Don't we ordinarily require them to be well grounded, to be based upon true belief? Bob believed that a broken clock was working. — creativesoul

Yes, for a true claim to be knowledge it must be well-grounded (i.e., all the premises that the claim depends on must themselves be true). But it's impractical to expect Bob to check every premise before he can justifiably make a claim.

That's why there is a difference between knowing that it is 3pm (which Bob doesn't know) and merely having a justified, true belief that it is 3pm (which Bob does have).

However, later you find out the clock is broken, and so you weren't justified after all. — Sam26

I think that people would ordinarily think that your belief was justified (reasonable, warranted, etc.). Here's a filled-out example to illustrate.

Alice: What's the time?
Bob: 3pm
Alice: How do you know?
Bob: I looked at the clock just now
Alice: Ah, OK.

That Bob looked at the clock is what justifies his claim that it was 3pm. He didn't just guess or make something up. I think that, with Alice, we would normally be satisfied with his justification.

If so, then Bob's claim was justified even if the clock were broken and it was really 4pm. In which case he would have had a justified but false belief.

If the clock stopped exactly 24 hours prior and it really was 3pm, then he had a justified and true belief. But he didn't know that it was 3pm. Which is the Gettier problem.

Now we could raise the justification bar and require that Bob check that the clock is working first and perhaps also verify the time against other clocks. But even that could conceivably fail to produce a true belief. And, more importantly, it starts to get away from what we ordinarily require for knowledge claims.

Right, so if aliens observed our usage if the term, then they'd see us using it in instances of when we do know and when we don't. — Harry Hindu

Yes, exactly.

We use it when our knowledge is true, and when it is false. — Harry Hindu

No. Just above you were talking about our usage of knowledge terms ("know", "knowledge", etc.), but now you're talking about our knowledge itself (what we do know), which is always true, never false.

So Alice can justifiably say, "I know it is raining" (if it appears to be raining) but if it is not raining then she does not know that it is raining. She has failed to acquire knowledge.

That difference between the usage and the reality is what the observing aliens notice. But Alice also notices it as well if she subsequently discovers her mistake. She becomes aware that her prior claim was an instance of using a knowledge term when, in fact, she did not know it was raining.

Truth conditions would not be a qualification for it's usage. Only justification. — Harry Hindu

Yes. The truth condition is only a qualification for acquiring or having knowledge, not for the use of knowledge terms.

For you, it seems, one could never say "I possess knowledge", but can only say "I know something". — Harry Hindu

Just to clarify this, one can say both, and they have the same root meaning. So Alice could justifiably say them in the example above. However one only possesses knowledge (or knows something) when one's belief is true. In that example, Alice did not possess knowledge that it was raining (or, equivalently, she did not know that it was raining).

The key point is the distinction between Alice's knowledge claims (which can be false) and Alice's knowledge (which can't be false).

You keep referring to how people use the term and I keep pointing out that people don't use the term correctly if their belief didnt have a truth condition. We agreed on this — Harry Hindu

We didn't agree on this and it's the key issue.

People use the term "know" correctly if their belief is justifiable. It need not be true. They only misuse the term if their belief is not justifiable.

Whereas knowledge is acquired - that is, the conditions of knowledge are met - if, in addition to being justifiable, their belief is true.

There is no guarantee or proof that any particular claim to knowledge is knowledge, no matter how justifiable.

How will she know if her belief is true when she only has justifications from which truths don't necessarily follow? — Harry Hindu

Your question assumes that she needs an infallible guarantee or proof. She does not. She knows her belief is true (if it is) by reflection on what made her belief justifiable (e.g., her observation). If her belief is not true, then she won't know that (unless she later discovers her mistake). That's the logic of the usage.

My argument is that a truth condition is not a qualification for knowledge. Justifications are the only qualifications for knowledge.

Truth is some state-of-affairs. Knowledge can be true or false, which fits how we use the term in an objective sense - outside of our awareness of whether our knowledge is true or not. — Harry Hindu

So, as you see it, knowledge is simply justified belief?

