See for example Irvine Anellis. I don't see that Anellis carries the case that Pierce's approach was complete. From the little I've seen Pierce used them to set out the permutations of three variables and so on, but I can't see anywhere that he made the connection with tautology and contradiction. I might be mistaken. But on a quick look around Anellis seems to be alone in his claim.

So unless a stronger case can be made, I'll credit Wittgenstein. In any case, it was the Tractatus that brought truth tables to the attention of the greater philosophical community. You are of course welcome to take a different opinion.

I'm not familiar with Peirce, so I'm not rejecting the notion that he used truth tables. I don't see anything that indicates Peirce used them such that "the truth table method, if appropriately formulated, can itself be used as a deduction system". In 4.46, Wittgenstein sets out how to use a truth table to adjudicate tautology and contradiction. In the absence of an alternative, I believe that to be original, but let me know if Pierce did anything similar.


What is original is that Witti points out how to use a truth table to determine tautology or contradiction.

In any case, "truth tables don't adjudicate contradictions" is yet another error on the part of @Leontiskos.

So after outlining the process, he says

4.46 Among the possible groups of truth-conditions there are two extreme cases. In one of these cases the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological. In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory . In the first case we call the proposition a tautology; in the second, a contradiction.

This is original.

Oh, yeah - I was just editing the post to acknowledge that. My understanding is that Pierce tabulated some bits of binary logic, but it appears that the use of truth tables to demonstrate tautology and contradiction is down to Wittgenstein or Wittgenstein and Russell in about 1912. It is an issue of some disagreement.

Ludwig Wittgenstein is generally credited with inventing and popularizing the truth table in his Tractatus Logico-Philosophicus, which was completed in 1918 and published in 1921.[2] Such a system was also independently proposed in 1921 by Emil Leon Post.[3] — Wiki.

Which is what Wittgenstein was working towards when he created truth tables.

4.31 We can represent truth-possibilities by schemata of the following kind (‘T’ means ‘true’, ‘F’ means ‘false’; the rows of ‘T’s’ and ‘F’s’ under the row of elementary propositions symbolize their truth-possibilities in a way that can easily be understood):

4.4 A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions.
— Tractatus

As it happens, truth tables don't adjudicate contradictions. — Leontiskos

An odd thing to say, since a contradiction will have "F" all the way down it's main operator

You posts do not come through on my mentions. That's somewhat discourteous.

But on an account that there is "nothing more to the rule than what one does in a particular circumstance," I'm not sure how you're supposed to explain these situations. — Count Timothy von Icarus

Learning the rules is not playing the game.

...people move the bishop diagonally because they know that's the rule. — Count Timothy von Icarus

And how does one demonstrate that they understand the rule, apart from moving the piece? There is a way of understanding a rule that is not found in stating it, but in following it or going against it in a particular case.

I suspect

"a foundational crises in mathematics" — jgill

is to be understood as "I don't get it!"

Writing "Assumption" to the right is a hangover from E. J. Lemmon.

So many of your claims have already been debunked in this thread. — Leontiskos

Not so. What has been clearly demonstrated is that you do not have a grasp of propositional logic.

That you do not understand validity, nor truth functionality, nor how to perform a deduction.

But perhaps you have unwittingly presented an account of the awkwardness of Aristotelian logic.

...much less ↪Banno's half-baked reductio:
ρ
μ
Contradiction, therefore ¬μ — Leontiskos

Another inane misattribution. Nowhere have I said that, and certainly not in the post linked.

Hmm. So you are agreeing that we have a shared world?

How do you infer that? — Michael

SO are you saying you can have my "mental percepts"?

The conversation I am having with Tones revolves around <your argument>, which is an instance of the form of reductio that I gave. — Leontiskos

No, it isn't. You missed out a line.

I would simply say that both of these proofs are invalid. — Leontiskos

And you would be wrong.

... if red is only a mental percept, then when you say “red” it refers to your mental percept, but when I say "red" it refers to my a mental percept. If we are going to be talking about the same thing then we need something that we both have access to. Hence there is more to being red than being a a mental percept.

That involves red things, in a world we have in common.

Here it is again.

1. A -> (B & ~B) {1}
2. A {2}
3. B & ~B {1, 2}
4. ~A {1} — TonesInDeepFreeze

And so, A -> (B & ~B) ⊢ ~A. This is a valid argument.

You made the claim that this was RAA:

B1. ρ
B2. Suppose: μ
B3. Contradiction, therefore ¬μ — Leontiskos

Which, as Tones pointed out, leaves out 3:

There is no rule of inference that allows us to draw (4) from (1) and (2). — TonesInDeepFreeze

It was this with which I was agreeing.

A rule isn't just "whenever behavior is the same." — Count Timothy von Icarus

Yep. So where are we now?

Tones was quoting me — Leontiskos

That was obvious. A mere typo.

If he had you would not have inadvertently agreed with me. — Leontiskos

I didn't.

Note that (4) is originally your conclusion, and we now both agree that it is invalid. — Leontiskos

This is inane. (4) cannot be invalid on its own. The argument is valid in classical prop logic.

The naive view that then projects these mental percepts out into the wider world as mind-independent properties of things is mistaken. — Michael

For the - I think seventh or eighth time - the claim is not that being red or sour or smooth is in no part mental, but that it is not exclusively in your mind alone. Hence the answer to

Does the color “red” exist outside of the subjective mind that conceptually designates the concept of “red?” — Mp202020

is "yes".

