What, specifically, is the difference between these? — Banno
including logical nihilism, Davidson's use of T-sentences, Anscombe's direction fo fit and a few other items — Banno
This isn't a rejection of bivalence. This is just pointing out certain words are vague. — Hanover
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."
something new, is seems - at least to me: that a statement can be assigned more than one truth value. — Banno
"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
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
I'm saying that it can be determined to be true and it can be determined to be false. — 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. — Banno
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
Fitch article in SEP — Banno
It's both. Vague propositions often don't have a single truth value, precisely because they're vague. — Michael
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
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”
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. — Banno
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”
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
Giant Molecules Exist in Two Places at Once — Ennui Elucidator
Only when we use the term in a way previously unintended do we run into these challenges — Hanover
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?
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