What, specifically, is the difference between these? — Banno

It's the difference between there being two ships with the same name and there being one ship (which maintains its name).

There are other people named Michael in the world, but they're not me. Whereas I'm the same person you've been speaking to for years.

including logical nihilism, Davidson's use of T-sentences, Anscombe's direction fo fit and a few other items — Banno

Per Nagase, Davidson isn't inherently realist. It's compatible with both realism and anti-realism. The only advantage is that it allows you to avoid correspondence theory, which in turn allows you to avoid propositions.

This isn't a rejection of bivalence. This is just pointing out certain words are vague. — Hanover

It's both. Vague propositions often don't have a single truth value, precisely because they're vague.

You're claiming that what a 40 year old is cannot be determined because there is no single truth value to the statement "a 40 year old is X."

I'm not saying that it can't be determined. I'm saying that it can be determined to be true and it can be determined to be false.

something new, is seems - at least to me: that a statement can be assigned more than one truth value. — Banno

A statement with 2 truth values is 2 statements.

"The ship that left is the ship that returned" is true if we define "ship" in terms of functionality. It is false if "ship" is defined as that which contains all the same boards.

X=X always. As long as we maintain definitions, we don't have this absurd result of X=Y and X<>Y.

"The ship that left is the ship that returned" is true if we define "ship" in terms of functionality. It is false if "ship" is defined as that which contains all the same boards. — Hanover

We don't start by defining "ship" according to some strict criteria and then use it in conversation. Rather we talk about a ship leaving, a ship returning, and then assess whether or not the two are the same (and then possibly derive the meaning of "ship").

Our assessment of whether or not the two are the same does not involve analyzing the meaning of the word "ship". We just consider the actual thing that leaves, the actual thing that returns, and the stuff that happens inbetween. And whether or not an identity persists doesn't have some single "correct" answer, as if it's a mind-independent fact that we either recognize or don't.

So to make it simpler, let’s say the ship that left was named the Theseus and that along with the part-replacements they adopted the name the Perseus.

Was the Perseus previously known as the Theseus?

We all agree that the material has changed but the function remains. The disagreement is over whether it's the material or the function or the sense of continuity (or something else) that determines identity. This is where the principle of bivalence fails (and, at least in the case where it's the sense of continuity that determines identiity, where the notion of recognition-transcendent truth conditions fails).

I'm not saying that we use the same name for the ship. I'm saying that it's the same ship.
— Michael

What, specifically, is the difference between these? — Banno

It's the difference between there being two ships with the same name and there being one ship (which maintains its name). — Michael

That's specifically the issue - does it count as one ship or two?

And "count as..." is a lexical marker for issues of convention.

I'm saying that it can be determined to be true and it can be determined to be false. — Michael

...seems you agree...?

Yep. Worth mentioning.

A statement with 2 truth values is 2 statements. — Hanover

Yes, I would have thought so. Hence my question - is any precedence for the view that one sentence can have two truth values?

That's specifically the issue - does it count as one ship or two?

And "count as..." is a lexical marker for issues of convention. — Banno

Which makes the truth a matter of convention, or even personal opinion (as I don’t need other people to agree with me; I can decide for myself whether or not it counts as one ship or two). That’s decidedly not the realist account of truth but an anti-realist account.

We all agree that the material has changed but the function remains. — Michael

If we can't agree as to what is a ship, why can we agree as to what is material and to what is functionality? Are holustic objects the only thing we can't agree upon, but we can agree upon their attributes?

...and so back to

Nothing in there about the objective-subjective divide. A realist can agree that the ship's components have changed and maintain that we can use the same name for the ship. — Banno

And again I’m not just saying that we use the same name for the ship. In fact we might even use a different name, as a rechristening during the journey. I’m saying that it’s the same ship. How does the realist maintain identity when the material that leaves isn’t the material that returns? Why is it not considered a new ship - a copy of the original - whether with the same name or a different one?

We don't start by defining "ship" according to some strict criteria and then use it in conversation. Rather we talk about a ship leaving, a ship returning, and then assess whether or not the two are the same (and then possibly derive the meaning of "ship"). — Michael

We do have strict criteria, which is why we can use the term meaningfully. Only when we use the term in a way previously unintended do we run into these challenges.

And what we do for ships isn't what we do for everything. We define "firearms" in a fine tuned sort of way, especially where the law says "no firearms allowed." The specificity demanded is context dependent and not always the same.

I’m saying that it’s the same ship. — Michael

Yep, you are. But you are making a conclusion about realism from that. What is your argument for that conclusion?

Trying to cut to the arguments here; it seems to me that you are working with a different account of realism to me.

Yes, I would have thought so. Hence my question - is any precedence for the view that one sentence can have two truth values? — Banno

There was the philosopher who came here and argued such a thing. Is this the guy? https://plato.stanford.edu/entries/dialetheism/

I was summarily ignored when I posted this yesterday in another thread, so I will try it again here.

