Strike 'nonsense', replace with 'bullshit'.

Gotcha. But that's not what I'm doing there. I've got three different voices, belief, reality and logic. Logic does not believe anything but tautologies of it's own construction. Reality is infallibly what it is, and Belief has to reach an accommodation with them or talk nonsense.

The bit in bold is the bit that doesn't make sense:

(p ∨ q) ∧ (¬p ∨ q) → q

It's not that at all. It's:

B(p ∨ q) ∧ (¬p ∨ q) — Michael

I don't understand your notation. What's B?

The third step makes no sense in context. — Michael

Yes it does. It expresses the part of the story where Gettier infallibly tells us That Smith is wrong about Jones owning a Ford. It's like when God says "Let there be light". It is so, whether He has gotten around to giving you eyes or not. That's another teaching story, but it works the same way - the story is the story and you have to make sense of it the way it is.

You can do what you like in your diary, or blog, dude.

It's when you want me to read stuff or publish it or respond to it that you have to take account of me.

S believes {1. p , 2. (p v q)}
Reality {3. ¬p , 4. (¬p v q)}
Logic (p v q) & (¬p v q) → q

In a way, this is an ancient problem; Descartes was looking for certainty. Logic cannot cope with a false premise, it falls apart. But false beliefs happen to humans. We need to reason about reality and apply our beliefs to it, but logic only deals in certainties. Reality is never wrong, logic is never wrong, but S and possibly one or two other folk are sometimes wrong. And one wrong belief for a logician leads to explosion.

So S and the rest of us need to take account of our fallibility in reasoning about our beliefs.

Logic never asserts anything about reality. One might say that it it only ever asserts implications - "If (premises) then (conclusion)". Reality is pure infallible assertion "¬p, q ..." So there is never a conflict between them.

But S fallibly asserts p, logically concludes (p v "I am a monkey's uncle"), and ends up lost in the
jungle.

So he needs to keep hold of the fallibility of the assertion, and convey it through the argument in the same way that pure logic prefaces all its assertions with an "if".

So I'm trying to find ways of doing that, with "believably p" or "probably p". And conclusions logically derived from such fallible assertions then have to carry the logical caveat "If really p, then (p v q)"

The result of this is S's belief is not the bald (p v q) any more, but retains the condition (that p) attached to it. S doesn't believe (p v q) unconditionally as Gettier and others here claim, but the conditional, "If really p, then (p v q)".

And this means that he cannot then be said to have the belief Gettier needs him to have, to break the conception of knowledge.

I'm not sure, but I think it gets you ((probably p) v q) and not (probably( p v q)). Help me out a bit here, but I don't think either is sufficient for Gettier, because probably p includes improbably ¬p, in which case improbably (¬p v q) ? So we have probably (( p v q) v improbably( ¬p v q)), which is a whole 'nother disjunction, with which I have no quarrel.

And I'm not willing yet either to give up using or forbid others from using standard rules of inference. — Srap Tasmaner

2. p ⊨ p ∨ q you can keep with my blessing, along with the other rules of inference, because you don't have "p", you only have "probably p" which does not get you to (p v q).

Yes. But my point is that premise 1 is "p", not "probably p and possibly not p". — Michael

Yes yes, premise 1 is p, the disjunction applies, and explosion happens such that Smith believes anything and anything because with authorial infallibility, ¬p. I think I have offered a way out that preserves both knowledge and logic. If you don't want to buy it, find your own way out, or a hole in my logic.

"Possibly" is already in the background underwriting "probably". — Srap Tasmaner

Whatever dude. As long as it is clear that you can't derive the disjunction. Annoyingly, Michael's quote ate my vital strike.

Smith's belief that Jones owns a Ford is true if and only if Jones owns a Ford. — Michael

Smith's belief that Jones owns a Ford is false, Gettier insists. Jones does not own a Ford.

So what?

