why do you think believing in the reality of universals would necessarily, or even on average, make people morally better (if that is what you believe)? — Janus

I invite anyone who thinks they do understand it — Janus

My best guess is universals are abstractions, for them to exist, immaterial, nonphysical as they are, is to open the gates and welcome into our ontology whatever immaterial, nonphysical thing one fancies. God? Soul?

@Olivier5

The earth is round. True
The earth is flat. False

What's the differenc between:

1. Knowing the earth is round [sounds ok]

and

2. Knowing the earth is flat [believe seems a better fit]

and

3. Not knowing the earth is round [looks, feels right]

and

4. Not knowing the earth is flat [something's off]

?

To cut to the chase, it doesn't look like we can know a falsehood.

Clarification

In Fitch's argument, p, whereever it appears, stands for true propositions. (p & ~Kp) = an unknown truth.

Regarding some members who want to say Fitch is talking about falsehoods, yes but only in the sense of their negations which are, well, truths.

It is not the case that for all sentences p, we have p -> LKp — TonesInDeepFreeze

False that all truths are knowable. For if it is, Fitch is right, all true propositions are known. Gödel's Incompleteness Theorems.

Well, maybe you'll get it one day, if you decide to apply your mind to it. — Olivier5

Fitch's paradox is about unknown truths. That's the essence of the argument.

¬p→K¬p = all false propositions are known propositions — Olivier5

You need to work on your logic.

Tithonus' boon/curse He's technically immortal but in actuality his condition is best described as a macabre form of torture - prolonging and aggravating all age-related problems. Tithonus, indeed does not die but he does age.

In later tellings, he eventually became a cicada (tettix), eternally living, but begging for death to overcome him. — Wikipedia

What does it mean to say that falsehoods are or are not in the scope of Fitch's paradox? What does being "in the scope" of a paradox exactly mean in this context? — TonesInDeepFreeze

A very difficult question to answer but let's just stick to the basics: Fitch's paradox is about unknown truths.

Notice that in your example: q = ~p , you used q (~p is true) and not p (p is false).
— TheMadFool
p: <- the false proposition.
q: <- the true proposition.
q = ~p <- makes true proposition q out of false proposition p.

Does your proof need a true proposition? Use q.

What's the problem?

p→Kp
— TheMadFool
p is true here, right?

Let's change labels from p to q. q→Kq. Now q must be true (because we changed labels), right?

So let's take the case where q = ~p, where p is false. q is still true, right? What did q have to be? True? Okay, well it is true. What did p have to be to extend to falsehoods? False? Okay, well, it's false.

Now, we can talk about p's that are false. And when you do your proof, you use q's for where you used to use p's. What's wrong?

We can do the same thing in reverse. Just take p, where p is true, and that's your typical application. To do falsehoods, take p where p is false. But we can't do the typical, we have to convert that to a true proposition. No problem; add a complement; if p is false, ~p. But the proof only works when p is a true proposition. Okay, no problem; relabel p's in the proof as q's, and say q=~p. Now we have a false p, and a proof that uses the fact that q is true. What's wrong? — InPitzotl

It seems we've been talking past each other.

1. What you're saying is true of course. If p is false then, ~p is true and indeed, $\neg p \rightarrow K \neg p$. If then q = ~p, it follows that $q \rightarrow Kq$. If by Fitch's paradox being extended over falsehoods means this to you, you and @Olivier5 are absolutely right. Negations of falsehoods, truth, are being utilized.

2. To me, if Fitch's paradox includes falsehoods within its scope, it can only be so if falsehoods themselves, not their negations which are true (see 1 above), can be part of Fitch's argument.

@InPitzotl @Olivier5

How can we embiggen the scope of Fitch's paradox to cover falsehoods?