The fact is that relativity does not contradict our everyday experience. Ask yourself, what would have been different from your point of view if simultaneity was absolute rather than relative? — SophistiCat

Indeed. The following Wittgenstein anecdote seems apt here.

[Wittgenstein] once greeted me with the question: 'Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis?' I replied: 'I suppose, because it looked as if the sun went round the earth.' 'Well,' he asked, 'what would it have looked like if it had looked as if the earth turned on its axis?' — G. E. M. Anscombe, An Introduction to Wittgenstein's Tractatus

Another thing to note is that this and other such thought experiments rather cavalierly assume that there is some specific surface of simultaneity associated with each observer. It may be argued that the assumption is natural, but there is no physical significance to it. The standard theory of relativity says that simultaneity is conventional; there is no fact of the matter about simultaneity of distant events. — SophistiCat

OK, though SEP notes that "The debate about conventionality of simultaneity seems far from settled". It seems that what is important here, as with any thought experiment, is to be clear and upfront about the assumptions made.

Philosophy has entered into my thinking about the twin paradox in this way: when some physicists contend that simultaneity at a distance is meaningless, I have a philosophical problem with that. IF I were that traveler, I don't think I would be able to believe that she no longer EXISTS whenever I am not co-located with her. (And I doubt that many other physicists believe that either). BUT many physicists DO believe that she doesn't have a well-defined current AGE when he is separated from her (at least if he has accelerated recently). THAT'S the conclusion that I can't accept philosophically: it seems to me that if she currently EXISTS right now, she must be DOING something right now, and if she is DOING something right now, she must be some specific AGE right now. So I conclude that her current age, according to him, can't be a meaningless concept. That puts me at odds with many other physicists.

What say the philosophers on this forum? — Mike Fontenot

The way I think of it is that every object has a present moment, just as every object has a location.

People on Earth (as with most matter in the universe) age at about the same rate because we all move at similarly slow speeds relative to the speed of light. So for all practical purposes, we can suppose that Alice's present moment on Earth is the same as Bob's on Earth. That is, their planes of simultaneity are approximately the same wherever they are on Earth or whatever their velocity. And so Alice's age in her reference frame is the same as Alice's age in Bob's reference frame (within a tiny error range).

That explains our natural intuition (backed by everyday experience) that other people are a specific and unambiguous age right now.

However if Bob rockets away at close to the speed of light, the present moments for Alice and Bob diverge. Thus Alice's age at the turnaround point in Bob's reference frame will be different to Alice's age at the turnaround point in Alice's reference frame.

The philosophical point here, I think, is that we make a simplifying assumption regarding the present moment because of our everyday experience on Earth. But if that assumption is false (as SR would seem to indicate), then that has consequences for other concepts that depend on that assumption. Such as, for example, what it means for distant objects or events to exist right now. This idea is explored further with the Andromeda paradox.

As you have defined it, you'd have to know that you know it is raining in order to say that you really know that it is raining. — Harry Hindu

In order to justifiably believe that it is raining, Alice needs to look out the window. If her belief that it is raining is true then she knows that it is raining.

In its simplest form, that is all there is to knowledge and that example captures how people ordinarily use the term.

There is no need to "know that you know". Your concern, it seems, is that Alice only has a justifiable belief but is no closer to (really) knowing that her belief is true. But that is to misunderstand the conditions of knowledge. Since she has a justifiable belief, she knows that it is raining just on the condition that her belief is true. There's nothing further she needs to do, or can do, in order to know it. And the same conditions apply when reflecting on her belief - if she knows that it is raining then she can further know that she knows it.

How do you know that you know if knowing and thinking are indistinguishable? — Harry Hindu

What distinguishes them logically is that knowledge has a truth condition, thinking does not. (Or, in Gilbert Ryle's terminology, knowing is an achievement word, thinking is a task word.) Alice can think it was raining at 3pm and later discover that it was not. But she cannot know that it was raining at 3pm and later discover that it was not.

So the two terms have different uses. To say that people used to know that the Earth is flat, for example, would be a misuse of the term "know" given that it has a truth condition and that that belief is unjustifiable today.