Isn't this what "probably p" already says? Why do this superposition analysis at all? — Srap Tasmaner

Yes, you could use probably and possibly instead. I think the superposition idea is a neat way of doing it, but if we go your way, we have something like this:]S believes {
1. Probably p & possibly ¬p
2. p ⊨ p ∨ q
3. p ∨ q
4. p ∨ q ⊨ ¬p → q
5. ¬p → q
6. p ⊨ ¬p → q) }

7. ¬p (Gettier's stipulation)

Without the unadorned premise "p", one cannot make the move to (p v q), and Gettier's justified true belief that is not knowledge cannot arise.

2b. Believably (p v q) but conceivably (¬p v q)

That might be more fun.

1. One or both of "Jones owns a Ford" and "Brown is in Barcelona" is false — Michael

No that won't do. Firstly, it is more like your 3 than your 1. And secondly, they could both have been true.

Incidentally, the only mentions I can find of rejecting disjunction introduction are paraconsistent logics. — Michael

That makes perfect sense to me, because what I have done is to divide the claim into two parallel but opposed logical realms, the believable and the conceivable. So the claim "S believes p" is not expressed by S as "p". Instead, because Gettier has had the decency after all this time to let him know that he can have justified false beliefs, S says

1a. " Believably p, but conceivably ¬p." In this way he runs 2 arguments in superposition :

2a. Believably (p v q) but conceivably ¬(p v q)

And so on. And the two lines of argument remain in superposition until either Jones or Gettier confirms absolutely that either his belief or his unbelieved contrary conception is uniquely true, at which point he sensibly discards whichever line starts with the untrue premis.

Yes, I'm with you.

So now we bracket that...

S believes {
1. p
2. p ⊨ p ∨ q
3. p ∨ q
4. p ∨ q ⊨ ¬p → q
5. ¬p → q
6. p ⊨ ¬p → q) }

7. ¬p (Gettier's stipulation)

And we have arrived at my (e), which is the explosion of belief. This is too volatile a situation to be tolerated. One false belief plus formal logic lead to the total collapse of knowledge.

I don't know about anyone else, but I am going to forbid S from moving from 1 to 2 unless p is a tautology, on the grounds that all other beliefs are not certain and therefore have the form "Believably p, but (&) conceivably ¬p". Now if S takes my advice and substitutes this formula for 1, then 2 does not follow from 'conceivably ¬p', and the bomb is defused.

One can be true to oneself, which means acting according to one's own inner feelings, or one can be true what one thinks is expected of oneself, by others. The former implies that the person, while being true to oneself, would be selfish, and might be dishonest to others, while the latter allows for self-deception. Which type of honesty do you think that the therapist wants to inspire in the client? — Metaphysician Undercover

Definitely the former. Part of the ethics of therapy is that the therapist should make clear from the outset, the limits of his support. So one might say, if you tell me of any crime you have committed, or give me reason to think that your own life or that of another is in immediate danger from you, then I must tell the authorities. This is an invitation to deceive the therapist where it is advantageous. "If you want to kill yourself, don't tell me because it is my duty to stop you by force if necessary. If you tell me you're buggering your niece, I'll have to call the cops."

Of course for the competent therapist, being true to oneself is 'congruent' with being true to the client and being dishonest to neither.

What's the problem? — Michael

I think it's called "Gettier" ;) . I'll try and formalise things as best I can.

On your side, we have:

a. If p then (p v q).

And on my side, we have:

b. If (p v q) then (if ~p then q).

The problem with putting these together is that (a) is conditional on p and (b) is a conditional on ~p.

This is not a problem under infallibility since both conditions cannot be met. But Gettier specifies that Smith believes p, but ~p. And this brings both conditionals into play at once. So we now have

c. If S believes p, then S believes (p v q)

d. If S believes (p v q) then S believes (if ~p then q)

This leads to:

e. If S believes p, then S believes that (if ~p then q).

Now (e) states that if S believes p, then S believes that if ~p, absolutely any and every proposition is true, including contradictions. I think it vastly overstates anyone's confidence in their beliefs. I am pretty damn sure that Trump is the president, but not so sure as to believe that if I am wrong about that, a thousand devils inhabit my left knee and also do not. After all, someone might have just assassinated the fruitcake (hope springs eternal). In other words, the formalisms of infallibility do not transfer to fallible beliefs.