An attempt was made by saying $\neg p \rightarrow K \neg p$ but

1. Isn't actually doesn't cut it because $\neg p$ is true.

and

2. Knowing also implies truth. We cannot know a falsehood.

Charitably, you take a false proposition p. You extend that by building a true proposition ¬p from it. I'm not sure your interpretation is charibable — InPitzotl

Notice that in your example: q = ~p , you used q (~p is true) and not p (p is false). So, you didn't expand the scope of Fitch's paradox to include falsehoods.

Which argument are you referring to? — InPitzotl

Fitch's paradox is about true propositions.
— TheMadFool

I know. I'm extending it to false propositions as well. Sue me. — Olivier5

Why are my Math LaTex commands causing the characters to get squished up together? Help!

¬p

I think you mean that if p is a falsehood, and q = ¬p, then q is true. So you have a falsehood p, and a truth q — InPitzotl

Yes, but for @Olivier5's argument to work $\neg p$ should be false. It isn't.

I don't think you're quite following this.

1. Let q=¬p.
2. Then ¬p→K¬p is simply q→Kq
3. q→Kq is the same as p→Kp with change of labels.

1: I'm just defining another variable.
2: When you see "¬p", you can replace it with "q". That's just substitution. Do you have a problem with substitution?
3: Specifically, we're relabeling q as p. Do you have a problem relabeling? — InPitzotl

Sorry for the confusion but

1. If q = $\neg p$, q is true. @Olivier5 claims that Fitch's paradox can be extended to falsehoods but $\neg q$ is not false.

What's wrong with it? — InPitzotl

$\neg p$ is true

Let q=¬p. Then ¬p→K¬p is simply q→Kq, which is the same as p→Kp (under a change in labels). — InPitzotl

:flower:

matching linguistic symbols (words, spoken or written) to their respective referents
— TheMadFool
...and you were the one talking about CAT tools as if that had anything to do with referents.

There's a giant difference between responding to "Can you pick up some bananas from the store?" ...by showing me the phrase translated (poorly or greatly) to Dutch; and responding to "Can you pick up some bananas from the store?" ...by showing up on my doorstep with a bunch in your hand. — InPitzotl

The word banna is mapped to the fruit banana - every word has a referent.

@Olivier5

Suppose p is a sentence that is an unknown truth; that is, the sentence p is true, but it is not known that p is true. — Wikipedia

Exactly — Olivier5

Let q=¬p. Then ¬p→K¬p is simply q→Kq, which is the same as p→Kp (under a change in labels). — InPitzotl

To both of you

Incorrect!

None other than precipitating searches for an explanation which may or may not imply new, currently unknown, physical laws at work. Relativity, QFT, statistical mechanics, evolution, etc still hold. — 180 Proof

I can live with that!

To get a more complete view of the problem. — Olivier5

You cannot.

I know. I'm extending it to false propositions as well. Sue me — Olivier5

I'm extending it to false propositions as well. — Olivier5

$p \rightarrow Kp$

To what end, may I ask?

So, if tomorrow a dead man comes back to life, it would have no implications for science?

Science Of Decay.

Seems relevant.

I am talking about removing any human"king" from the system and substituting them with a Process....as we have done with Science. — Nickolasgaspar

Nice! I didn't think of that. We would then need some kind of method à la the scientific method. Any ideas?

It depends from the standards we use to define failure and success. — Nickolasgaspar

I think the only way democracy is a failure is if you redefine "failure" as success. Nevertheless, I do concede that it's the least worst option we have.

You could claim that it's true but it may still be false. Makes no difference anyway. There is no such a thing as an unknown proposition, whether true, false or anything in between! — Olivier5

Yes, but Fitch's paradox is about true propositions. Restrict the domain of discourse to true propositions and you'll get it, hopefully.

A proposition can be false or undecidable. — Olivier5

A proposition can be false, yes but when you state it, it means you're claiming it to be true.

