Your computer knows it...

Your computer knows it... — Olivier5

My computer hasn't the ability to distinguish a proposition from garbage.

Then how can it make a proposition?

Then how can it make a proposition? — Olivier5

What do you mean by "then"? The hidden premise here is that in order for the computer to create a proposition, the computer needs to distinguish propositions from garbage. Why would you hold that premise?

A mother fox and a father fox can make a baby fox. Not one of these things know they are foxes. A computer can generate displays of the mandelbrot set. Computers don't know what mandelbrot sets are. Why should propositions be special?

Because a proposition is a statement that is proposed as a fair or accurate representation of some state of affairs. If your computer doesn't understand that, at best it is writing a sentence, at worse it is spraying black dots on a screen, which you interpret as a proposition.

Because a proposition is a statement that is proposed as a fair or accurate representation of some state of affairs. — Olivier5

On October 1, 2021, I caused a computer to generate statements that are accurate representations of states of affairs. The computer generated those statements at 10:03:44pm on that day.

At best, your computer is writing a sentence, at worse it is spaying black dots on a screen, which you interpret as a proposition. — Olivier5

You have the same problem classifying strings as sentences... either you don't know these words mean or you're special pleading.

There are strings I would interpret as propositions, and strings I would not interpret as propositions. This implies that there's a classification of strings I would interpret as propositions:

it makes no sense to say that a proposition no one knows about is true. — Olivier5

1. It "makes sense to say" that strings that fall into the class of strings I would interpret as propositions, are propositions.
2. I have sufficient justification to say, before I interpret the strings produced by this program (i.e., at 10:03:44pm), that they are propositions in the sense introduced in 1.
3. Likewise, there are some propositions which, should I understand them and assign truth values to, I will assign the truth value of "true" to.
4. It "makes sense to say" (see above) that such propositions are true propositions.
5. I have sufficient justification to say, before I interpret the strings produced by this program (i.e., at 10:03:44pm), that the "propositions" (see 2) are "true propositions".

On October 1, 2021, I caused a computer to generate statements that are accurate representations of states of affairs. The computer generated those statements at 10:03:44pm on that day. — InPitzotl

That you interpret as such. I don't.

That you interpret as such. I don't. — Olivier5

That's fine, and I have no problem with that per se, except that you did explicitly appeal to the "makes no sense to say" criteria (which you even bolded, FTR), and it's that which I'm demonstrating. If you can prove it does not genuinely make sense to say what I'm saying, that would be relevant. Otherwise, you cannot appeal to the "makes no sense to say" criteria to defend your own interpretation.

To know S is a proposition, it is not necessary to know S.

Why is this so difficult? — InPitzotl

Because on the face of it, the sentence is a ridiculous contradiction, for to say “to know S is a proposition, it is not necessary to know S (is a proposition). Only when understood that the S known as a proposition is not the S it is not necessary to know, does the difficulty disappear. But that understanding is not implicit in the sentence itself, it must be deduced from it, in order to reconcile the contradiction. It follows that the only relevant deduction can be that the S to know is a form, the S not necessary to know, is a content. What remains is, to know S is a proposition, it is not necessary to know what is contained in S.

Some people, not difficult; most people, irrelevant.

Also not the difficulty to which I directed my comment.

We've been through this. A proposition needs to be proposed as a true representation. Otherwise it is at best a sentence. You do all the proposing, your computer none. Your computer is merely your sockpuppet. Enough with this nonsense already.

We've been through this — Olivier5

No, Olivier5, we haven't been through "this", because "this" refers to what you just linked to. That "this" is a post where I pointed out your bolded "makes no sense to say that" criteria. Not only did I point that out in the reply you're pretending to reply to, but that was the entire point of the post you're pretending to reply to!

And whereas you are not even trying to employ the "makes no sense to say that" criteria, you're not even going over "this" in your reply.

A proposition needs to be proposed as a true representation. Otherwise it is at best a sentence. You do all the proposing, your computer none. Your computer is merely your sockpuppet. — Olivier5

None of these are in the form "it makes no sense to say that". What is the thing you're claiming it makes no sense to say? Without that thing, you're not even going over "this" in this reply.

I'm not in any realistic sense the one who proposed proposition 6. I did technically meet the criteria you called out for in that post, but not in any way you're spinning your wheels arguing... I can call what the computer generated propositions because I know "about" them ("it makes no sense to say that a proposition no one knows about is true"), not because I "proposed" them, or because my computer "knew" them, or even because I knew what they were. I didn't propose prop 6. My computer didn't understand prop 6. My computer didn't know prop 6. My program didn't know prop 6. I didn't know what prop 6 was at 10:03:44pm. But I did know "about" prop 6, at that time, because I wrote the program.

I'm not in any realistic sense the one who proposed proposition 6. I — InPitzotl

So who is doing the proposing then?

So who is doing the proposing then? — Olivier5

Not my concern. I'm not bound by your theories that propositions require a proposer, so I don't have to name one. If you can't find one, once again, that's a you problem, not a me problem. If you can figure out an answer, knock yourself out. If you can't, maybe consider giving that up. I don't require it; so I'm all good.

I'm not bound by your theories that proposing requires a proposer, so I don't have to name one — InPitzotl

Okay so you're not quite sure whether it's true or not that "QMCVNBOO" is lexically prior to "SHXCBJYN" now?

As formulated, the statement is a bit unclear because "lexical" means "relating to words or the vocabulary of a language as distinguished from its grammar and construction". Nothing to see with indexing nonsensical strings of uppercased letters...