But people use the term, "know", to refer things that aren't so. They don't know that they don't know. They think they do, which is why they use the word. — Harry Hindu

If Alice looks out the window before claiming that she knows that it is raining, then her use of the term "know" is justifiable. If her claim is false, then she will not actually know what she thinks she knows. That is, she has used an achievement verb, but has not actually acquired knowledge. Nonetheless, it is a perfectly ordinary and acceptable use, and does not indicate that she doesn't know what it means.

We used to know that the Earth was flat until we learned that it wasn't. — Harry Hindu

Compare with "It used to be true that the Earth was flat" (which is an unconventional use). Since knowledge entails truth, people used to think the Earth was flat (as you say below), but they could not have known it was flat.

We used to think the Earth was flat based on observations. It took a more objective observation to show that we were wrong (looking at the Earth from space). How do we know when we have reached the most objective observation to say that we then possess knowledge? — Harry Hindu

The issue is that in many scenarios, it's possible that the state-of-affairs is such that you could be mistaken no matter how carefully you investigated it.

Short of deductive proof, there is not going to be a guarantee of truth, only criteria that justifies the belief or claim (such as looking out the window when checking for rain). The same goes for finding mistakes. It's not an infallible process but it is a self-correcting process.

Like I said, if people say that they know that it is raining, when it isn't, then how are they using the word that is meaningful? How is how people use the term evidence that they know how to use it? — Harry Hindu

Consider the parallel with people saying that it is true that it is raining, when it isn't. Or simply that it is raining, when it isn't.

People know perfectly well what rain is (and how to use the term "rain"), but can nonetheless be mistaken in a given instance.

That's the case with the term "know". When Alice looked out the window and saw what looked like rain, her belief that it was raining was justifiable. If she later discovers that it wasn't actually raining then she would presumably agree that she didn't know it was raining after all - she was mistaken. So that demonstrates a consistent understanding of the meaning and proper use of the term "know".

Yes. It's the standard dictionary definition, so it shouldn't be surprising to people.

"1. Having or showing knowledge of a subject or situation." — informed - Lexico

We don't have different ideas about what the definition of a duck can include. Acting like a duck entails all the acts of a duck, which includes laying eggs. Looking like a duck entails all the appearances of a duck. There is also the taste and sound of ducks. All of these things together make one a duck. Cherry-picking among them doesn't make one a duck. — Harry Hindu

Correct and that's important. But to say that a duck is all those things together that make a duck leaves us none the wiser about what a duck is. Neither does saying that a duck is whatever acts and looks like a duck. Both those definitions instead rely on a prior intuition (or definition) about what ducks are. For a definition to be useful, it needs a genus and differentia.

We don't even have to use words to define what it is to be a duck. We just observe, over time, the similarities and differences between different organisms and group them in our minds without the use of language. — Harry Hindu

So differentiating and grouping (categorizing) just is the activity of defining noted above. Language is not fundamentally about arbitrary word symbols and sounds, but about the objects and activities they pick out. So we can ask about what people are doing when they use the word "know" or "observe". How are they using the term and what can we learn from an analysis of that use?

If we can only know what something is (like knowledge) by empiricism, then knowledge doesn't fall into your category of propositional knowledge. It isn't something pre-defined like who won the World Series in 2004. — Harry Hindu

Knowing that it is raining outside is an example of propositional knowledge (the proposition being, "it is raining outside"). If you look out the window and see what looks like rain then you can justifiably claim it is raining. If it is raining (the truth condition), then you know that it is raining. Whereas if someone was hosing the window while watering the garden, then you don't know it is raining (even though you may think you do).

The principle is the same whether talking about rain or the Red Sox. People can be informed (knowledgeable) or mistaken about either.

Right, so truth is a condition of observations. — Harry Hindu

OK. Another way to put it is that 'observe' and 'know' are achievement verbs (Gilbert Ryle's term). You can't observe what isn't there or know what isn't so.

Right. And you can then know that you reflected by reflecting upon the reflection, ad infinitum. — Harry Hindu

Yes, if you wanted to do that.

