:
a) Necessarily, if I know that p, then p is true
and
b) If I know that p, then necessarily p is true.
(a) is true; (b) is false. There is no false knowledge, but not all knowledge is knowledge of necessary truths.
To confuse (a) and (b) is to commit a scope fallacy. The modal operator in (a) has wide scope, in (b) narrow scope.
As for ‘specious,’ in logic it is never used to refer to valid (logically correct) reasoning or to sound reasoning (valid reasoning from true premises) or plausible reasoning. Specious reasoning is reasoning that (falsely) appears valid or sound or free of informal fallacy, but is none of these.
But yes, ‘specious’ is an antagonym like ‘cleave.’
And why is that? As I understand it, ‘specious’ is from the Latin ‘speciosus’ from ‘species’ which translates the Greek ‘eidos’ which can mean form, figure, shape, beauty. Is there a classicist in the house? There is a long tale to be told here, but I am not equipped to tell it.
Now Dmitri, your mother tongue is Russian, nicht wahr? If so, I must say you are quite en rapport with the English language!
Bro Bill, I had never encountered the idea of a “scope fallacy” before this. Thank you for pointing the thing out.. — Catacomb Joe.
“You’ll never learn younger.” — Grandma Gertrude Maley Odegaard.
Hi Bill
I already knew when answering your quiz that I’m probably going to miss something as modal logic, philosophical logic and epistemology are subjects I am barely familiar with (unlike mathematical logic which I used to study at graduate level and liked). But being right for wrong or incompletely stated reasons is still being right…
Thanks for the explanations — as usual I am more knowledgeable after reading your intelligence stimulating blog. I’d need some time to think about point a). I see a deep metaphysical point/commitment in accepting it. I Googled and saw a paper arguing against accepting what the author calls the “epistemological orthodoxy” https://link.springer.com/article/10.1007/s11406-019-00113-4. The author suggests an alternative conception there: “knowing that p requires at least knowing the truth of p, plus, understanding the content of p.”, but evaluating this paper is not an Xmas eve type of exercise, at least for me. It would be great to hear from you on this subject if you will find it worthy your time.
Re English and me: I’m reading mostly in English for a very long time & enjoy well written word in any language I know.
Dmitri,
“Page not found”
If subject S knows that p, then p is true. (There is no false knowledge.)
Now ask yourself: is the conditional statement necessarily true or only contingently true? I say it is necessarily true. If you disagree, tell me why?
But from NEC (p –> q) one cannot validly infer p –> NEC q.
Exercise: apply the point to ‘Que sera sera.’ ‘Whatever will be will be.’
Louie Armstrong and Ella Fitzgerald chime in. Enjoy.
https://www.youtube.com/watch?v=XApryV3jF0s
The Harvard philosopher Hilary Putnam back in ’62 borrowed the title “It Ain’t Necessarily So” for a discussion article he published in The Journal of Philosophy.
Trivia question: Quine’s essay collection “From a Logical Point of View” is named after which song?
Hi Bill
About my thoughts on whether “If subject S knows that p, then p is true” is necessarily or contingently true. I’m leaning towards the latter because I have a certain problem with a prerequisite to answering this question. In thinking about what is knowledge as opposed to other concepts in the vicinity — especially what is it for a subject S to know P. Why?
What are we to think of “Socrates knows that the Last Fermat Theorem is true”? The theorem is true as was proved not too long ago, but attributing to the historical person Socrates, his genius notwithstanding, this knowledge, even if he in fact held a belief that the LFT is true seems strange to me. This does not appear to be a species of knowledge that can be attributed to the subject.
So I think that “no false knowledge” is a good approximation, but it casts too wide a net as it counts S’s guesses as his knowledge.
Dmitri,
For any proposition whatsoever, IF Socrates knows that p, then p is true. So if Socrates knows that there are no natural numbers x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2, then that proposition (Fermat’s Last Theorem) is true.
Now Socrates never heard of Fermat or his theorem: not only did he not know whether the theorem is true or false, proven or unproven, he did not know the identity of the proposition. But all of this is irrelevant to my question.
It is obviously true that IF any subject S knows that p, THEN p is true. My question: Is the conditional statement necessarily true or only contingently true? The answer is the former. That ought to be blindingly evident.
Bill
I am not in a position to meaningfully argue with you on this subject as I am out of my depth. But it is not completely clear to me whether the conditional ‘IF any subject S knows that p, THEN p is true’ is true necessarily or contingently. Your answer is not self-evident to me. If I understand you correctly, you say that the answer is completely independent of what counts as knowledge (e.g. in my example Socrates’ correct guess counts for you as knowledge whereas to me it is not the same as the genuine piece of knowledge that Wiles arrived at by actually proving LFT). It struck me now that what bothers me with admitting “my” Socrates really knew LFT is that he only knew the theorem as opposed to Wiles who knew the theorem AND proved it.