I think we both want to escape (e) and our difference is more or less whether it is better to reject (c) or (d).

Edit. It occurs to me that the explosion at (e) is the equivalent of the formalism that from (p & ~p) anything follows. And that is what Gettier has set up for us - Smith believes p but ~p.

That's an implication of p, that I am questioning. Look at the implications of the disjunction that I put to you.

p1. (B v T)
p2. ~B
c1 T

p1. (B v T)
p3. ~T
c2. B — unenlightened

But let's continue with this example, as you seem to be OK with it. — Michael

Let's not. Let's look at the formal implications of a disjunction that I laid out and you ignored.

Yes. I believe Trump is, and Clinton is not. Or to use your informal locution, I believe that one of Trump and Clinton (namely Trump) is president.

But what you present here is a perfectly valid disjunction that I would have assented to before knowing the result of the election "Either Trump or Clinton will be President". You need to do better than keep asking these rhetorical and irrelevant questions. The disjunction is valid because if either one of them was not elected, the other would have been, in other words there is a real connection between the two sides of the disjunction. Now do try and address the argument a little.

Sure, but we're talking about belief. — Michael

So you believe it's Bill, and you don't believe it's Ted. But should it turn out that Bill is not yours, because your wife had an affair, you do not thereby conclude you have fathered Ted.

p1. (B v T)
p2. ~B
c1 T

p1. (B v T)
p3. ~T
c2. B

I think this demonstrates the implications I have indicated, and the necessity of including falsehood in any expression of a disjunction. To believe the disjunction is to believe " if it's not Bill, it must be Ted." And that is unbelievable. But note that when you paraphrase the disjunction informally as "one of the kids in the phone booth is mine", you contrive to avoid the implication by avoiding the disjunction. That's cheating.

Two kids, Bill and Ted. One of them is yours. If it's not Ted, it must be Bill, and if it's not Bill, it must be Ted.

The justification for Smith saying it, is the fact that there is no connection. "Either Jones owns a Ford or Brown is in Barcelona" is Smith's certainty being put on display. The problem, of course, is that Gettier's account is inadequate for properly representing Smith's believing the disjunction. — creativesoul

Exactly so. which is to say it is rhetorical. It only follows and then trivially if he is right about Jones.

This changes with Gettier though. Gettier knows Jones does not own a Ford. Gettier knows Brown is in Barcelona. Gettier also knows that Smith believes the disjunction because Smith believes Jones owns a Ford. If we fill out my solution with Gettier's belief we arrive at a different disjunction(s) than Smith. None of which are problematic. — creativesoul

Yes, Gettier has authorial infallibility. He knows what he knows absolutely in his invented world, and he knows in this instance that Smith does not know what he rationally believes. But since Smith is defined to be rational, he knows that his rational belief p can be false and he knows that its falsehood does not imply the the truth of q. So he cannot believe (p v q) precisely because that implies that if perchance he is wrong about p, then q would be true. It is impossible for him to assent to this because even Gettier tells us, for realism's sake, that he forms several disjunctions mutually contradictory under ~p which is infallibly true, unknown to Smith.

No rational person would think it's reasonable to believe A but unreasonable to believe A ∨ B. — Srap Tasmaner

Then I must be an unreasonable person, because I think that to reason thus: "Probably A, but if not A then definitely B" is cuckoo.

Why? — Michael

Because the disjunction is explicitly saying that one or other may be false. So it does not say p is true it says p might be false, but in case p is false, then q must be true. And it also says that q might be false, but in case q is false p must be true.

But since there is in fact no connection between p and q, there is no justification for saying it.

Now do it with false.

