I've already stated my argument — Michael

But your argument is invalid.

Let me give you a clue. The premise that you need is something like this:

If p is true then p ∨ q is true.
If there is strong evidence that p is true, then p is true.
Therefore, if there is strong evidence that p is true then there is strong evidence that p ∨ q is true.

Unfortunately, the premise that you need is not true, even according to Gettier.

If you have a valid argument but you have a hidden premise, disclose the hidden premise and present the valid argument. I accept your premise, but your argument is invalid as stated. make the valid argument.

It is if you accept the principle that evidence is closed under entailment (or, more specifically, under disjunction introduction), which I do. Although clearly you don't. I honestly don't know how you go about convincing you of it. It's so obvious to me as to be pretty much axiomatic (like disjunction introduction itself). — Michael

No. The argument you presented is invalid. How you go about convincing me is to present a valid argument. I accept the premise, but I reject the conclusion, until you present a valid argument.

If p is true then p ∨ q is true. Therefore, if there is strong evidence that p is true then there is strong evidence that p ∨ q is true. — Michael

That argument is invalid.

"Why wouldn't there be?" is not a justification for your assertion. I have already presented in great detail considerations as to why there wouldn't be, and it is your job to provide some justification, not rhetorical questions. but to repeat myself as demanded, there wouldn't be because logic conserves truth, and justifications are not the same as truths, or guarantees of truth.

I don't think it affects my argument; the implication conserves truth, and justification is no more truth than belief is.

So far as I can see, that brings us right back to the beginning: How, according to you, is recourse to probabilistic analysis of Gettier's puzzles relevant to our evaluation of Gettier's arguments and our assessment of the conception of justified true belief as a criterion for knowledge? — Cabbage Farmer

Ok, let's go back to the beginning. Gettier's claim is that B(p) -> B(p v q) for all q. My complaint about this is that the logic conserves truth, but belief is not truth. Now the difficulty with all the analysis above is that it separates the probable and improbable in order to then apply the rules of logic. The reason for bringing up probability was to try and get at the difference between belief and truth.

Now my suggestion has been that the way to express this is as a disjunction, (p v ~p), which we can annotate with percentages to illustrate the inclination of the belief, thus: (p75% v ~p25%). In this way the belief and the doubt are kept in one expression that can be asserted as true of necessity, and that truth can thence conserved by logical operations.

So then the Gettier disjunction becomes ((p75% v ~p25%) v (q1%)), or S could make the conjunction, ((p75% v ~p25%) & (q1% v ~q99%)). The point being that to make the disjunction with an arbitrary q, the first term must be true100%.

One party states are precisely states that eliminate the space of the political in order to claim it entirely as it's own.

A distinction might help: Claude Lefort famously made the distinction between 'politics' and 'the political', where 'politics' accorded to the realm of the party-room and instruments of the state, while 'the political' encompassed actions in the everyday life of people, protest, words, and so on, up to and including the official mechanisms of the state. When I speak of depoliticization, I mean it in the second sense, and not the first. — StreetlightX

Why not call it disempowerment and oppression? I would guess Arendt has in mind life in the concentration camp as the end state of dehumanisation. And I suppose in that sense, depoliticisation is appropriate; one does not talk about the politics of cattle in the slaughterhouse.

I think this is a rather accurate diagnosis. — StreetlightX

It looks a bit lopsided to me - quite close to Nietzsche's view of Christianity. But to put the doctrine of divine right of kings together with the Quaker anti-slavery campaign, the political machinations of the popes, the liberation theology of S America, and all the manifold entanglements of church and state into one basket of dismissal is a bit simplistic. I see threads of anarchy as strong as the threads of quietism in Christianity.

We hear lot about the ‘politicisation’ of this or that; most recently perhaps the ‘politicisation of sports’ in the US. But what about depoliticization? — StreetlightX

Seems to me that when it it is said that sport has been politicised, it is not that there is a politics of sport in the sense that there is a runners party and a jumpers party, but simply that sport is exploited as an arena for propaganda on other issues. This is rather different from the politicisation of race or gender, say, which is the formation of a social identity and consciousness in oppositional mode. There is a women's movement.