So I wasn't going to comment, but then this article kept showing up in my suggested reading. I happen to be a fan of Graham Priest and once upon a time he briefly participated in the old forums as a guest philosopher. This particular article is super accessible.

Graham Priest on Beyond True and False

On a less approachable note, see paraconsistent logic and dialethia.

In short form, there are lots of truth values out there besides true and false (some of which are useful in specific applications such as data analysis). Here is a discussion of some of it SEP on Truth Values. A major issue with rejecting the LNC is something called explosion. This objection is as simple as "anything can be proven from a contradiction" and is demonstrated by "negation introduction" and similar forms of indirect proofs. Based on logic as traditionally conceived, permitting something to be both true and false at the same time is a major no no.

As a historical aside, the problem of future contingents has been around since Aristotle and serves as an easy demonstration that our thinking is impoverished by imagining that any proposition must be true or false, but not both, at every moment.

I can add more if anyone wants.

Yeah, the view that A and ~A can be true at the same time.

Thinking A neither true nor false would be paraconsistent.

But Michael would have it that A is both true and false. Which is... different.

OK, I'm interested. the Fitch article in SEP sets out how antirealism can survive if it relies on paraconsitent logic. that was part of what motivated this thread.

Where now?

Fitch article in SEP — Banno

Sorry for being dense, what is the title of the article?

For the sake of expedience, I am just going to assume you mean the one on Fitch’s Paradox of Knowability.

It's both. Vague propositions often don't have a single truth value, precisely because they're vague. — Michael

To say someone middle-aged is young or old is not so much vague as it is senseless unless there is a context in which a comparison is being made. By contrast we can sensibly say a child is young because it is implicit in that, that compared to the larger demographic of adults a child is young. When it comes to saying a forty year old is young, it is meaningless unless some explicit or implicit (given by the context) comparison is included. So, for example, it can sensibly be said that a forty year old person is young compared to octagenarians, It can also be sensibly be said that a forty year old is middle-aged, although that would be somewhat vague, but not senseless.

Clean living and a pure heart - pays off every time . . .

The SEP Fitch article is here: https://plato.stanford.edu/entries/fitch-paradox/

My apologies.

https://plato.stanford.edu/entries/fitch-paradox/

ah - @EricH beat me to it.

3.5 in particular, yes? But my sense is that you don’t want a discussion of what is presented there, but a reaction. I further suspect that my reaction is going to go sideways, so I apologize in advance.

In brief, people don’t like the idea of anti-realism in-so-far as it relates truth to knowledge because clearly there must be things that are true that we don’t know, yet anti-realism suggests that all truths are necessarily known, i.e. there is nothing that is true that we don’t know (Fitch’s Paradox). Your classic case of the height of Mt. Everest before it was surveyed (a discrete fact seemingly manifested in the “real” world) seems to embody this type of unknown truth for which anti-realism cannot account.

So how does paraconsitent logic help anti-realism? It pulls an interesting trick - rather than denying that Mt. Everest has a height if no one knows it, somehow it accepts that the height is both known and unknown. So we can satisfy both the intuition that not all truths are known and the requirement of anti-realism that all truth be known. This much I assume (or perhaps hope) we can more or less agree on.

My suspicion is that you would be amenable to anti-realism if the “middle way” was not absurd (e.g. leads to a contradiction either in logic or intuition). Given that paraconsistent logic seems to save the middle way in anti-realism, you are questioning what else you must commit to if you accept a type of this logic.

Are we on the same page as to where we are and the sort of response you are looking for to “where now?”


P.S. On pain of equivocation (and certainly not to agree with him) I am vaguely reminded of the great perceiver required by the idealism of Berkeley. If this were the case, that there were actually two categories of perceivers (humans as traditionally conceived and something transcendent), it could be analogous to how something could be both known and unknown in a meaningful way and not of necessity collapse the middle way into naive anti-realism. I think there is a little ambiguity in what qualifies as a “knower” for Fitch’s paradox to the extent that our intuition is that humanity (collectively) is not omniscient and yet there are truths that are unknown by us.

Another strategy, however, is suggested by Berkeley’s reference in PHK 3 and 48 to “some other spirit,” a strategy summarized in a further limerick:

Dear Sir, your astonishment’s odd
I am always about in the Quad
And that’s why the tree
continues to be
since observed by, Yours faithfully, God
— “SEP on Berkeley”

A is both true and false. Which is... different. — Banno

And in case you didn’t read the Priest article I linked, here is a quote that you may find interesting.

At the core of the explanation, one has to grasp a very basic mathematical distinction. I speak of the difference between a relation and a function. A relation is something that relates a certain kind of object to some number of others (zero, one, two, etc). A function, on the other hand, is a special kind of relation that links each such object to exactly one thing. Suppose we are talking about people. Mother of and father of are functions, because every person has exactly one (biological) mother and exactly one father. But son of and daughter of are relations, because parents might have any number of sons and daughters. Functions give a unique output; relations can give any number of outputs. Keep that distinction in mind; we’ll come back to it a lot.

Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false truth values. Normally, and following Aristotle, it is assumed that ‘value of’ is a function: the value of any given assertion is exactly one of true (or T), and false (or F). In this way, the principles of excluded middle (PEM) and non-contradiction (PNC) are built into the mathematics from the start. But they needn’t be.

To get back to something that the Buddha might recognise, all we need to do is make value of into a relation instead of a function. Thus T might be a value of a sentence, as can F, both, or neither. We now have four possibilities: {T}, {F}, {T,F} and { }. The curly brackets, by the way, indicate that we are dealing with sets of truth values rather than individual ones, as befits a relation rather than a function. The last pair of brackets denotes what mathematicians call the empty set: it is a collection with no members, like the set of humans with 17 legs. It would be conventional in mathematics to represent our four values using something called a Hasse diagram, like so:

{T}
↗ ↖
{T, F} { }
↖ ↗
{F}

Thus the four kotis (corners) of the catuskoti appear before us.

In case this all sounds rather convenient for the purposes of Buddhist apologism, I should mention that the logic I have just described is called First Degree Entailment (FDE). It was originally constructed in the 1960s in an area called relevant logic. — “Priest on Beyond True and False”

I agree with the summary. But this:

rather than denying that Mt. Everest has a height if no one knows it, somehow it accepts that the height is both known and unknown. — Ennui Elucidator

I don't think that quite right - rather it accepts that the height is neither known nor unknown; and hence paraconsistent.

Since Logical Nihilism I'm amenable to giving consideration to a paraconsistent anti-realism. So I don't think the “middle way” is absurd.

The question may be were it is appropriate to apply anti-realism rather than a blanket acceptance or denial.

The priest article also notes that "The notion that some things might be both true and false is much more unorthodox". Such a view cannot be part of a consistent system, for obvious reasons, without re-defining what it might be to be consistent.

Priest's treatment of the third value of a trinary logic as ineffable is tempting, but I'm struck by the possibility of a different interpretation - nonsense. The devil will be in the detail, but to use his own example, if p is nonsense, then ‘p and pigs can fly’ is nonsense too.

But that is indeed an interesting take. Please, where now? Is there something here that counts specifically against realism?

Oh, and I should add my appreciation for assisting digestion.

I don't think that quite right - rather it accepts that the height is neither known nor unknown; and hence paraconsistent. — Banno

Not to dwell on the disagreement, but I think the motivation to paraconsistent logics is precisely about explosion rather than about propositions without a truth value. We may get off on the wrong foot if we think that Beall is not asking us to accept the contradiction implied by Fitch’s paradox, but to do so in a logical system where such contradiction doesn’t lead to “triviality”, i.e. adopt a paraconsistent logic.

In the literature, especially in the part of it that contains objections to paraconsistent logic, there has been some tendency to confuse paraconsistency with dialetheism, the view that there are true contradictions (see the entry on dialetheism). The view that a consequence relation should be paraconsistent does not entail the view that there are true contradictions. Paraconsistency is a property of a consequence relation whereas dialetheism is a view about truth. The fact that one can define a non-explosive consequence relation does not mean that some sentences are true. The fact that one can construct a model where a contradiction holds but not every sentence of the language holds (or where this is the case at some world) does not mean that the contradiction is true per se. Hence paraconsistency must be distinguished from dialetheism (though see Asmus 2012).
— “SEP on Paraconsitent Logics”

Beall suggests that the knower gives us some independent evidence for thinking Kp∧¬Kp, for some
p, that the full description of human knowledge has the interesting feature of being inconsistent. With a paraconsistent logic, one may accept this without triviality. And so it is suggested that one go paraconsistent and embrace Kp∧¬Kp as a true consequence of the knowability principle. Beall concludes that Fitch’s reasoning, without a proper reply to the knower, is ineffective against the knowability principle.
— “SEP on Fitch’s Paradox”

Hm.. Let's check our usage. I said this concerning @Michael's apparent claim:

it's not paraconsistent logic - which holds that A, ~A ⊨ B is not a valid inference; this is the view usually associated with anti-realism.

it's not quite dialetheism, which holds that for some A both A and ~A can be assigned the value "true". - that there are true paradoxes. — Banno

So paraconsistent logic denies explosion.

Dialetheism, quite distinctly, holds that there are cases in which a statement and it's contradiction can be true.

Do we agree?

(Michael's position seems to be a third alternative - that a statement can be both true and false.)

Giant Molecules Exist in Two Places at Once — Ennui Elucidator

Yes, the double slit experiment works with macromolecules. Maybe it would work with human beings thrown to crash into a screen too, for all we know.

Only when we use the term in a way previously unintended do we run into these challenges — Hanover

Then see the final two sentences here:

So to make it simpler, let’s say the ship that left was named the Theseus and that along with the part-replacements they adopted the name the Perseus.

Was the Perseus previously known as the Theseus?