Specifically, it says that an uneaten chicken cannot be eaten without ceasing to be an uneaten chicken, so we cannot logically speaking eat an uneaten chicken.

Note that we also cannot eat a chicken that has already been eaten. And since a chicken is either eaten or not eaten, it follows that logically speaking, we cannot eat any chicken. — Olivier5

Logically speaking, you can't have your chicken and eat it too.

To be clear, the difference with that to the knowability paradox is that "p & ~p" is a contradiction - it can never be true. Whereas "p & ~Kp" is not a contradiction. It can be true, but never known to be true.

Indeed, and that's the point. When we discover that a former knowledge claim was mistaken, we retroactively downgrade its status from knowledge to belief. We say that they didn't know it after all, since we no longer believe that it was true then.
— Andrew M

But this misses the point that what we used to call knowledge wasn't knowledge in light of new observations, but observations is what allowed us to assert knowledge that we didn't have in the first place. So how do we know that we've made every possible observation to assert we possess knowledge? — Harry Hindu

We don't. But "every possible observation" is not the standard for making knowledge claims or forming beliefs. Good evidence is. If good counter-evidence emerges, then we should change our minds and retract the former claim.

You can look out the window at the moment your trickster brother sprays the window with a hose. — Harry Hindu

In which case you wouldn't know it was raining, you would just think you did.

Is it possible to believe a truth? How would that be different than to know a truth? — Harry Hindu

Yes. To know it also requires good reason, or evidence, or justification.

How do we ever know that we have all the evidence necessary to assert knowledge over belief? — Harry Hindu

Your question assumes a standard of infallibility or Cartesian certainty. But you can say that you know it is raining (or not) by simply looking out the window. That's the relevant standard for making knowledge claims.

The proposition "Joe Biden is President of the United States" was known to be false in 2016 and is known to be true now. — Michael

I'm not saying you're wrong; I'm merely noting that what you have said appears to contradict what @sime has said. Does the Fitch proof use a non-standard meaning of "knowledge", perhaps?

I note that the SEP article defines the epistemic operator "K" as:

‘it is known by someone at some time that.’ — SEP article

This also appears to be different to sime's statement that:

the epistemic operator K is usually assumed to be factive and used in the future-tense in standing for "Eventually it will be known that ...", where K's arguments are general propositions p that can refer to any point in time. — sime

To be clear, the difference with that to the knowability paradox is that "p & ~p" is a contradiction - it can never be true. Whereas "p & ~Kp" is not a contradiction. It can be true, but never known to be true. — Andrew M

Yes, but for the exact same reason than you can't eat an uneaten chicken. Fitch says that one cannot know an unknown truth, because as soon as one knows it, it cease to be an unknown truth. Likewise the Olivier5 chicken paradox states that one cannot eat an uneaten chicken, because as soon as one eats it it ceases to be an uneaten chicken.

Like in Fitch, one of two things follows from the Olivier5 chicken paradox: either not all chicken can be eaten, or all chicken have already been eaten (omnigallinavorousism).

I lean toward the former: not all chicken can be eaten.

Like in Fitch, one of two things follows from the Olivier5 chicken paradox: either not all chicken can be eaten, or all chicken have already been eaten (omnigallinavorousism). — Olivier5

You haven't explained the logic behind your "chicken paradox". And as I mentioned here your symbols were wrong anyway.

Fitch says that one cannot know an unknown truth, because as soon as one knows it, it cease to be an unknown truth. — Olivier5

And as I said here, you're equivocating. There's a difference between saying that we cannot come to know something that wasn't known before and saying that something cannot be both known and known to be unknown. Fitch is saying the latter.

Knowability principle: p $\to$ ◇Kp where the epistemic operator K = know

Non-O: There's an unknown truth = p & ~Kp

Substituting (p & ~Kp) in the knowability princple, we get:

(p & ~Kp) $\to$ ◇K(p &~Kp)

Now, foe Fitch's argument to work, the following hasta be true:

◇K(p &~Kp) $\to$ K(p & ~Kp). None of the rules used by Fitch in the SEP article allow this move. Also, intuitively, it looks/feels wrong.

◇K(p &~Kp) → K(p & ~Kp). None of the rules used by Fitch in the SEP article allow this move. Also, intuitively, it looks/feels wrong. — Agent Smith

Compare with:

1. If God is omnipotent then it is possible for God to create a rock that he cannot lift
2. If God creates a rock that he cannot lift then ...