I don't know why the struggle for food should be excluded from politics, it seems an odd notion. Steinbeck's Grapes of Wrath is a political novel that describes - surely - a political struggle, for food, for decent treatment?

the problem of depoliticisation is, perhaps, among the biggest problems we face today. Giorgio Agamben, among others, has gone so far as to declare that, ‘European society today is no longer a political society’ and that ‘political life has become impossible’. While I don’t share Agamben apocalyptic outlook - not yet anyway - I do think the concern is real, and pressing. At the philosophical level, two things are worth stressing. The first is that politics is a 'good'. The attempt to eliminate politics - contestation, world-building, etc - leaves us poorer off. The second is that politics is fragile - if not cherished and cultivated, it might well disappear. Our very status as zoon politikon - political animals, as Aristotle called us - is liable to disappearance. Perhaps the chief political task of the modern age is simply a reflexive one - to keep politics itself alive. — StreetlightX

Again, to make political life impossible is a process of disempowerment; the attack on organisations representative of identities - trade unions, for example, combined with distraction "look at these terrible people disrespecting your flag". Again it seems odd to call a process of disempowerment and subjugation 'depoliticisation', as though a one-party state is non-political.

I almost feel that the entire discussion of politicisation and depoliticisation is a deliberate distraction and disempowerment technique in action intended to delegitimise opposition and justify the entrenchment of the power of vested interests.

We know a song about that.

For some proposition (statement, claim, postulate), p, if attainable evidence is consistent with both p and ¬p, then further knowledge thereof is unattainable. It’s like a difference that makes no difference — not information. — jorndoe

I'd like to see some evidence of this, just to make sure it's not dismissing itself.

IF (probably p) THEN (probably (p V q). — Cabbage Farmer

Yes, it certainly seems on the face of it that a deduction from probable p inherits (at least) the same probability.

IF (Improbably~p) THEN (improbably ~p v q)

This seems to be just as valid, only less probable.

IF (probably p) THEN (probably (p v ~q).
IF (Improbably~p) THEN (improbably ~p v ~q)

And these too. Does that worry you at all? It worries me.

In 1961 Henry Kyburg pointed out that this policy conflicted with a principle of agglomeration: If you rationally believe p and rationally believe q then you rationally believe both p and q. Little pictures of the same scene should sum to a bigger picture of the same scene. If rational belief can be based on an acceptance rule that only requires a high probability, there will be rational belief in a contradiction! To see why, suppose the acceptance rule permits belief in any proposition that has a probability of at least .99. Given a lottery with 100 tickets and exactly one winner, the probability of ‘Ticket n is a loser’ licenses belief. — SEP

Epistemic paradoxes.

So I don't see Smith as overstepping the bounds of reason and landing in a puddle of nonsense. I see him as a victim of chance. Something extraordinarily unlikely happens, and it will challenge his otherwise orderly process of belief formation. — Srap Tasmaner

Well let me ask you a question in return. If you have a reasonable belief p, and a reasonable unconnected scepticism q (say p - that aspirin is an effective painkiller, and q - that Bluebeard's treasure is buried on Easter Island), what is to be gained by forming the disjunction, (p v q) ? How does S advance his knowledge, or understanding or in any way profit from forming his disjunction? Does it enable a test of p, or the building of a deeper theory or something?

According to your calculus, does (p(99%) V ~p(1%)) imply ((p V q)99%)? Or how are your probabilistic weightings related to propositional logic? — Cabbage Farmer

It's not a calculus, merely annotation. In propositional logic, "probably p" or "believed p" does not add up to p, but to (p v ~p)

What here do you disagree with? — Srap Tasmaner

Nothing much.

I'll just note that science, probability, and induction/abduction are what S does to arrive at his belief p. No quarrel with him there.

How do I access the 'just is reality'?.. — Reece

Hush. You just is, already.

IF p, then (p v q). That's valid, sound, true and contentless
— unenlightened

It's only sound if p is true. — Srap Tasmaner

No, it's always sound, because it already has your 'if' incorporated. I put it in capitals so you would notice. It is contentless because it does not claim that p is true. S wrongly makes the claim, that p is true, and then uses this formula to arrive illegitimately at (p v q).

The conclusion of an inference merits no more or less credence than what you grant your premises. If you're uncertain about your premises, then you should be just that uncertain about your conclusions. — Srap Tasmaner

Where do you derive this principle from? It isn't a law of logic. If I might use an analogy, the higher you want to build, the more secure you need to make your foundations. But suppose it is true...

Consider q, that S has no reason at all to believe, except that Jones must be somewhere. Let's say q(0.01%)

Then q is (100 times) less likely than ~p.

