Dorothy's red slippers, and man's ability to understand.

[Prof Bulani]

Terrapin, just try it yourself.

X = X is true
~X = X cannot possibly be true
X < X cannot possibly be true

Try X = 4, X = "apple pie", X = "pineapple on pizza is delicious". Try other values of X

Okay, so let's say "shoes = shoes" --is that true? Who knows. That's not a normal usage of the equals sign. What shoes are we talking about? What are we saying about them? What does it mean for shoes to equal shoes? Shoes equal shoes in what sense?

And then "not shoes equal shoes"--what the heck would that be saying? What is equality for shoes?

We'd have to wind up with essentially a statement.

Statements are the sorts of things that can be true or false.

... As if on cue...

The expressions "X = X", "~X = X", "X < X" and so on ARE statements. As such, they may be evaluated as true or false, as shown. X itself doesn't have to be a statement, but can be. X is a variable that can be substituted into the statements expressed.

Let X = "shoes". "Shoes are equal to shoes" is true. "Not shoes are equal to shoes" is false. If you want to know what shoes you are talking about, you can be more specific. No need to complain that your own example is too vague. So, let X = "a pair of size 11 yellow and grey Nike Air-max trainers". As such, "a pair of size 11 yellow and grey Nike Air-max trainers is equal to a pair of size 11 yellow and grey Nike Air-max trainers" is true, and "not a pair of size 11 yellow and grey Nike Air-max trainers is equal to a pair of size 11 yellow and grey Nike Air-max trainers" is false.

Any questions?

[Prof Bulani]

So, as I asked, can you quote Terrapin Station, or anybody else, stating something that is logically equivalent to "X is not X" or "an apple is not an apple"? I've repeatedly asked RJG the same thing. He declines to do so.

~X=X is an "I'm not really familiar with logic" way--and something that we often see from Randroids, with Ayn Rand as a good example of someone who wasn't really familiar with logic but who often liked to appeal to logic nevertheless--of stating a contradiction. Most logics do not have an equals sign as an operator/connective. The standard logical way of writing what you're getting at is ~(P&~P), which is the principle of noncontradiction in traditional bivalent logics.

[Steve3007]

"An apple is not an apple" seems to be about analyticity (see for a discussion of this Quine's "Two Dogmas of Empiricism"). As with Quine, I agree that analytic truths/falsehoods are simply a matter of the (variable) meanings and concepts that individuals apply.

In this case we're saying something about how people utilize concepts, and we're noting that they usually do that in a consistent way.

I recently bought a second hand copy of "Methods of Logic" by Quine. Would you say that's a reasonable introduction to his work?

I think, in the context of this topic and its recent posts, any analysis of what you've said above, interesting as it might be, will just muddy the waters. As far as I'm concerned, this topic's recent few posts, like most of what gater and RJG say, are a simple case of a straw man argument. In my experience, if you don't keep it very simple it's all too easy for people to latch onto a single, incidental thing you've said, obsess about that for a while and then declare "unless you discuss this, and this alone, I will not engage with you." You've done it. I've done it. Many have done it.

The main feature of this website is people fruitlessly talking across each other.

[Steve3007]

So, as I asked, can you quote Terrapin Station, or anybody else, stating something that is logically equivalent to "X is not X" or "an apple is not an apple"? I've repeatedly asked RJG the same thing. He declines to do so.

~X=X is an "I'm not really familiar with logic" way--and something that we often see from Randroids, with Ayn Rand as a good example of someone who wasn't really familiar with logic but who often liked to appeal to logic nevertheless--of stating a contradiction. Most logics do not have an equals sign as an operator/connective. The standard logical way of writing what you're getting at is ~(P&~P), which is the principle of noncontradiction in traditional bivalent logics.

That's not an example. Did you read it? In that quote he simply suggests an alternative way of stating the proposition "~X=X". You may think he's being condescending there, but you can't say he's proposing "X in not X".

Show somebody proposing that "X in not X", or its logical equivalent, is true.