Is knowledge an infinite regress of aboutness? Or is knowledge some kind of set of rules for interpreting sensory impressions? To know that you reflected upon what you reflected seems to just be applying the same set of rules to some sensory impression or thought process. Sometimes the rules we have don't work and we have to come up with new ones. — Harry Hindu

Justification (or warrant) comprises the rules that warrant someone making a knowledge claim. For example, your looking out the window warrants your claim that it is raining (or not raining). If the claim is true then knowledge has been acquired. (Gettier counterexamples aside which imply a further condition.)

The connection with language use is just that this is how we ordinarily use terms like "observe" and "know". But, of course, we can be sometimes be mistaken about what we think we know (such as when reading the time of a stopped clock).
— Andrew M

Right, so mistaken, or false, is a condition of knowledge. — Harry Hindu

No. Note that I said "think we know". You can't know false things. So if a mistake is discovered then any claim to knowledge is retroactively retracted. For example, if I later find out that the clock was stopped then I also realize that I didn't know that it was 3:00 earlier despite my claim back then being warranted.

It is true that the clock says 3:00. You assume from experience (knowledge, or your rules that you have learned about what clocks do) that it is 3:00, until you observe another clock that says something different. Observations check our knowledge. — Harry Hindu

Observations check our knowledge claims. A knowledge claim (or justified belief) can be false, knowledge can't. You can be warranted in making a knowledge claim (such as with the 3:00 example) but such warrant doesn't guarantee that the claim is true.

I asked how do you know some statement is true when we seemed to agree that observations determine truth, not language use. So truth is a condition of observations, not of language-use. — Harry Hindu

You can only observe that it is raining if it is raining (if that's what you're referring to).

I also asked how knowledge can be turned on itself to say things like, "I know that I know". Isn't that similar to saying that "I observe that I know"? — Harry Hindu

If I know that it's raining because I observed rain, then I can also know that I observed rain (by reflection). In that case, I would also know that I know (that it is raining).

The connection with language use is just that this is how we ordinarily use terms like "observe" and "know". But, of course, we can be sometimes be mistaken about what we think we know (such as when reading the time of a stopped clock).

Ducks are a particular type of species - ones that produce fertile offspring. Ducks are part of the genus we call "birds", because they have wings and feathers. Human actors and robots are of a different category altogether with one of the attributes that defines them is their adaptive abilities and ability to mimic other organisms to a wide degree. — Harry Hindu

Yes. So a robot could be built that had wings and feathers. In that sense it would be like a bird. But it would not be a bird even if we couldn't easily distinguish them. That's because a bird has other characteristics that it inherits from its genus (such as being a living organism) that serve to exclude robots.

Of course a different usage could arise that does combine bird-like robots and birds, but we're investigating the usage we currently do have.

What is propositional knowledge vs other kinds of knowledge? — Harry Hindu

It is common in epistemology to distinguish among three kinds of knowledge. There's the kind of knowledge you have when it is truly said of you that you know how to do something—say, ride a bicycle. There's the kind of knowledge you have when it is truly said of you that you know a person—say, your best friend. And there's the kind of knowledge you have when it is truly said of you that you know that some fact is true—say, that the Red Sox won the 2004 World Series. Here we will be concerned with the first and last of these kinds. The first is usually called “knowledge-how” and the last is usually called “knowledge-that” or “propositional knowledge.” — Knowledge How - SEP

Saying that truth is a condition of propositional knowledge is also saying that false is property of propositional knowledge. — Harry Hindu

No it isn't. Per the example above, we know that the Red Sox won the 2004 World Series. But no-one can know that they lost it, since they didn't lose it. That's what it means for truth to be a condition of knowledge (and not falsity).

A handy feature I just found if you want to see the source of an equation in another post.

Right-click on the math and select "Math Settings | Math Renderer | Plain Source" from the context menu. You will then see the text that goes between the [ math]...[ /math] delimiters. The default renderer is HTML-CSS.

What you just wrote, is indeed the gist of it. I wonder if the proof can just be phrased like that? Would it still be considered a proof? — alcontali

I think so.

Concerning the expression in B, instead of being true for all true sentences, it will be true for all false sentences. So, B is then an instance of the diagonal lemma that is (false,false) for function ~f.