The weight of incredibility of q exceeds the strength of credence of the premise, p on which it (p v q) rests.

Aren't you just conflating validity with soundness? — Srap Tasmaner

No.

IF p, then (p v q). That's valid, sound, true and contentless.

But if not, then q can really just fuck off.

What's a person to do then? — Srap Tasmaner

A person is to acknowledge the fallibility of his beliefs and refrain from making arbitrary unconnected pointless disjunctions of them as if they were necessarily true, because they ain't.

The answer is as obvious as my syllogism below, if you want to eliminate people who would otherwise exist (given a natural course of events), then practice birth control — Victoribus Spolia

What makes a course of events unnatural? Is doing it on a mattress unnatural?

So in your view we are only entitled to infer p v q from p if p is a necessary truth. — Srap Tasmaner

No, only if it is an actual truth. Only if it is known, because then it is true. If it is only believed then it may not be true. But in practice, beliefs are normally not known to be knowledge unless they are necessary. But this is not merely 'my view', it is the way logic works, as developed over the millennia.

I still don't see how adding skeptical couching helps to address this specific problem. — Cabbage Farmer

However one couches it, the sceptical element amounts to, by malign accident, improbable circumstance, alternative interpretation of the evidence, or whatever, '~p'.

This gives a weighted disjunction, (p(99%) v ~p(1%)). And that does not lead to (p v q). It's so simple it seems to be invisible to everyone, but as soon as it is possible that ~p, the damaging disjunction (p v q) cannot be made at all.

But to the topic. There is perfect comfort and peace in the tomb, but this side of it easy is boring, and free is easy. We all hate health and safety because they take the pain out of living. The illusion is that we even want to be endlessly happy and never suffer.

Reducing the superfluous complexity of — Bitter Crank

Did you mean "simplifying"? I have always hated the physicalites of writing and typing, and so have developed a somewhat telegraphic style intended to minimise the length to content ratio. Yet a certain amount of redundancy is essential - illustrative examples - repetitions 'in other words', recapitulations and summaries. Style is fascinating and develops, one hopes at least, from the manifold priorities that the individual has for precision, flow, emotional tone, exuberance of language, erudition, and all kinds of everything, ( sorry, I mean 'etc') some but not all of which involve consideration for the 'poor reader'. Sometimes, I actually want most of my readers to be unable to make sense of what I say, because then I don't have to get involved in dealing with too many tedious and trivial responses. And in such cases superfluous complexity is just the jolly old ticket.

The op is what I might call 'Dickensian' in his style and Dickens was not a bad writer, as they go, and not addicted to the avoidance of superfluous complexity, even though he wrote with the intention of being widely read.

Peter gave himself up for lost, and shed big tears; but his sobs were
overheard by some friendly sparrows, who flew to him in great
excitement, and implored him to exert himself. — Beatrix Potter

Now when was the last time you implored anyone to exert themselves? It's hardly appropriate for children these days is it? "Run Spot, run!" is more where it's at.

Mr Lockhart reminds me of the good old days, when cliches were avoided like the plague, and sentences of less than half a page were considered hardly worth reading. I seem to remember finding a sentence of Hobbs at over 600 words; now that must surely be a train worth catching the gist of.

Cabbage Farmer describes Smith somewhere as having a defeasible warrant to assert that p, and that's all he needs. — Srap Tasmaner

No, that's not all he needs, and that is my whole point. From "defeasibly p", (p v q) does not follow. In logic a thing follows or it doesn't; there is no 'defeasibly follows'.

I'm not sure I follow. — Cabbage Farmer

You're not alone, and I wish I could make clearer to others what is very clear to me.

In Case II, he has "strong evidence" that Jones owns a Ford. It's not made explicit how Gettier makes sense of the warrant for "Brown is not in Boston, Barcelona, or Brest-Litovsk". Say: Smith has a good idea of the history of Brown's whereabouts and Brown's plans for the next few weeks, thus believes accordingly it's extremely unlikely that Brown's at any of those three places, so has good reason to assume Brown's not in any of those three places. — Cabbage Farmer

The argument is that if S has a justified belief p, then by pure logic he has a justified belief (p v q), where q is any proposition whatsoever. I don't think he can justify the second belief because it relies entirely on the truth of p, and not at all on the justification or the belief of p. Now to believe p is to believe the truth of p, but this belief is still not the truth of p, but only the belief of p.