[Terrapin Station]

Let X = "shoes". "Shoes are equal to shoes" is true. "Not shoes are equal to shoes" is false.

What the heck would we be saying by "Shoes are equal to shoes"?

What does "equal" amount to there?

[Terrapin Station]

That's not an example. Did you read it? In that quote he simply suggests an alternative way of stating the proposition "~X=X". You may think he's being condescending there, but you can't say he's proposing "X in not X".

Show somebody proposing that "X in not X", or its logical equivalent, is true.

The reason that P & ~P is a contradiction is because of the way that truth tables work. The whole gist of "~(P&~P)" as the principle of noncontradiction is that no matter what truth value we assign to P "P&~P" is false (in traditional logics) and thus "~(P&~P)" is true.

With X=X etc., we don't have that unless X is another variable for a proposition, or a statement.

A word like "shoes," or the item the word picks out, does NOT have a truth-value.

[Terrapin Station]

Oops, left out a comma above, "no matter what truth value we assign to P," <---important comma there.

At any rate, as I was noting, if we're just saying that "'shoes equals shoes' is true," (a) we'd better explain just what the heck we're claiming, because I don't think that's at all a clear usage of "equals," especially in an oddly ungrammatical sentence, and (b) a statement like that, in itself, has nothing to do with logic per se, because it's not at all about the implicational relationships of statements.

[Prof Bulani]

That's not an example. Did you read it? In that quote he simply suggests an alternative way of stating the proposition "~X=X". You may think he's being condescending there, but you can't say he's proposing "X in not X".

Show somebody proposing that "X in not X", or its logical equivalent, is true.

So to bring you up to speed, the reason RJG responded to Terrapin's comment by making the point "~X = X cannot possibly be true" wasn't because Terrapin claimed that ~X = X can be true, but because Terrapin is arguing that ~X = X isn't a valid logical statement to begin with.

RJG then lists a few general logical statements, which Terrapin continues to argue are not valid.

Terrapin proposed that an example of a logical statement would be something like "P & ~P" (which would always evaluate to false) where P is a statement that can be evaluated to true or false. While he is not wrong, he doesn't see why the distinction between the statements RJG listed and his example is relevant.

The distinction is simple. P is a statement, which can be evaluated to true or false. "~X = X" is a statement. If P = "~X = X", then P is always false for all values of X.

As a note, "P & ~P" is not another way of saying "X = ~X". That is because while P can only either be true or false, X can be substituted with anything. Also the operations "=" and "&" are not equivalent operations.

Terrapin seems to have some trouble understanding the correlation between truth statements in pure mathematics and truth statements in logic, going so far as to ignorantly and arrogantly assert that they have nothing to do with one another. As long as this attitude persists, I expect conversations on this topic with him will be slow and arduous.

[RJG]

As far as I'm concerned, this topic's recent few posts, like most of what gater and RJG say, are a simple case of a straw man argument. In my experience, if you don't keep it very simple it's all too easy for people to latch onto a single, incidental thing you've said, obsess about that for a while and then declare "unless you discuss this, and this alone, I will not engage with you."

Firstly, you continually misuse "strawman fallacy". A strawman fallacy is when one makes up something (differently than what someone has said), and then attacks that position as if that someone said it in the first place.

Secondly, to put it simply and bluntly, if you and Terrapin are unable to recognize a logical impossibility of the form ~X=X or X<X, then yes, any discussion with you is fruitless. If you cannot see and accept/admit the Simple Logic of...

• X=X is true
  ~X=X is logically impossible
  X<X is logically impossible

...then, we are wasting our time discussing anything.

Which just so happens to be Gater's point of this topic! -- If you (Steve and Terrapin) can't grasp Simple Logic then you can never see the "red slippers" that can bring you to "Kansas" (to truth).

[Steve3007]

(Comma added)

The reason that P & ~P is a contradiction is because of the way that truth tables work. The whole gist of "~(P&~P)" as the principle of noncontradiction is that no matter what truth value we assign to P, "P&~P" is false (in traditional logics) and thus "~(P&~P)" is true.