The whole point of the proof is that the practice of requiring that a sentence stays off the diagonal for f will always force the sentence onto the diagonal for ~f. This is the case for both true and false sentences. — alcontali

Yes and renaming ¬f to g makes that visually clear:

$\begin{align}(s\wedge g(\ulcorner s \urcorner)) \vee (\neg s\wedge \neg g(\ulcorner s \urcorner)) \end{align}$

I think that the main issue left now, is to come up with a succinct way of phrasing this principle. — alcontali

Yes, in effect, with the negated lemma you have $s \leftrightarrow g(\ulcorner s \urcorner)$ for all logic sentences s.

No, because now we can recognise that there are two distinct questions here - "what is knowledge?" and "when do we have knowledge?" — Bartricks

Thanks for your reply, just one question below for the moment:

sometimes we can have knowledge without a justification — Bartricks

What is an example of that, on your view?

How else do you find out what something is, except empirically? — Harry Hindu

Glad we agree!

Can a human actor or a mechanical robot lay an egg like a duck? No. Of course not. So you can distinguish between human actors or mechanical robots and ducks because human actors or mechanical robots can't behave (and look) exactly like a duck, or else how would you be able to distinguish between the them to be able to use different terms to refer to them? — Harry Hindu

Yes, they are distinguishable. But we seem to have different ideas about what your duck definition can include. The common definition for a duck specifies the genus which serves to exclude other things that just happen to have a similar appearance or behavioral characteristics.

Yes, so either something else is interfering with Mercury's orbit, or we need to posit a different theory, in which case our knowledge would change. Is knowledge something that can change, or is it a black and white case of either you have it or you don't, and if whether you have it or not is dependent upon whether it is true or not? — Harry Hindu

I'm of the view that truth is a condition of (propositional) knowledge which I regard as a thesis about how people ordinarily use those terms.

Do you think it works? — alcontali

Still thinking about it, but a couple more things. When you consider A, I think you can omit the s1 discussion and just note that A is an instance of the diagonal lemma that is (true,true) for function ~f. So, per the negated lemma, A can't be true.

But that still leaves disjunct B that could be true. So you would also need to show a case where B fails.

I think the negation of the lemma needs to contain a disjunction as follows (since for the negation every tuple must be either (true,false) or (false,true)):

$\begin{align}(s\wedge \neg f(\ulcorner s \urcorner)) \vee (\neg s\wedge f(\ulcorner s \urcorner)) \end{align}$

Let's now look at A: $\begin{align}s\wedge \neg f(\ulcorner s \urcorner)\end{align}$. It must hold true for every sentence s. — alcontali

Shouldn't this be that it must hold true for every true sentence s? The conjunction is simply false when s is false. (Whereas B handles the case where s is false.)

Take Russell's case of the stopped clock. Well, in that case it seems as if the fact the true belief was acquired by fluke explains why Reason did not adopt the knowledge attitude towards it. Thus her 'reason' (in the 'explanatory' sense) for not adopting the knowledge attitude towards that true belief was that it was acquired by fluke. — Bartricks

OK.

So I see no reason - no justification, no normative reason - to think that Reason has no reasons. — Bartricks

OK. So we can investigate why Reason adopts a knowledge attitude towards some beliefs and not others, such as the 'no fluke' condition above.

Thus we can say that what beliefs count as knowledge are the beliefs that Reason adopts a knowledge attitude towards. And the beliefs that Reason adopts a knowledge attitude towards are those that are justified, true and something else to be determined (such as the 'no fluke' condition).

So aren't we, in effect, back where we started? That is, we are inquiring about the conditions of knowledge, albeit mediated by Reason.

I do not think those are the same question. The latter has as no definitive answer - it would be like asking me why I find delicious what I find delicious (it varies) - but is also irrelevant to the question at issue. The question at issue is what knowledge is, not why it exists. — Bartricks

So Reason has no reasons, as it were. She is inscrutable.

As for the former question - well, our reason is our source of insight into what Reason approves of.