Regardless, you can always apply Gettier's reasoning to the second. — Michael

I don't think you can. Smith's belief that "at least one of two statements, 1 and 2, is true" is not the same as the belief that "statement1 and/or statement 2", for reasons that you have dismissed without criticism. Now Smith, by hypothesis, does not know or understand unenlightened's law, so we must forgive him if he conflates them. Nevertheless, if we asked him to justify his belief, he would say something like, " well I've no idea about 2 but I'm sure of 1 because... " you know the story.

And that would satisfy you, but not me, creative, or Gettier. Gettier says Smith has a justified true belief that is not knowledge, creative says that he does not believe what he says he believes, And I say it's all you logicians fault for neglecting the meaning of language and only looking at the form.

Surely you understand what I mean when I say that one or both of "London is the capital city of England" and "pigs can fly" is true? Because that's all the disjunction is saying. — Michael

Indeed, I understand and accept your conjunction as phrased in the first sentence, because there is a connection made between the statements mentioned as distinct from used concerning their truth or falsity. But this connection is not made when they are conjoined in use in the disjunction. A claim that mentions statements is not identical to a claim that uses them, and your use of quotation marks indicates that you understand that.

""London is the capital of England" is true" means the same as "London is the capital of England" - or so it can be argued, anyway. But it cannot be argued that ""Pigs can fly" is false" means the same as "Pigs can fly". And since the claim is that one statement can be false, the identity you propose cannot be maintained.

"London is the capital city of England or pigs can fly" is true if London is the capital city of England or if pigs can fly, and so if I believe that London is the capital city of England then I will believe that "London is the capital city of England or pigs can fly" is true. — Michael

I believe that there is no connection between the name of the capital of England and the aerial abilities of pigs. So I believe you are making an unjustified disjunction devoid of meaning. All you really believe, and all you can honestly assert is that London is the capital of England. As it happens, I can assure you that pigs can and do fly on a regular basis, but they invariably fly as baggage, so you are unlikely to have noticed them unless you are involved with baggage handling.

The relevance of this is that it solves the problems raised by Gettier, and prevents people from claiming as 'logical truth' certain things that are patent nonsense.

I agree Smith knows what the disjunction means.

Knowing what a disjunction means requires knowing what makes it true.
— creativesoul

Yes, and he believes it to be true. And it's true. So he has a true belief. — Michael

Michael knows what this means:

(c) If unenlightened does the rain dance, it will rain tomorrow.

He also believes it and believes it is justified (because it rains every day) and true.

The guy's clearly not worth talking to. :D

(p1) Whatever unenlightened does, it will rain tomorrow.

(p1) is true, and entails (c). (c) is patent nonsense. Michael has to claim that (c) is not patent nonsense, and therefore has to claim that it does not mean what we all understand it to mean. Only by denying the common meaning can he maintain that logic preserves truth.

But if logic cannot follow the workings of language, and help us untangle sense from nonsense, we might as well forget logic. Language and meaning is prior to logic; logic must enhance our understanding, not ride roughshod over it.

Looking at the problem again, notice that (p1) means that what unenlightened does is unconnected to the rain, whereas (c) makes just such a connection. It is the making of this connection that is illegitimate, and makes a nonsense from sense. So I propose a new rule:

Thou shalt not connect the unconnected. (p v q) for example is empty rhetoric - empty of meaning or false, unless there is a connection between p and q, because it declares that there is such a connection.

Thus we allow, 'Socrates is a man, and all men are mortal', and 'the glass contains water and/or vodka', but not, 'the glass contains water, and/or all men are mortal'.

Looking at that account through the lens of our current concerns, it is perhaps significant that the account of the crisis involves a dissociation from others - a loss of meaning in human relations on the one hand, and a finding of meaning in relations with nature. Personally, I talk to trees on a regular basis, but I would be annoyed if they started to talk back; if I want that sort of relationship, I'd rather have it with cyberspace. But there is a sense in which their silence speaks acceptance...