Hi, Bill. You wrote:
>>But from NEC (p –> q) one cannot validly infer p –> NEC q.<<
Right. If I recall the lesson from modal logic and the Latin of the Medieval logicians, we should avoid confusing the necessitas consequentiae (the necessity of the entailment relation between p and q) with the necessitas consequentis (the necessity of the consequent, which in this case is q).
>>Exercise: apply the point to ‘Que sera sera.’ ‘Whatever will be will be.’<< 'Whatever will be will be' does not entail 'Whatever will be MUST be.' From: □ (If something will be the case, then it will be the case) it doesn’t follow that (If something will be the case, then □ it will be the case) Necessarily, if DeSantis wins Iowa, then he wins Iowa. That proposition is a logical truth and thus a necessary truth. But it doesn’t follow that if DeSantis wins Iowa, it is necessarily the case that he wins. If he wins, which seems unlikely, it will be a contingent fact that he wins. His victory, if it occurs, is not necessary. He doesn’t win in every possible world. It’s not fated to happen. Suppose Haley reasons to herself: “If DeSantis will win Iowa, then he’ll win Iowa. That much is clear. It couldn’t be otherwise. Therefore, he’ll necessarily win Iowa. Que sera sera. I should give up in Iowa and focus on New Hampshire.” In this case, Haley would commit an error of modal logic and likely a political mistake by ignoring Iowa. Her confusing the necessitas consequentiae with the with the necessitas consequentis would lead to a poor campaigning decision.
>>It is obviously true that IF any subject S knows that p, THEN p is true. My question: Is the conditional statement necessarily true or only contingently true? The answer is the former. That ought to be blindingly evident.<< Right. Truth is a necessary condition for knowledge. For any S, S’s knowledge that p entails that p is true.
Elliot,
Thanks for your totally clear and totally accurate explanations in the last three comments.
Dmitri,
How could you possibly (or rather, justifiably) disagree with anything Elliot said above?
I’d like to dig into some of the epistemology in Bill’s post. I’ll try to be concise.
Bill wrote:
>>If subject S knows that p, then p is true. (There is no false knowledge.)<<
Bill’s point is correct. In You Can’t Handle the Truth: Knowledge = Epistemic Certainty, the author (Mizrahi) refers to this point as “the factivity of knowledge” and notes that “It is a commonly held view among contemporary epistemologists that knowledge is factive.”
https://www.pdcnet.org//collection/fshow?id=logos-episteme_2019_0010_0002_0225_0227&pdfname=logos-episteme_2019_0010_0002_0097_0099.pdf&file_type=pdf
Coincidentally, I’ve been drafting a reply to Mizrahi’s argument that knowledge is epistemic certainty. I think there are plausible arguments for the thesis that propositional knowledge entails ep. certainty, but I don’t find Mizrahi’s argument convincing as it stands. Here’s his argument:
(1) If S knows that p on the grounds that e, then p cannot be false given e.
(2) If p cannot be false given e, then e makes p epistemically certain.
(3) Therefore, if S knows that p on the grounds that e, then e makes p epistemically certain.
I’ll post a synopsis of my evaluation here to see if my thinking is on the right track. It seems to me that, though the argument is valid, (1) is questionable. The factivity of knowledge alone does not seem to entail that the proposition known cannot be false given its evidence. To obtain that conclusion, one would need a supporting assumption about the nature of evidential justification, namely, that justification must be infallible. In other words, (1) seems to presuppose something like the following:
If S is justified in believing that p such that the justification is based on evidence e, then S’s belief that p cannot be false given e.
And this assumption requires a supporting argument, since many epistemologists hold that propositional knowledge is consistent with fallible justification. Mizrahi does not provide a supporting argument.
Bill, what do you think about my evaluation so far? Does (1) presuppose that justification must be infallible? And shouldn’t this presupposition be defended given that some epistemologists hold that knowledge is consistent with fallible justification?
(Note: Evidential justification is infallible iff, whenever evidence e justifies p, p CAN’T be false given e. Evidential justification is fallible iff, whenever e justifies p, p CAN be false given e.)
Elliot,
I puzzled over Mizrahi’s article myself a while back. One problem is that he gives no examples. Would the following be an example of (1):
If Tom knows that it is raining on the ground that he sees water droplets on his windshield, then ‘it is raining’ cannot be false given that Tom sees water droplets on his windshield.
But ‘it is raining’ can be false even if Tom sees water droplets on his windshield. For the water droplets might have come from the windshield washer of a vehicle in front of him.
This seems to be the same question you are raising.
We are not told what evidence is. Is the evidence for a proposition itself a proposition?
The distinction between psychological and epistemic certainty is also unclear to me. How could a proposition be epistemically certain out of all relation to a knower?