Take the Gettier cases mentioned earlier. It used to be thought that possession of a justified true belief was sufficient for knowledge. But then Gettier cases are brought to our attention. And, for most of us, it is clear enough to our reason that the subject in a Gettier case lacks knowledge even though they possess a justified true belief. Now, that isn't arbitrary - people are not just randomly deciding, on the basis of nothing at all, that the subject in a Gettier case lacks knowledge. No, their reason tells them that the subject in that case lacks knowledge. — Bartricks

It seems that you regard human reason as a kind of intuition or feeling that derives (however imperfectly) from Reason. Through a glass darkly, so to speak.

If so, do you regard it as futile to try to determine the conditions for knowledge? That there just are none (other than emanating from Reason)?

But that feeling - the knowledge feeling - does make a belief into knowledge when Reason has it towards a belief. That's what I am proposing, anyway. — Bartricks

How would we distinguish between those beliefs Reason approves of and those she does not?

Or to put it another way, why does Reason approve of the beliefs she does?

I don't see how you can define knowledge in such a way and then say that a person fits that definition yet doesn't possess knowledge. It's like saying, "It walks, talks and acts like a duck, but isn't a duck". — Harry Hindu

The issue is that we're trying to empirically find out what knowledge is (or, linguistically, how people use the term), not legislate it.

A human actor or a mechanical robot that walks, talks and acts like a duck satisfies the above definition, but isn't a duck.

Why doesn't the person have knowledge if they fit all the requirements? Find what is missing and make it part of the definition. — Harry Hindu

Right. So JTB is like Newton's theory of gravity. Newton's theory predicts the planet's orbits really well. Except for Mercury. So the question just is to find what is missing (or to posit a different theory altogether).

Here is my proposal: for a belief to qualify as knowledge is for Reason to be adopting a certain attitude towards your possession of it. Sometimes the presence of luck will mean she does not adopt that attitude towards your possession of it; sometimes it will not. — Bartricks

The ancient Greeks called her Athena. These days she's the natural patron of universities and apparently it's well worth seeking her favor.

It is traditional at exam time for students to leave offerings to the goddess with a note asking for good luck, or to repent for accidentally breaking any of the college's numerous other traditions. — Athena

Now, I have argued that Reason is a person - a mind, a thing - not just stated it. So, you need to defeat this argument before you're entitled to use the term 'reify'.

1. Reason makes assertions
2. Minds and only minds can make assertions
3. Therefore Reason is a mind

Otherwise all you're doing is describing my view and using a term to describe it that implies it is mistaken. But you're not showing it to be mistaken at all. So, do you dispute 1 or 2? — Bartricks

I dispute 1 and 2.

Per premise 1, I can point to people making assertions. But you can't point to reason making assertions since it is an abstract term. Premise 1 depends on personifying (anthropomorphising) an abstraction.

Minds - or persons, or 'subjects of experiences' the terms can be used interchangeably (I certainly use them interchangeably) - are the only kinds of thing that can make assertions, or value anything, or command anything, or hope, or desire, or prescribe. — Bartricks

That's an unusual usage. As defined here, "mind" ordinarily refers to a faculty or ability of a person, not that it is a person. Anyway since they're interchangeable for you, I can just read your use of "mind" as "person".

I have argued that Reason is a person, a mind, a subject of experiences and I am talking about her accordingly. — Bartricks

My argument is that you're reifying an abstract term (reason) as something substantial. And your motivation, it seems, is that you want to model assertions as a kind of performative utterance. So Reason is posited as a mistake-proof assertor, analogous to the meeting chair who adjourns the meeting. But that outcome should be an indicator that the model doesn't fit.

Now, if you assert something to be the case, you are claiming it is true. That is, you are representing it to be true. But no matter how sincerely one does that, it remains the case that what is actually true, and what we represent to be true, are not necessarily the same. There's a gap. So, truth is not plausibly constituted by my assertions — Bartricks

Agreed.

- and my evidence that it is not, is that Reason asserts it not to be. — Bartricks

The evidence that it is not is that we can recall assertions that were later shown to be mistaken. Or point to two people making contrary assertions, only one of which can be correct.

Truth is simply a function of a meaningful assertion in some context. For example, this is an apple (points to apple), this is a table (points to table). If the apple is on the table (the context) and Alice asserts that the apple is on the table then her assertion is true.