In assuming that this applies only to true propositions. In fact it applies to any proposition, true or not. An unknown proposition is an unproposed proposition. It's like an unthought thought: a contradiction in terms. — Olivier5

When one makes a proposition or knows a proposition, truth is implied.

p (a propisition) = p (is true)

Buddha was not a gentleman, was he?

You have two 3's here... could I request a renumber? (Be careful; you reference things by number a lot). — InPitzotl

F**k!

Profit! Output > Input? Sacrilege! Unnatural! Sorcery!

Does nature make a profit?

There was this Triad: God, Man, Nature. They made sense together, because God created Man 'in His image'. This gives Man an 'unnatural aspect' - no one would have put it that way, but you are atheistic scum so it doesn't matter. So the existence of God is what keeps Man and Nature separate and distinct. — unenlightened

George is 6 feet tall, and George is a boy.
Know that George is 6 feet tall, and know that George is a boy.
Know that George is 6 feet tall. (By simplification.)
Therefore George is not a boy. — god must be atheist

K = known

L = possible

LK = knowable

1. (p & p is unknown) = p is an unknown truth = p & ~Kp (this is a truth)

2. All truths are knowable

3. K(p & ~Kp) = p is an unknown truth is known [from 2, assume]

4. Kp & K~Kp [from 2, knowing a conjunction is to know the conjuncts]

5. Kp [4 Simp]

6. K~Kp [4 Simp]

7. ~Kp [from 6, $Kq \rightarrow q$]

8. Kp & ~Kp [5, 7 Conj]

9. ~K(p & ~Kp) [3 - 8 reductio as absurdum]

10. p & ~Kp [assume]

11. LK(p & ~Kp) [2, 10, if true, knowable that true]

12. ~LK(p & ~Kp) [9, if not knowable, not possible that knowable]

13. LK( p & ~Kp) & ~LK(p & ~Kp) [11, 12 Conj]

14. ~(p & ~Kp) [10 - 13 reductio ad absurdum] {there are no unknown truths}

15. ~p v ~~Kp [14, DeM]

16. ~p v Kp [15 DN]

17. $p \rightarrow Kp$ [16 Imp]

18. If there is a proposition then, that proposition is known

QED

Where does Fitch commit an error, make a boo boo?

No there is no inconsistency - an artist can bite his patron on the leg, and deem it to be art. An artist can do anything and deem it to be art. — Pop

In other words, anything and everything is art. Why define it then, definitions being restrictive criteria?

Were you forced to resign? I think it's implicit, no? — Caldwell

Forced to, yes! What does it matter implicit/explicit?

Accordingly, within many religious communities, "miracles" happen every day, Fool, and I doubt any scientific community would designate as "miracles" any unexplained, problematic (or outside the prevailing paradigm) events – there aren't scientific criteria for determining whether or not a phenomenon is "miraculous". I'd expect, therefore, no "reaction" out of the ordinary in either case. The word "niracle" is just confabulatory shorthand (outside of a laboratory, or experimental, context) for what the fuck is / was that? like 'god-of-the-gaps' (we don't know or even have a clue). :eyes: — 180 Proof

It maybe true that for the religious, miracles are more common phenomena than for the irreligious but these miracles aren't of the same kind as those allegedly performed by Christ.

The miracles I'm referring to are the Jesus-level miracles in a manner of speaking. Miracles are, as per one of the most vocal critics of religion, the late Christopher Hitchens, suspensions/violations of the laws of nature. If such were to occur, scientists would need to rethink/review/discard their theories which are wholly predicated on the laws of nature being/remaining unmolested.

Onanistic wordplay. — 180 Proof

Suppose a miracle occurs in the next 24 hours. What would be the reaction of the religious establishment and the scientific community? :chin:

Objects are arbitrarily deemed to be art. Art’s only necessary distinction from ordinary objects is the extra deemed art information. — Pop

Inconcistency detected. Art, by the first sentence, is arbitrary. Then the second sentence mentions there's got to be something "...extra..." (art information).