Oh, understood.

I moved Universities between logic courses, and was first taught natural deduction and then axiomatic systems, without the difference being made clear. So I tend to mix the two styles, with somewhat idiosyncratic results.

There is no rule of inference that allows us to draw (4) from (1) and (2). — TonesInDeepFreeze

Yep. The example Leo gave is not an example of RAA. And this:

But it's not. — Leontiskos

What to conclude except that Leo does not understand validity.

Heh. Why is (2) "discharged" and not (1)? — Leontiskos

That he asks this is quite odd, since our purpose here was A -> (B & ~B) ⊢ ~A.

Because a sour taste is a mental percept — Michael

And being sour is a property of lemons...

We don't generally have the "mental percept" of "sour" in the absence of lemons or some other such food. But you talk as if there were nothing going on here that was not "mental". And indeed, that's perhaps what you are thinking. But it's muddled. Lemons are not "mental phenomena".

So rather than us having to guess what you think is going on, set it out for us all. Are there lemons? Or are there only the oxymoronic "mental phenomena"?

But if by "the lemon is sour" you mean "a sour taste is a mind-independent property of the lemon" then I disagree. This is the naive view that is inconsistent with the science of perception. — Michael

And if I say "A sour taste is not only a 'mind-dependent' property of a lemon"?

My point is that if people are thinking about rules differently then there is a difference, regardless of whether or not their behaviors are identical. Your wife might act the same way if she feels duty bound or somehow coerced into acting like she loves you as if she really loved you, but surely her interpretation of what she is doing (playing the loving wife versus being in love) matters. — Count Timothy von Icarus

This just shows a misunderstanding of "rule".

Well, no, you didn't. This is the bit where you claim to have made a point that you haven't carried through.

Sure.

...and?

And here we go again.

The berry is red. The berry is rough. The berry is sour.

These involve the berry. They are not purely mental.

Again, if folk agree that the berry is smooth, red and sour, then presumably they agree that there is a berry, and not only a perception-of-berry.

... if "berry" refers to the perception-of-berry, then when you say “berry” it refers to your perception-of-berry, but when I say it it refers to my perception-of-berry. If we are going to be talking about the same thing then we need something that we both have access to.

This in reply to my pointing out that what you claim is a reductio is not a reductio.

B1. ρ
B2. Suppose: μ
B3. Contradiction, therefore ¬μ — Leontiskos

It's not even a valid argument.

I do not think the bad faith is mine alone.

As a noun, the words "colour", "pain", and "red" refer to mental percepts. — Michael

There's that verbal sleight of hand again. "Red" is not a mental property, whatever that might be. It's a colour.

You are enabled by the choice of colour in the OP. What if had chosen touch - would you be arguing that being smooth was a mental phenomena?

And for the third or fourth time, I am not denying that there is an aspect of being red that is mind dependent - again using your language. I am pointing out that it is not only mental.

yep.

B1. ρ
B2. Suppose: μ
B3. Contradiction, therefore ¬μ — Leontiskos

That's obviously not the reductio.

Stubbing one's toe is not a "mental phenomena".

I have to say something about that term. A phenomena is something observed. "Mental phenomena" is oxymoronic. One does not usually observe that one is in pain, one just is in pain. Being in pain is not making an observation. One does not observe a pain in one's toe, one has a pain in one's toe. There is a metaphysical slight of hand happening in your language use.

That the overwhelming agreement that some X is Y is not proof that Y is not a mental phenomenon. — Michael

Sure, in your somewhat illicit terms this might be so. What is shown is that being red is not private. That is, that there are red things is a part of our shared world.

Now how do you explain that sharing?

Some folk seem to think that things are either mental or they are not mental, with no other option.

But why should this be so? Minds are embedded in the world.

That overwhelmingly folk agree that stubbing one's toe is painful does not show that pain is not a mental phenomenon. — Michael

So what.

Can you pass me your pain?

There is simply no connection between your premise and your conclusion. — Michael

It appears that you have not understood the argument. Again, the claim is not that there is no mental component in a thing being red, but that there is more to red than mere experience.

Wouldn't this just be behaviorism? — Count Timothy von Icarus

Well, no. It's not about conditioning.

You then go on to describe situations that differ yet to suppose that they are in some way the same. I don't see the relevance. You set up your Turing machines, and therefore set the differences.

If your point I that different "metaphysical positions" might produce identical actions, then I agree.

"presume" doesn't mean "know". — Michael

No. it doesn't. Well done.

No it doesn't. — Michael

Ok. one can lead a donkey to water but not make them drink. I don't know what you must mean by "private', then, but you are not using it the way other folk do. The fact that we distinguish red pens from black pens shows pen colour not to be private.

Is there not a sense in which worlds are intersubjectively constructed through forms of life? — Joshs

Sure. In the world.

but presumably the pain I feel when I stub my toe isn't "quite different" to the pain you feel when you stub your toe. — Michael

How could you know that?

As mentioned before, this is a non sequitur. — Michael

yet

... if red refers to the experience, then when you say “red” it refers to your experience, but when I say it it refers to my experience. If we are going to be talking about the same thing then we need something that we both have access to. — Banno

That overwhelmingly folk agree on some things being red and others being not-red shows that red is not a private phenomena. Indeed, the controversy surrounding that dress shows that colour is not private.