No, Reason would have to be a person - a mind - because Reason asserts things (and values things, and prescribes things) and minds and only minds can assert things (and value things, and prescribe things). — Bartricks

Mind isn't a person. Mind is an abstraction that refers to a person's ability to think and reason. Only a person can assert things.

What could the solution to world peace be if not whatever Reason asserts it to be? I mean, when we try and figure out what the solution to world violence is, what are we doing? Consulting our reason, surely? — Bartricks

You seem to be treating reason as a homunculus. But consulting your reason is not like consulting your lawyer. It is instead a metaphor for thinking intelligently about something.

Note too that an analysis of truth is not going to give you the answer to substantial questions about what's true. — Bartricks

Agreed. But in this case, an analysis of truth has yet to be made. Positing Reason as a person who asserts truth just pushes that analysis back a step (like the homunculus) while creating the illusion of having provided it.

So, we will be happy we have the true theory of truth when our question "what is truth?" is answered with proposition whose representative contents seems to all rational reflectors to be something Reason is asserting to be the case.

If that's true - and I don't see how a reasonable person could deny it - then that itself should be what we consider truth to be. That is, truth is the property of being a proposition that Reason asserts to be the case. When Reason asserts that something is the case, it is the case. Her asserting it, and its being true are one and the same. — Bartricks

Isn't that like saying that the solution to world peace is what Reason asserts it is?

Also capitalized Reason is poetic, but what does it refer to? Our everyday reasoning? A God's-eye view?

But it makes comments about the error on the following posts confusing. — Brett

You would just provide appropriate context if need be. For example, include an asterisk next to the correction and at the bottom of the post note the original mistake and perhaps credit Janus for pointing it out. That's the kind of thing news articles do (including, as it happens, the NY Magazine article you linked to).

Well I don’t like to actually edit an OP. My correction is still clear at the bottom. — Brett

Some people won't bother reading that far if they encounter glaring mistakes. Correcting such mistakes just makes it easier for your readers.

Edit: and Janus had corrected it in the following post. — Brett

I know. But my first impressions of your OP had already been formed. Anyway, just a suggestion.

Edit: obviously my year 3000 figure is wrong. My poor maths. — Brett

It could be useful to your readers if you edited your original OP with the corrected figure. And also provided a link to a relevant scientific study or UN report.

We can see, given the facts, what ought be done; and yet do not act. — Banno

Maybe people think there is no relation between is and ought?

That may be a philosophical problem...

Imagine tomorrow the proposition "p & ~p" becomes somehow true! — Pippen

A possible analogy: The rules of chess specify that players can only move a bishop along the diagonal. Moving the bishop vertically would be invalid. Suppose, tomorrow, a player moves the bishop vertically. One response is to reject the move. Another response is to change the rules of chess to accommodate the move.

The conventional rules of logic include the law of non-contradiction (LNC) which specifies that it is impossible for states-of-affairs p and ~p to obtain simultaneously. Or, propositionally, that propositions p and ~p can't be true simultaneously.

Suppose per hypothesis that, tomorrow, "p & ~p" becomes true. One response is to reject the hypothesis. That is, to say that such a scenario is impossible and thus cannot obtain. Another response is to change the rules of logic to accommodate the scenario.

Now the "changing the rules" response - rejecting the LNC - collapses to trivialism. (Note: unless explosion is also rejected, as with paraconsistent logics.)

Whereas under the existing rules the hypothesis that, tomorrow, "p & ~p" becomes true is, per the LNC, provably false. Thus, according to the existing rules, this scenario couldn't happen tomorrow.

Isn't that a proof by example that logic is not necessary? — Pippen

Not if the rules of logic include the LNC. But note, as with the chess example, one can always propose one's own rules. However they may have undesirable consequences (such as trivialism).

If, as the experiment reveals, the outcomes are indicating the system (person A and the dice) is objectively probabilistic, then it must be that the initial states are probabilistic. After all the outcomes are determined by the initial states.

What do you think? — TheMadFool

That is a consequence of how you've defined the system. It seems to me that what you're pointing out is just that a predetermined initial state is incompatible with objective probabilities.