Fitch is using the same reasoning:

1. If p is true and not known to be true then it is possible to know that p is true and not known to be true
2. If it is known that p is true and not known to be true then ...

:ok:

Such an important step and the rule is left unmentioned. Odd!

You haven't explained the logic behind your "chicken paradox". And as I mentioned here your symbols were wrong anyway. — Michael

My "chicken paradox" follows the exact same structure as the "Fitch paradox" and should thus rightly be called the "chicken transposition of the Fitch paradox".

If there is a flaw in my chicken paradox -- as I strongly suspect is the case :razz: --, then the exact same thing is wrong with Fitch.

You pointed yourself to that flaw here, as I and many others have done before you, about the non-chicken version of Fitch.

Let me walk you through this. You pointed out:

It is possible for us to later eat something that is currently uneaten, or for something that we have eaten to have before that time been uneaten. It isn't possible for us to eat something and for it to remain uneaten. — Michael

Transposing your point to Fitch (eat --> know)

It is possible for us to later know something that is currently unknown, or for something that we know to have before that time been unknown. It isn't possible for us to know something and for it to remain unknown.

Note the flagrant similarity with this point of mine, about Fitch:

If in the formalism of Fitch you introduce the idea that knowledge changes over time, you may arrive at something that in English means: he now knows what he knew not before. That is an unproblematic statement about learning something new. But erase time from Fitch (or from that bold sentence), and you get: he knows what he knows not, ie a contradiction. — Olivier5

the sentence "p is an unknown truth" is true today; and, if all truths are knowable, it should be possible one day to learn that "p was an unknown truth" up untill that day. — Olivier5

If there is a flaw in my chicken paradox -- as I strongly suspect is the case :razz: --, then the exact same thing is wrong with Fitch. — Olivier5

The first flaw in your proposed paradox is what I explained here. Your symbols are wrong. It should be:

∀x(Cx → ◊Ex)
For all things, if that thing is a chicken then it is possible to eat that thing.

∃x(Cx → ¬Ex)
There is at least one thing that is a chicken and hasn't been eaten.

Fitch's paradox, however, uses the correct symbols.

You pointed yourself to that flaw here, as I and many others have done before you, about the non-chicken version of Fitch. — Olivier5

That's not a flaw with Fitch's paradox. That's me explaining to you how you're misinterpreting/misrepresenting Fitch's paradox by using ambiguous wording that leads to equivocation.

Chickens, pfhhf.

Everything is a goat.

yet,

• Goats eat everything.
• Eating is asymmetric. That is, if A eats B, then B does not eat A.
  Therefore,
• There is at least one non-goat.

How can such a straight forward argument lead to such a counterintuitive conclusion?

The problem must be with the second premise. Hence there must be a goat that is uneaten, and yet eats everything.

The alternative, that the Great Goat eats itself, is unpalatable.

The first premise should be "Goats eat everything":

The principle that ‘goats eat everything’ says that they actually do this, not just that they can or might do this. Everything can and everything does go down a goat’s throat. Everything is eaten by a goat. Goats are not just omnivorous, but omnivoracious.

Fitch's paradox, however, uses the correct symbols. — Michael

The exact same critique can be made about Fitch, but for some reason you fail to see it.

The exact same critique can be made about Fitch, but for some reason you fail to see it. — Olivier5

It can't be made about Fitch because his premises work. You just don't seem to understand propositional logic.

Watch me:

∀x(Px → ◊Kx)
For all things, if that thing is a proposition then it is possible to know that thing.

∃x(Px → ¬Kx)
There is at least one thing that is a proposition and hasn't been known.

That doesn't address what I was saying about your argument. Formal logic is concerned with the relationship between propositions. In the case of a → b, both a and b are propositions. In your argument you want a to "stand in" for a chicken, which doesn't make sense. Chickens aren't truth apt and can't be the antecedent of a material implication.

Or perhaps you meant for a to be the proposition "the chicken exists"? In which case the consequent of your material implication, ◇Ea, says that it is possible to eat the proposition that the chicken exists, which is of course absurd; you can't eat a proposition.

Fitch's argument, however, correctly utilises formal logic. p → ◇Kp: if the chicken exists then it is possible to know that the chicken exists.