I would say that hearing voices is a very minor problem, though. I could say that my fingers are taking dictation from a voice in my head, and it would hardly raise an eyebrow, but if I make the trivial mistake of locating this voice outside my body, suddenly, I am dangerously deluded, and suffering from an organic disease. Now suppose, instead of getting in a panic when someone hears trees talk, one interests oneself in what the trees say, then one is focussing on the meaning of one's relationship with that person, rather than the trivial argument about the location of the voice. It is as though someone wants to talk through the agency of a sock puppet to distance themselves from the pain of what they are saying, and the psychiatrist's response is to run about in a panic saying 'socks can't talk, socks can't talk'.

Should we follow the inter-subjective definition which requires that we suppress some natural feelings, or ought we allow natural feelings to flow freely in therapy? Each would be a somewhat opposing sense of "honesty". — Metaphysician Undercover

Do you know of Client centred therapy (Rogers) at all?

Client-centered therapy operates according to three basic principles that reflect the attitude of the therapist to the client:

The therapist is congruent with the client.

The therapist provides the client with unconditional positive regard.

The therapist shows empathetic understanding to the client.

Congruence here is equivalent to honesty. So if it is the case that you do not in fact have unconditional positive regard for the client, then there is no point in pretending that you do, or trying to have a therapeutic relationship. The equivalent in traditional psycho analysis is that one has to have been analysed to do psychoanalysis, the presumption being that analysis frees one from such conflicts, at least to the extent of being able to lay them aside for a hour.

I don't mind agreeing with Gettier if he will allow that his argument and my agreement is meaningless. :)

Yes. To believe that this conditional is true is not (necessarily) to believe that the antecedent is the cause of the consequent. — Michael

Well is this not exactly what @creativesoul has been trying to articulate, that one can assent to the truth only by denying the meaning? When someone says 'Hands up or I shoot', the convention is that if you put your hands up, they don't shoot, and if you put your hands up and they shoot you anyway, you are entitled to be pissed off, and they might as well not have said anything.

To repeat my earlier question, do you believe that this statement is true?

London is the capital city of England and/or I was born in Leeds. — Michael

Michael, try my newly minted Anti-Gettier.

Given that it is the case that it rains every day, do you believe that "if I do the rain dance it will rain tomorrow"?

Logic insists it is true; common sense insists that if you believe in the efficacy of rain dances, you've gone badly wrong somewhere.

I seems to me that the logic of conditionals, conjunctions, disjunctions, fails to take any account of semantic content.

I'm wondering if all the difficulties can be resolved by adding a fourth criterion to the tradition: Knowledge is justified true meaningful belief. This would allow me to answer your question, "No. I believe London is the capital of England, and where you were born has nothing to do with it." And it would allow you to answer me, "No, I believe it will rain tomorrow whether you dance or not"

And these "no's" are denials of significance rather than of logic.

I will say my prayers before bedtime, and/or someone will die in the night. Justified true belief. Forming meaningless connectives is like dividing by zero; there ought to be a law against it.

Here in the Welsh mountains, it rains very nearly every day. Thus (a) is probably true, even though (a1) 'If I have not performed the rain dance, it will rain tomorrow' is also probably true. Does that change your belief in (a)?

I admit that was a bit telegraphic.

inference is not expected to confer truth, but to preserve it. — Srap Tasmaner

Belief, nor justification, nor inference confer truth. Per Gettier, one can have justified false beliefs. Put truth back on the shelf a minute. Consider justification, consider inference. Can we say that inference transforms one or more propositions into another proposition? Can we say that it would be foolish, if not impossible to believe, and thus to honestly assert a proposition one does not believe, unless bracketed in an "If (p)"? So one makes inferences from (justified?) beliefs to new propositions that are justified by the inference. One does not, thought one theoretically could, infer (p v q) from p, because - there's no point, apart from sowing dissent in the ranks of philosophers.

(a) If I have performed the rain dance, it will rain tomorrow.
(b) I have performed the rain dance.
(c) It will rain tomorrow.

(a) is justified inductively (probabilistically?) by the fact (videos enclosed) that I have performed the rain dance five times, and each time it has rained the next day.
(b) is justified by my memory augmented by the video (enclosed).
(c) is justified by inference.