A simpler example would be a computer simulation of a hundred dice throws. The results appear random to an observer, but they are merely the outcome of a complex deterministic algorithm. With the same seed, the results are repeatable on subsequent runs.

The only issue then is how the initial state (the seed) is set - whether to a predetermined value or to a random external input.

In turn, accepting inconsistency seems to take one out of the bounds of meaningful language.
— Andrew M

Not really. It just means trivialism, i.e. everything becomes true, but I can still talk and be understood on an ostensive level. That sounds enough meaningful to me. — Pippen

On trivialism, the statement of mine that you are disagreeing with is trivially true. So your disagreement assumes non-trivialism (i.e., you think my statement is false). Can you give an example of ostensive talk that doesn't assume non-trivialism?

Back to Hume. How does he prove that logic is not a matter of fact but something higher? IMO he can't, so his "fork" is pretty much made up from speculation and tradition. — Pippen

I think you're right.

But your answer implies that it could happen and so we'd need to adjust our logic and math, — Pippen

As I see it, if the world seemed inconsistent then that would point to a problem of representation, not that the world was inconsistent. That's the approach physicists have taken with quantum mechanics since it is standardly represented using classical logic and algebra (though, of course, new mathematics such as matrix mechanics was developed).

but that means the problem of induction also applies to logic and math so why did Hume not agree? — Pippen

As you may know, Hume drew a distinction between "relations of ideas" and "matters of fact and real existence". For the broad ramifications of that, see Hume's fork. If one inquires whether the "relations of ideas" are themselves "matters of fact" then the distinction starts to break down or become circular. So the problem of induction only makes sense in a context of deductive certainty per Hume's distinction.

If that distinction is rejected, then you are left with something like an Aristotelian view (or pragmatic view) where the meaning, or use, of terms like "possible" are understood in the context of the law of non-contradiction or ostensive demonstration. In turn, accepting inconsistency seems to take one out of the bounds of meaningful language. But one needs meaningful language to state one's position in the first place.

1. We know that the system (person A and the dice) is deterministic because person B can predict every single outcome.

2. We know that the system (person A and the dice) is probabilistic because the experimental probability agrees with the theoretical probability which assumes the system is non-deterministic.

There is a contradiction is there not? — TheMadFool

If there is a contradiction, it is only in how the system is being represented. In this scenario, person B has complete information about the system whereas person A has only partial information. The difference is not in the system but in the information that each person has.

Which is to say, you can represent the system (person A and the dice) from either person A's point-of-view or person B's point-of-view, which avoids contradiction.

I wonder, what does the realist say about abstracts/mathematics; is it something human's created, or did it always exist and we just uncovered/discovered its truth... ? — 3017amen

It depends on the realist - what they think about concrete or physical things doesn't necessarily apply to abstract objects (or universals). For example, W.V.O. Quine was a nominalist while Bertrand Russell was a Platonic realist. Other options are also available such as Aristotle's immanent realism. Here's a useful taxonomy of the various alternatives.

Again: Why is it impossible that we wake up tomorrow in a world where one tiny particle has the property to be and not to be (which would make the whole world inconsistent)? That would make MP invalid and kill all our logic, right? — Pippen

No, we would just look for ways to model the world that avoided inconsistency. Which is just what occurs in quantum mechanics where the state of a particle in superposition is represented as the sum of two or more distinct states.

What that means is a separate question.

I basically agree. Practicality and efficiency render skepticism unhelpful in terms of getting on with our daily lives; however, this wouldn't by any means render the initial argument null and void. — PessimisticIdealism

Right, the argument shows that one can't know that realism is true (via contradiction).

Interestingly, we can see what is going on here via the earlier hypothetical of the apple. We can posit that no-one in Bob's world, including Bob, knows that the apple is there. That demonstrates the realist premise since, in the hypothetical, the apple exists independently of being known to exist. But it is also impossible for any actor in that world to know that the apple independently exists at precisely those times that they don't know it exists.

So my only disagreement is with your final conclusion. I think realism is the operating assumption for everyday communication and the growth of knowledge (and is therefore tenable) but is not, itself, something that is known to be true.