>>But ‘it is raining’ can be false even if Tom sees water droplets on his windshield. For the water droplets might have come from the windshield washer of a vehicle in front of him.<< Right. It seems that Mizrahi would have to say that the example of Tom is not an example of (1) and that examples of (1) must include infallible justification. The following would seem to be an example of (1): If Tom knows that he is in pain on the ground that he feels pain in his lower back, then 'Tom is in pain' cannot be false given that Tom feels pain in his back. The assumption that justification must be infallible is likely to be rejected by those who hold that knowledge based on fallible justification is possible. One problem with the fallibilist position, however, is that it leaves open the possibility of epistemic luck, which is what Gettier showed 60 years ago (and what Russell recognized before Gettier). Consider this modification of your example: Tom sees water droplets on his windshield and concludes from this evidence that ‘It is raining.’ However, Tom is unaware that the water droplets were produced and delivered to his windshield by the windshield washer of a vehicle in front of him. Thus, Tom’s justification is fallible. Moreover, it is in fact raining where Tom is, but the rain drops have not yet fallen on Tom’s car. Thus, ‘It is raining’ is true. Tom has a (fallibly) justified true belief that ‘It is raining.’ But Tom does not know that it is raining. His true belief is luckily true.
Hi Bill
Elliot’s points are the same as yours. I thought about these points for a couple of days. Truth of p as a necessary condition for S knowing p has a strong intuitive and logical appeal, but there are some edge cases — well known in epistemology as I have understood after some research — that make its universal applicability somewhat questionable. The point that I was making above Socrates and his LFT guess is not a valid counter argument to the necessity of the condition that p is true for S knowing that p. The potentially valid counter cases are similar to the widely popular Russell’s broken clock example. Whether it counts against the principle is doubtful to me as such examples seem to show that one can know p from false evidence, but they don’t show that p itself is false in the world so to speak. On the contrary the truth of p is used to justify the claim that S knows p despite inferring it from a false premise.
If Mizrahi’s argument presupposes that justification must be infallible, one would need an adequate reason for believing so. One reason is that infallible justification seems to be the best way to avoid epistemic luck and hence to solve the various “Gettier problems,” each of which seem to involve such luck.
>>Is the evidence for a proposition itself a proposition?<< Good question. It seems clear that there is non-propositional evidence (e.g., being in a state of physical pain) and that some propositions are self-evident (e.g., ‘2+2=4’ and ‘Murder is morally wrong’) and thus need no other proposition for justification. Agrippa’s Trilemma seems relevant here. If the evidence for a proposition must itself be a (separate) proposition, then either no proposition is justified, or the justification is an infinite chain of propositions, or the justification is found in a circular series of propositions. To avoid these three unpalatable horns, it seems we need a foundational justification such as a self-evident proposition or a self-justifying experience like felt pain or the properly bitter taste of espresso coffee sans sweetener (Which I like! But it’s probably an acquired taste).
Elliot @ 6:34
>>The following would seem to be an example of (1): If Tom knows that he is in pain on the ground that he feels pain in his lower back, then ‘Tom is in pain’ cannot be false given that Tom feels pain in his back.<<
Very good. That sort of example occurred to me. But notice that Mizrahi distinguishes epistemic certainty from psychological certainty and associates the latter with indubitability. This suggests that M. would not take your example as an example of (1).
I distinguish between subjective certainty and objective certainty. I cannot doubt my felt pain. That I am in pain is both objectively certain and subjectively certain by contrast with 'I am suffering from sciatica' which is subjectively certain only.
Elliot @ 9:43
Agrippa’s Trilemma definitely seems relevant to this discussion.
I don’t see how a self-evident proposition could be the justificatory foundation of a contingent proposition. Do you? ‘I am in pain’ if true is self-evidently true. But it could not be the foundation of ‘My pain is due to a pinched nerve.’
But here is a deeper and nastier problem. The properly bitter taste of espresso is not a proposition. It is a non-proposition. Can the justification relation have as one of its terms (relata) a non-proposition? Or must both of its terms be propositions or structured like propositions?
This is the Problem of the Given about which there is a dilemma whch I will write a post about.
Furthermore: is there a distinction between the truthmaker of a proposition and its non-propositional foundation?
Elliot: This coffee is too hot!
Bill: what’s your evidence?
Elliot: It burns my tongue!
Bill: What’s your evidence for that proposition?
Elliot: Burning sensation!
Bill: How can a non-proposition justify (provide evidence for) a proposition?? The sensation is a mere THIS with no discursive structure. How can the ineffable serve as justificatory ground of the effable?
Bill, you wrote:
>>The sensation is a mere THIS with no discursive structure. How can the ineffable serve as justificatory ground of the effable?<<
That is a very good question. I have never thought about the problem in quite that way before. Thank you for that question. I now have a new way to approach the (various) problems associated with justification!
If there is no way to explain how a non-proposition, such as a sensation (with its non-discursive and ineffable qualitativeness), justifies a proposition, then foundationalism (at least some versions of it) seems to be in trouble. And I am inclined to foundationalism! Time to re-think that view!
https://iep.utm.edu/foundationalism-in-epistemology/#:~:text=Foundationalists%20maintain%20that%20some%20beliefs,support%20from%20the%20basic%20beliefs.
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