So, to write it longhand, ~(P&~P) = true is:

"The proposition Not(P and not P) is true for any proposition P".

Or, longer:

"Given any proposition, P, the proposition: "P and its contradiction are simultaneously true" is always false".

With X=X etc., we don't have that unless X is another variable for a proposition, or a statement.

A word like "shoes," or the item the word picks out, does NOT have a truth-value.

Yes, I see the point here and I was trying to illustrate something similar in the other topic with the syllogism that your identified as the undistributed middle fallacy.

But I think it's lost on RJG because he doesn't care. He thinks he's making a wider point, which all stems from his conviction than he can build certain knowledge (which he refers to as objective knowledge) from a single quasi-Cartesian axiom.

[Steve3007]

irstly, you continually misuse "strawman fallacy". A strawman fallacy is when one makes up something (differently than what someone has said), and then attacks that position as if that someone said it in the first place.

Quote somebody making this statement, or its logical equivalent:

"~X=X is logically possible."

[Terrapin Station]

So to bring you up to speed, the reason RJG responded to Terrapin's comment by making the point "~X = X cannot possibly be true" wasn't because Terrapin claimed that ~X = X can be true, but because Terrapin is arguing that ~X = X isn't a valid logical statement to begin with.

RJG then lists a few general logical statements, which Terrapin continues to argue are not valid.

??

I didn't write anything like "~X=X can be true" or argue about anything he said being valid or not.

Terrapin proposed that an example of a logical statement would be something like "P & ~P" (which would always evaluate to false) where P is a statement that can be evaluated to true or false.

I've explained over and over and over that P & ~P is a logical contradiction, and the significance of that is that if we want to claim that something is logically impossible, we need to forward the logical contradiction (the instance of P & ~P) in question, because the definition of logical impossibility is "something that is or that entails a logical contradiction" while the definition of logical possibility is "something that isn't a logical impossibility."

Further, as I've explained over and over, logic is about the implicational relationships of statements. We don't have the implicational relationships of statements if we don't have statements and a supposed implicational relationship among them.

Terrapin seems to have some trouble understanding the correlation between truth statements in pure mathematics and truth statements in logic, going so far as to ignorantly and arrogantly assert that they have nothing to do with one another.

Again, something I didn't actually write.

It's not that they have nothing to do with one another, but they're simply not the same thing. See "logicism" for a good explanation why.

[Terrapin Station]

(Comma added)

The reason that P & ~P is a contradiction is because of the way that truth tables work. The whole gist of "~(P&~P)" as the principle of noncontradiction is that no matter what truth value we assign to P, "P&~P" is false (in traditional logics) and thus "~(P&~P)" is true.

So, to write it longhand, ~(P&~P) = true is:

"The proposition Not(P and not P) is true for any proposition P".

Or, longer:

"Given any proposition, P, the proposition: "P and its contradiction are simultaneously true" is always false".

With X=X etc., we don't have that unless X is another variable for a proposition, or a statement.

A word like "shoes," or the item the word picks out, does NOT have a truth-value.

Yes, I see the point here and I was trying to illustrate something similar in the other topic with the syllogism that your identified as the undistributed middle fallacy.

But I think it's lost on RJG because he doesn't care. He thinks he's making a wider point, which all stems from his conviction than he can build certain knowledge (which he refers to as objective knowledge) from a single quasi-Cartesian axiom.

Is he a Randroid? (Do we know?) Those are classic Randroid moves.

[Steve3007]

So to bring you up to speed...

Do some research on RJG's posts. Note him continually telling people that they are claiming X = ~X.. If this is not a straw man argument, then people have, in fact, claimed that X = ~X, or something logically equivalent to it. So to show that it is not a straw man argument, quote someone claiming that X = ~X, or the logical equivalent.

[Steve3007]

(Comma added)

Is he a Randroid? (Do we know?) Those are classic Randroid moves..

No. I think not. He's just utterly fixated, and has been for literally years, on a single idea in which he has invested far too much time to be told that it's based on misunderstanding logic. His pattern is: "argue, lose, pause, repeat."