As I suggested to another earlier, if you don't understand formal logic then address the argument in natural language. The reasoning is the same. If you accept the knowability principle and the non-omniscience principle then it follows that all truths are known. Therefore, you must either reject the non-omniscience principle or the knowability principle.

There's been some discussion on the issue. This is as Capra sets it out, taking on his version for discussion. There is the weaker version, "Goats eat anything", but that is obviously too weak to reflect reality.

Sorry, not sure if I was clear, but that quote was from the article you posted. Capra explicitly sets out the argument as:

Premise 1: Goats eat everything.
Premise 2: Eating is asymmetric. That is, if A eats B, then B does not eat A.
Therefore:
Conclusion: There is at least one non-goat.

Not sure where you got the "can eat" from?

Oh, my mistake. Transcription error. Thanks.

I’ll try and come back to the rest of your post, but if the above is correct, then this would seem to contradict Michael’s claim that a proposition can be known to be true at one time and then known to be false at a later time. If K refers only to what is eventually known, then a proposition which is ultimately known to be false cannot earlier be known to be true. — Luke

As Wittgenstein said in On Certainty

"I know" seems to describe a state of affairs which guarantees what is known, guarantees
it as a fact. One always forgets the expression "I thought I knew".

If the epistemic usage of "to know" is considered to be the same as "to be certain", then knowledge changing over time is no big deal for the verificationist and simply means that one's beliefs are changing as the facts are changing. But this doesn't necessitate contradiction.

For instance, if p is "Novak is Wimbledon Champion", then p today, and hence K p (assuming verificationism). Yet on Sunday it might be the case that ~p and hence K ~ p. But any perceived inconsistency here is merely due to the fact that the sign p is being used twice, namely to indicate both Friday 8th July and Sunday 10th July.

If instead p is "Novak is Wimbledon Champion with respect to the years 2011, 2014, 2015, 2018,2019, 2021" and q is "Kygrios is 2022 Wimbledon Champion" then we will still have K p whatever happens, even though the domain of the operator 'K' has enlarged to include q.

Of course, not every observation, such as the contents of a fridge, has an obvious time-stamp that places the observation into an order with every other observation of the fridge, but contradictions can at least be averted by using fresh signs to denote present information. "Never the same fridge twice".

That doesn't address what I was saying about your argument. — Michael

It does, it's the exact same logic. The original version says one cannot know an unknown truth. The chicken version of Fitch says one cannot eat an uneaten chicken. There's no fundamental difference between the two ideas. They are both equally ridiculous.

The original version says one cannot know an unknown truth. — Olivier5

No it doesn't. It says that if you accept the knowability principle and the non-omniscience principle then it follows that all truths are known.

As I said here, you're equivocating. The phrase "one cannot know an unknown truth" is ambiguous and you're using the wrong interpretation. It can mean one of these:

1. If some p is not known to be true then it is not possible to (ever) know p
2. It is not possible to know that p is true and that p is not known to be true

The first is false, the second is true.

The chicken version of Fitch says one cannot eat an uneaten chicken. — Olivier5

And your logic is flawed, as I have explained. You don't understand formal logic. You're also trading on the ambiguity as explained above. There is a difference between these:

1. If some chicken has not been eaten then it is not possible to (ever) eat it
2. It is not possible to eat a chicken and for that chicken to remain uneaten

The first is false, the second is true.

I mean the second interpretation of course, in both cases. They are both equally trivial, equivalent to: you can't have your cake and eat it too. That's hardly a philosophical scoop.

I mean the second interpretation of course, in both cases. — Olivier5

And that's precisely why the knowability principle fails, as Fitch's paradox shows. It isn't possible to know that p is true and that p is not known to be true, even though there is some p that is true and not known to be true. Therefore, some truths are unknowable.

We don't. But "every possible observation" is not the standard for making knowledge claims or forming beliefs. Good evidence is. If good counter-evidence emerges, then we should change our minds and retract the former claim. — Andrew M

Which isn't any different than saying knowledge is an interpretation that changes with new evidence - not that you never had it.

What qualifies as good evidence? Isn't there a chance that good counter-evidence emerges later? If yes, then you can never say that you possess knowledge. You would never know that you know or you would know something unknowable.