Assuming you mean something like "comes in alphabetic order before", then the statement could be interpreted as a true proposition.

As formulated, the statement is a bit unclear because "lexical" means "relating to words or the vocabulary of a language as distinguished from its grammar and construction". — Olivier5

Lexical has another sense: "relating to or of the nature of a lexicon or dictionary". That's closer to what is meant. "Lexically" in this particular sense refers to "how" the strings are prior/successive to each other, i.e., in what sense they are; it's referring to a lexical ordering.

A lexical ordering is the same as dictionary ordering, and refers to the type of ordering words have in a dictionary.
https://en.wikipedia.org/wiki/Lexicographic_order

It's slightly distinct from "alphabetical order", in that it formalizes the concept of the ordering and generalizes it.

Assuming you mean something like "comes in alphabetic order before", then the statement could be interpreted as a true proposition. — Olivier5

It's slightly more precise to say "lexical", since that describes what the sorted function does with strings. "alphabetical" works because I'm limiting this to strings containing only capital letters and 8 characters, but then, so does "numerical" with your prior mapping given this description, which is why I didn't bother commenting on it then.

It's slightly more precise to say "lexical", since that describes what the sorted function does. — InPitzotl

So it's computer language. That's why is sounds odd in regular English.

As I read the article in Stanford, Fitche's Paradox is using the word "truth" in the sense of a statement about the real world (reality, existence, the universe, everything that is the case, etc - pick a word that works for you).

Your program is generating arithmetic truths: 2 > 1, 3 > 2, etc.

Put differently, Fitch is talking about apples and your program is doing math. So not even apples & oranges.

But that aside, suppose your program were to write each line out to a file and then delete that file before generating the next line? Would you still consider your program to be generating propositions?

Please note that I'm not saying you're wrong. Much of this discussion relates to the question of how we define/use the words "proposition", "truth", "knowability", etc.

(1) Just to be clear, Fitch does not hold that

for all p we have p -> Kp.

Rather, the import is that

if for all p we have p -> LKp, then for all p we have Kp,

but since it is not the case that for all p we have Kp, it is not the case that for all p we have p -> LKp, so we reject that for all p we have p -> LKp.

(2) SEP gives the argument with quantifiers ranging over sentences, but I'm not sure that is necessary, and so I am not sure that necessarily the argument is second order. I don't see why the argument can't be as proof schema for a language of sentential modal logic with two primitive modal operators 'L' and 'K', letting 'p' and 'q' and 'r' be metavariables ranging over sentences:

Axiom schemata:

(a) Kq -> q

(b) K(q & r) -> (Kq & Kr)

(c) q -> LKq [this is the axiom presumably to be rejected]

Inference rule:

(d) from |- ~q infer |- ~Lq

Proof:

1. K(p & ~ Kp) assume toward RAA

2. Kp & K~Kp from 1 and (b)

3. ~Kp from 2 and (a)

4. ~K(p & ~Kp) from 1 by RAA

5. ~LK(p & ~Kp) from 4 and (d)

6. p & ~Kp assume toward RAA

7. LK(p & ~Kp) from 6 and (c)

8. ~(p & ~Kp) from 6 by RAA

9. p -> Kp from 8 [note that non-intuitionistic logic is used here]

So from the rules (a) - (d) we proved for arbitrary sentence p that p -> Kp. But we don't believe that for all sentences p we have p -> Kp, while (a), (b) and (d) seem eminently reasonable, so we reject (c).

(3)

The SEP article explains some of the arguments against Fitch's argument.

Also, this book looks like a great overview:

Salerno

As I read the article in Stanford, Fitche's Paradox is using the word "truth" in the sense of a statement about the real world — EricH

I'm fine with that. Here, I've analyzed TMP's latest proofs, and don't have any particular issues with them, outside of the fact that they could probably be made a bit clearer by organizing it a little better.

Put differently, Fitch is talking about apples and your program is doing math. So not even apples & oranges. — EricH

Understood; the point of the program was just to test certain ideas about what a proposition is. It kind of had to be mathematical, because I wanted it in the post, this makes it short, and that would make it much easier to explain to someone who might not be familiar with programming if need be. I also felt it worthwhile to make the examples concrete rather than hypothetical.

But that aside, suppose your program were to write each line out to a file and then delete that file before generating the next line? Would you still consider your program to be generating propositions? — EricH

Sure. I'm perfectly happy with counterfactuals, and it suffices for me that "were I to read it, I would classify it as a proposition". I think I apply the same criteria to other things; "were I to see this animal, I would classify it as a fox" suffices for me to call the thing a fox; "were I to see this object, I would call it an ice cube" suffices for me to call it an ice cube, etc.

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!

@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

To both of you
Incorrect! — TheMadFool

What's wrong with it?

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:

What's wrong with it? — InPitzotl

$\neg p$ is true

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. Surely I can do that?
2: When you see "¬p", you can replace it with "q" (per 1). That's just substitution. Do you have a problem with substitution?
3: Specifically, we're relabeling q as p; what was p, you can call anything else. Do you have a problem relabeling? I seem to recall you actually relabeling for me just earlier today!

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.

If q = ¬p, q is true. — TheMadFool

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. So if there's logic requiring q to be true, you can put your falsehood into 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.

¬p

Yes, but for Olivier5's argument to work ¬p should be false. — TheMadFool

Which argument are you referring to?