Everyone seems to agree with Gettier that we can have justified false beliefs, but this is not reflected or accounted for in the proposition S makes his argument from. He believes p with good reason, but he is not thereby entitled to argue formally from p, but only from (p v I am mistaken about p). And from that premise, he cannot logically move to (p v q), but only to ((p v I am mistaken about p) v q) which is harmless.

If S knows p, then by force of logic, he knows (p v q). This works, because if he knows p, then p is true, by the definition of knowledge. But he doesn't know p and cannot possibly know p, because p is not true, and it is because beliefs are not always true that the truth preserving logic does not work for beliefs.

Yeah, there are people like that. They don't run the country, though, they don't represent a consensus of feminism even, and they are therefore straw women. If you hang out with such people and hear that every day, you need to change your life some, maybe become a refugee.

he had recurrent nightmares of nuclear Armageddon since he was a teen — Wosret

Get him to read The Lathe of Heaven, Ursula LeGuin, one of my favouritest bookses.

Did you actually panic when you saw that? — Agustino

No. I realised I was in a precarious position and paused to consider - left, right, up, down, but not for too long, as the longer you stay in a strained position, the weaker the muscles get. Beautiful place tho.

Logical possibility alone isn't sufficient to justify a position. — Agustino

Of course not. I wouldn't dream of trying to justify it. It's just an observation, that having faced death in that rather graphic way, that was the thought I had immediately afterwards, because it was surprising to me that I was at the top of the cliff not the bottom, and ever since then, the difference between top and bottom, life and death, has just seemed trivially small at the personal level - a clump of grass that does, or does not bear your weight for a second.

But this is not to recommend free climbing with no experience on hundred foot cliffs while on LSD.

Many years ago I took a trip to the Cornish seaside with some friends - LSD it was. So I was scrambling about on the rocks, wondering if the sea shaped the land or the land shaped the sea, when I saw one my friends waving to me from the top of the cliff. So I started to climb up to him. Unfortunately, about twenty feet from the top, and about a hundred and twenty feet from the bottom, I came across a layer of very crumbly rock; I grabbed at the next handhold, and a five kilo lump came away in my hand. I watched fascinated as it floated gently down and smashed itself to dust on the rocks below.

I considered trying to climb down, but climbing down without a rope is much harder than climbing up, because one's eyes are at the wrong end for seeing the next foothold. There was nothing for it but to fly rapidly up the crumbly rock, touching it as little as possible. So I did.

There are two possibilities: either I managed by a miracle to finish the incredibly dangerous climb in spite of being completely off my box, or I am lying broken at the base of the cliff, hallucinating these subsequent 50 odd years as I die. Well actually there are loads of other possibilities as well, but anyway, the possibility of already being dead, and this being an afterlife takes the sting out of death completely.

I need help.

What is real?

I feel stripped of any aspiration/motivation and only have unanswered questions. — Reece

This cannot be real. You are motivated to question, and aspire to answers. Congratulations!

The real is that from which you cannot awaken, that to which you belong whether you like it or not. What we know is that we need help, and that ideals - love, justice, whatever, are not real, except to the extent that we realise them by living them. Welcome to the circle of wakeful dreamers.

We could still have a situation where Smith is right about the probability — Srap Tasmaner

Weasel words these, if you don't mind my saying. If I'm right about something, probability no longer applies. If improbably I have the winning lottery ticket, what are the chances I have won the lottery?

Gettier's paper is a critique of the concept of knowledge, not a critique of belief and justification, and not a critique of the validity of disjunction. It seems to me he takes ordinary epistemological concepts of belief, justification, and truth for granted in his paper. For instance:

If these two conditions hold, then Smith does not KNOW that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.
— Gettier — Cabbage Farmer

Indeed, and this is really annoying. If justified true belief does not amount to knowledge, then what the eff is knowledge and what does amount to it? Where I'm at with this at the moment is that Smith does not arrive at his belief 'p' by formal logic, but by informal induction, and therefore he is not entitled (by logic) to treat his belief as a certainty, which is required to form the disjunction with a random 'q'. If Smith had the humility to assert in the first place, not 'p', but '(p v (I falsely believe p))', which is all he can confidently assert, he would save himself from justified true beliefs that he did not know, and us from a lot of head-scratching.

I predict great success for the hypothesis that it was either coffee or something else. But the issue is getting past tautology and giving some substance to the something else. — Srap Tasmaner

Indeed, the whole idea is that such a formulation is necessarily true. Because otherwise S is only reasoning about his beliefs and giving substance to nothing. "I believe p, therefore I believe p v q." I tells us nothing about the world.