You can look out the window at the moment your trickster brother sprays the window with a hose.
— Harry Hindu

In which case you wouldn't know it was raining, you would just think you did. — Andrew M

Yet we asserted that we did know and were wrong, which is good evidence that you could be wrong again, and again, and again - hence no such thing as knowledge unless we define knowledge as an interpretation that changes - not that you never had it. So, using your "good evidence" definition, you have good evidence that you can't ever possess good evidence. Your argument defeats itself.

Is it possible to believe a truth? How would that be different than to know a truth?
— Harry Hindu

Yes. To know it also requires good reason, or evidence, or justification. — Andrew M

As I pointed out, it is very possible that your good reason or evidence isn't actually a good reason or evidence, and you only find that out after you get good reason or evidence, yet it is very possible that your good reason or evidence isn't actually good reason or evidence, and you only find that out...,etc. It's an infinite regress.

How do we ever know that we have all the evidence necessary to assert knowledge over belief?
— Harry Hindu

Your question assumes a standard of infallibility or Cartesian certainty. But you can say that you know it is raining (or not) by simply looking out the window. That's the relevant standard for making knowledge claims. — Andrew M

No. It is you that assumes a standard of infallibility or Cartesian certainty by saying that "good evidence" is what is needed to possess knowledge. I'm simply asking you to define what that means, if not that "good evidence" is a state of infallibility (knowing the truth). I already pointed out that looking out the window is not good evidence because your brother could be spraying the window with a hose.

Formal logic is concerned with the relationship between propositions. — Michael

You keep using this term, "proposition" that you've you admitted to not knowing what they are. If you don't know what propositions are, then how can you even know what kind of relationship exists between them? You just continue to post scribbles on this screen and asserting that there is a relationship between them, but don't know what the members of that relationship actually are.

Is a proposition a relationship - a relationship between some scribbles or utterances and what those scribbles and utterances are about? So formal logic would be the relationship between one string of scribbles and what that string of scribbles is about and another string of scribbles and what that string of scribbles is about. It seems to me that you'd first have to determine what the scribbles are about (like an assertion of what is the case, like the cat being on the mat) before understanding the relationship between them.

You keep using this term, "proposition" that you've you admitted to not knowing what they are. If you don't know what propositions are, then how can you even know what kind of relationship exists between them? — Harry Hindu

I don't need to have some kind of in-depth metaphysical understanding of the nature of language and reasoning to make use of formal logic, just as I don't need to have some kind of in-depth metaphysical understanding of the nature of numbers to do maths.

I don't know what numbers are, but I know that 2 is a number, that a chicken isn't a number, and that 2 + 2 = 4.

I don't know what propositions are, but I know that "it is raining" is a proposition, that a chicken isn't a proposition, and that modus tollens is a valid rule of inference.

If you want an in-depth metaphysical discussion on the nature of numbers and logic and whatever then that's a topic for another discussion. It's not relevant to this one.

I don't need to have some kind of in-depth metaphysical understanding of the nature of language and reasoning to make use of formal logic, just as I don't need to have some kind of in-depth metaphysical understanding of the nature of numbers to do maths. — Michael

I wasn't asking for an in-depth metaphysical understanding of the nature of language. It's not necessary to answer a simple question. You said, "I don't know". I'm just asking for a simple definition of "proposition". What do you know, if anything, of what a proposition is? You have to have some understanding of the nature of numbers to do maths, or else what are you doing when you do maths?. :roll:

I'm just asking for a simple definition of "proposition". What do you know, if anything, of what a proposition is? You have to have some understanding of the nature of numbers to do maths. — Harry Hindu

I can't give you any meaningful definition of "proposition", just as I can't give you any meaningful definition of "number". I can give you examples of things which are either numbers or not numbers, and examples of things which are either propositions or not propositions.

But, again, this has nothing to do with Fitch's paradox. If you want to talk about what propositions are then start another discussion.

I can't give you any meaningful definition of "proposition", just as I can't give you any meaningful definition of "number". I can give you examples of things which are either numbers or not numbers, and examples of things which are either propositions or not propositions.

But, again, this has nothing to do with Fitch's paradox. If you want to talk about what propositions are then start another discussion. — Michael

That's not necessary. You've already shown that you have no idea what you're talking about, which is the point I was trying to make. Thanks. :smile: