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Suppose there is proposition p, and the sentence is:

[1] That [whatever it is] neither proves nor disproves p. [In a sense, it is irrelevant.]

Can I state it in one verb, like:

That does not [verb] p.

Some possible candidates (but not what I am looking for as it contains the word “truthfulness”):

[2] That does not affect the truthfulness of p.

[3] That does not verify the truthfulness of p.

Or, is it the case that:

[4] That does not disprove p.

implicitly contains [1]?

  • Please don't use code blocks to cite text—they don't break and cause no end of display oddities; they are reserved for inserting computer code. Instead, start each paragraph in a quote with “>”. That will give you a nice, clear block quote. – Janus Bahs Jacquet Dec 26 '14 at 13:25
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    There aren't any such words that are used the same way, as verbs. Prove and disprove are polar opposites, and define a cline of belief between "almost proved" and "almost disproved". The terms on this cline are not verbs, however. And exactly what do you mean by "combine"? Since the 2 verbs are opposite, nothing can be both proved and disproved (except for jokes in Gödel, Escher, Bach), so the meaning you're asking for is unclear, since it would require a negative and hence be an idiomatic NPI. – John Lawler Dec 26 '14 at 15:58
  • Does "test" not work? – Rusty Tuba Dec 26 '14 at 16:14
  • John, I agree that the title itself is unclear. However, with the examples I gave, I think what I am trying to ask is clear. – blackened Dec 26 '14 at 18:03
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The adjective inconclusive comes immediately to mind.

ADJECTIVE

Not leading to a firm conclusion or result; not ending doubt or dispute:

Inconclusive is different than irrelevant (and many of its synonyms). While something irrelevant is disqualified from impacting a conclusion, something inconclusive may impact the conclusion, but is insufficient to form the conclusion in itself.

"The circumstantial evidence was inconclusive in the murder investigation, but the price of eggs in China was irrelevant."

It seems the positive action of proving is not "verbally" comparable to the inconclusive status of the argument. The verb conclude "combines" prove and disprove by defining an action at the intersection of prove and disprove. In any frame of reference, proving p as true simultaneously disproves p as false. One could coin antonyms of conclude, like contraclude to mean "not closing (the investigation)", but we are simply stating that the argument has not yet "combined" prove and disprove in a conclusion.

This is a very interesting convergence of philosophy and language. You can imagine yourself in a plane looking down on two Interstate highways. From the perspective of your question, they seem to "intersect", but from every other perspective, they clearly pass over one another without touching.

Since p and the truthfulness of p are separate entities,

The simplest way to express the concept you are considering is:

"That leaves p (or the truthfulness of p) open for investigation (or discussion)."

  • Though your answer was inconclusive, I take it as a thoughtful side note. – blackened Dec 26 '14 at 15:18
  • I'm examining verbal forms. This is a great challenge. – ScotM Dec 26 '14 at 15:19
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A single word that provides the sense you want could be one of resolve, determine, decide, or settle. They are all approximate synonyms in this context.

The definition of resolve is:

: to find an answer or solution to (something) : to settle or solve (something)
: to make a definite and serious decision to do something
: to make a formal decision about something usually by a vote
(Source: Merriam-Webster)

So, in your sentence:

That line of reasoning, while interesting, does nothing to resolve the proposition p, and is therefore tangential to our discussion.

  • The words you propose are excellent options, @jxh but your last clause is tangential and irrelevant :) A line of reasoning need not be either tangential or irrelevant to be inconclusive. In fact an inconclusive line of reasoning can be one small step from proof. – ScotM Dec 27 '14 at 1:30
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    @ScotM: The "does nothing" qualification is intended to convey that the line of reasoning does not move the logic either way. The statement itself does not justify why that is true, but it is only an example. – jxh Dec 27 '14 at 1:33
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Great question.

In fact, writers will often simply use both "prove" and "disprove" in this context. For example:

What does an experimental test of quantum contextuality prove or disprove? (link)

Experiments are controlled tests designed to prove or disprove a hypothesis. (link)

In fact, these two simple and randomly chosen examples both contain a single word that can refer to the concept of proving and disproving: test.

Here's the relevant verb definition from Merriam-Webster online:

to put to test or proof

The verb definition actually uses the noun definition, so let's have a look at that as well (or at the relevant definition), because it contains more precisely what you're looking for:

a critical examination, observation, or evaluation : trial; specifically : the procedure of submitting a statement to such conditions or operations as will lead to its proof or disproof or to its acceptance or rejection

If you want more generally to state that something is not relevant to an argument, then you can use any one of the words synonymous with irrelevant (which is the relevant word that you, in fact, used in your post):

not germane

not related

not applicable

Or, my favorite, because of its dual meaning, both of which may be pertinent if you're peeved that someone is offering an opinion or statement that is neither relevant nor polite:

impertinent

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In the legal arena, one would say that the (discussion, fact, statement, etc) is not dispositive, in that you are not able to "dispose" of the issue, i.e. resolve it one way or the other. One is often hoping for dispositive evidence in a trial, since it will allow one to close the case.

http://legal-dictionary.thefreedictionary.com/Dispositive+Fact

http://www.law.cornell.edu/wex/dispositive_fact

  • As I reread the OP's question now, I do wonder about the original context. One would use something like dispositive if the fact/statement might be evidence in favor of or against the truthfulness of P, but still does not provide conclusive proof or falsification. If one is hoping to imply instead that the fact/statement is unrelated to the truthfulness of P, then one would likely not use dispositive, and would use a term like irrelevant. – Mark Thompson Dec 27 '14 at 9:10

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