To put it another way, if S or any other philosopher wants to adhere to the strict implications of logic, they have to do so from the start. What is hidden in Gettier's account is what I have been accused of here, which is conflating what S believes with what Gettier defines to be the truth in his world. S believes p, but S doesn't assert ' I believe p', he asserts 'p'. He is not entitled to assert 'p' as a logical necessity, but he can assert my disjunction (p v ae) which is necessary and says in effect 'what I believe is true unless I am wrong in my belief.' It is S's failure to acknowledge in his assertion the real possibility of error on his part that leads him and us into the logical quagmire when he then makes strict logical deductions.

So, I think we agree that "S believes p" does not imply "p". And if we can see that as reasonable people, Smith should also see it as a reasonable person. And if that is the case, he cannot assert p in the first place. Instead, he can only assert a connected disjunction along these lines: "(p, or some other explanation of whatever justifies my belief)". Call that "(p v ae)" (This disjunction is of the either/or variety, I think, so the logicians must amend the formula as necessary.)

And then, even if he is so ill-advised as to form the logically implied assertion, ((p v ae) v q), he is safe from ever believing or seeming to believe q, because (p v ae) is necessarily true, given justification - J, even if the substance of "ae" is that J is a lie, or an hallucination, and so it can be safely reasoned from.

There had been, a long time ago, a study linking coffee consumption to increased risk of cancer. But coffee drinkers are more likely to be smokers. Controlling for smoking, coffee's risk was downgraded. Then it went back up. The latest I think is that there's a risk associated with very hot drinks, not coffee per se.

Tests produce results, but they don't tell you why they produce the result they do. That's why justification can point away from the truth instead of toward it. — Srap Tasmaner

Well you have set up the beginning of a Gettier; Smith reads the study and believes that coffee causes cancer, a JFB. And then he sets up a connected disjunction "coffee causes cancer, or something else that coffee drinkers do causes cancer." Which is perfectly reasonable, and leads to further investigation. It is in fact a way of sceptically questioning his belief. Whereas Smith's arbitrary disjunction per Gettier does the opposite, it relies entirely on the unquestioned truth of his belief to make a claim that has no value in itself and can lead only to the entrenchment of his belief. It neither leads to a test of his belief nor an expansion of his knowledge in terms of Jones' whereabouts or anything else.

And since we all agree that it is possible and quite likely that we we all have the odd justified false belief, our attitude as scientists and equally as philosophers ought to be, because we are justified in being, sceptical rather than complacent concerning our beliefs.

trying to save it from the disjunction case seems like a wasted effort anyway. — Michael

You may be right. I'm just exploring, but the way you tell it, I don't see Max as much of a problem. But I agree that there is a problem with JTB anyway. That's why all this is interesting. Does Gettier 'get at' the problem? Do you or he have a solution? Epistemology is a bit of a mess, and it seems to have infected politics.

Gettier just constructs an artificial example to show how this works. It happens when you think you're testing p but you're actually testing p v q v r. — Srap Tasmaner

Favour us with a less artificial example, you have my attention.

Then what if Smith has strong evidence to suggest that it's water but in fact it's vodka? He has a justified true belief that "the glass contains water of vodka". — Michael

If Smith has a justified belief that the glass contains water, why would he want to think, claim or believe that it contains water or vodka? He wouldn't, he would think claim and believe it contains water - wrongly. The circumstance where he would perhaps form the disjunction is if he saw that it contained a clear, colourless liquid, and that someone had sipped from it (not white spirit then), but didn't know exactly what liquid. If he thinks he knows what is in the glass, he has no reason to think the disjunction. And then it is as arbitrary and pointless as an unconnected disjunction.

Now, how do you test "If really p, then p v q"? — Srap Tasmaner

My view is that you don't test it because it's a matter of pure logic. Science doesn't formulate unconnected disjunctions and then try and establish which arm is true. Nor for that matter does the average Smith. Though logic permits the move, it's not a useful, revealing move as far as I can see.

The sort of thing science busies itself with is connected disjunctions - "the glass contains water or vodka" - and then we get the hydrometer out. "The glass contains water or my neighbour has a beard" is not something it is sensible to consider, never mind claim as a belief, or try and test.

So I don't actually understand your criticism. — Michael

That has been my justified belief for some time. ;)