Where is your belief at this point? I'm betting you are somewhat sceptical of (a) because (insert long-winded justification of choice). Your justification and mine are competing, conflicting.

@creativesoul

Well I just waded through all this, and I have to admit to some skimming. I'll make a few preliminary remarks, and see who wants to swallow them whole and who wants to bite their heads off.

1. (p v q) appears to say more than p, but actually says less. 'The glass contains water or the glass contains vodka' says less than 'The glass contains water'.

2. Nobody in the real world forms arbitrary unrelated disjunctions of things they believe and things they have no belief about, or believe to be false, except for rhetorical purposes, or I'm a monkey's uncle.

3. I'm not a monkey's uncle.

4. Logical implication is a justification.

5. Think of a whole number between 1 and 100. I have justification on the grounds of probability for believing that it is not 92. I have the same justification for thinking it is not any of the other numbers. So I can form the propositions: 1. You did not think of 1, 2. You did not think of 2, and so on. All are equally justified, all but one are correct, all are equally believed.

6. Nevertheless, I have no idea which number you thought of.

philosophy is not a frivolous game; not a kindergarten playground for humanity's faint- hearted, sensitive plants. — John Gould

Ah, poor John, did Nursey take your favourite rattle?

The stereotype that seems to dominate is that males are morally inferior.

What could be more negative than saying that a class of humans is worse than everybody not in their class simply due to the way they were born? — WISDOMfromPO-MO

If this were the case, one would expect to find women dominating in matters pertaining to morality, in the judiciary and the priesthood, for examples. But they don't. Quite the reverse, because the dominant stereotype is the exact opposite - that women are morally weaker, and this is part of the justification for male dominance in every other sphere. If the dominant stereotype was that men are morally inferior, we would not put them in charge of everything.

I believe honesty and deception go far deeper than verbal communication. — Metaphysician Undercover

Right. I might have recourse to my stick insect example. The poor stick insect is genetically condemned to, all unknowing, pretend to be s stick. Or a cat is instinctively programmed to stand sideways, raise its hackles, and arch its back under threat in a pretence of being bigger than it is. I remember a schoolfellow who, whenever he was frightened by 'the authorities' broke into a placatory smile, and got into lots of trouble because it was often (mis)interpreted as 'dumb insolence'.

In my mother's case, I never talked to her about the incident, and I very much doubt she was aware of what she did, attached any significance to it, or even remembered it. so my story is all there is of it. But in all these cases, my own feeling is that honesty/dishonesty is not even applicable. Cats, stick insects, the schoolboys, my mother, seem to be 'doing what come naturally'; there is deception perhaps, but no intention to deceive.

Where I find a more agonising grey area, is the notion of self-deception. I can wonder, for example if @McDoodle's father might have been deceiving himself that he was 'doing the right thing' and 'helping his son to grow up' and so on, when in fact he was recoiling from the expression by his son of his own feelings of hurt.

Sometimes, I find that in my shyness I do not say what I should say. Later, I may feel discomfort, a sort of guilt, for not saying what I should have said when the time was right. So I can only interpret this feeling of guilt as being derived from a type of dishonesty which I see in myself. — Metaphysician Undercover

I do understand that shyness can inhibit honest expression, but one could also say that forced expression can cover up honest shyness. So basically you're fucked either way. :D There was this thing a few years ago 'assertiveness training'. It was aimed at women mainly. One of my sisters was into it for a while, and it would have been great if she had actually had anything to assert, but as it was, it became selfish bitch training, I'm afraid.

Anyway, honesty - vitally important but I don't really know what it is. Perhaps we have to say that it is your best effort to respond fully in the moment, in the condition that you're in, as far as you know. And then your second-guesses afterwards are perhaps self insights, or perhaps deceptive self-flagellation, and it will take your best third guess to decide which.

Says man from future?

Did the Romans have a more complicated view of their slaves because they served as tutors and teachers as well as ditch diggers? — Bitter Crank

I don't think it was a race thing at all, but a class thing. But ask a time traveller.