# Is "Truth" something like a Dirac Delta Function?

To me, Truth is simply what is the case. It is not a matter of reasoning, and it could not be otherwise. Knowledge is a set of beliefs which accord with reality (what is true). Beliefs can be false. Knowledge cannot be false, by definition, because it must fit with what is. (Perhaps this is Pragmatism, I just started reading about it.)

So, my question is: if Truth is simply what is, and we accept that what is can change over time, is the state of Truth something like a Dirac Delta Function: It has a value of 1 at one point of time, and 0 at every other point of time? (See the linked Wikipedia article for a diagram)

Addition: The idea I had in mind was to contrast with another function (diagram) which looks like this: before now, the probability (or actuality) of a state of affairs was zero. After now, it slowly and continuously rises, as it becomes "possible to occur". This is how the Ego looks at the world: "What I want has not happened yet, but as I look to the future, it can, and is more likely over time." The Ego is wrong. What happens has 100% chance of happening, right now, and what does not happen has 0 chance of being the case. This is always true. Things do not "get better", they just ARE.

• I think you may be confusing truth with fact. For many, a fact is "what is", while truth is a property of statements (formal or otherwise). According to this distinction, it is certainly the case that a (well-defined) collection of facts can change with time, but this is not necessarily the case with every collection of facts - some facts persist over an interval of time. The idea of the collection of all facts is problematic since it does not appear to be well-defined.
– nwr
Feb 9, 2016 at 2:54
• Function with value 1 at one point and 0 at every other point is not the Dirac delta function, it is the indicator function of that point. "Dirac delta function" is not a function at all, and to the extent that one can make sense of it as a function it is undefined, or infinite, at that one point. But shouldn't the state of truth being 1 last more than an instant? Perhaps even all the way to infinity in some cases? Feb 9, 2016 at 3:33
• @Conifold It is one for the conditions in effect at the next instant.
– user16869
Feb 9, 2016 at 3:38
• Are you referring to the concept of the present implied by the phrase "The past is gone. The future is yet to come." ? Feb 9, 2016 at 5:52
• @nocomprende Ahh. Sutras can be hard to explain using Western terminology. The result can also be troublesome. Consider that the Faith Mind Sutra obviously says something about our perception of time. Is it better to replace our perception of time with a perception of mathematical functions, especially exotic ones? Feb 9, 2016 at 15:27

Truth depends on the meaning of sentences. However the meaning of sentences such as "I am hungry" or "it is raining" depends on the time and place where the sentences are uttered and on the locutor of the sentences. Other sentences could have their meaning depend on the intention of the locutor: "the fridge is empty" could have a different meaning if the intention is to have dinner or to clean the fridge. More generally a sentence has meaning only in context. These aspects are addressed by pragmatics in the philosophy of language.

Time is not the only contextual element, and even if it were, it doesn't have to be a discrete instant ("it is raining" must refer to an extended period to be meaningful). Contexts are rather complex entities. For these reasons I don't think applying dirac functions or similar mathematical tools is relevant. Either you consider the sentence and its truth value depends on many aspects, not only instantaneous time, or you consider the proposition (the meaning-bearer associated with the sentence, which could be expressed by specifying all contextual elements) and then a truth value is sufficient.

• So what is the word for what is, if not truth? How do we get out of word-wrangling and get down to actuality? Think of Douglas Harding, who discovered that he had no head. No place for thoughts there, just what is. Subject-Object nonduality.
– user16869
Feb 9, 2016 at 13:20
• A proposition expresses what is, and it's true if it corresponds to what is (according to the correspondence theory of truth at least). We get down to actuality, with words--how else would we express what is the case if not with words? Feb 9, 2016 at 19:05
• Take my example: "the fridge is empty". It expresses a state of affairs in the world. My point is: which precise state of affairs it expresses (for example "the fridge is empty on February 9th, 2016") depends on the time the sentence is uttered (and other parameters). Feb 9, 2016 at 19:11
• Now perhaps you have presentist intuitions (that actually is not atemporal, or that facts are what is true at present)? Then your question hinges on the philosophy of time somewhat. Feb 9, 2016 at 19:15

As truth on a subject can be too broad or too specific, I would compare it more to an indicator function, being the space, the product of time and circumstances. For example, let the statement be "Today is Monday". It would be true not in one point of time but whenever it's Monday. Even more, given two different local zones, it will be true for one but false for the other for some hours. This tells us that truth can be subjective. Anyhow, given all the conditions an statement can only be true or false, not a linear combination of both (it can only be or not be Monday at a fixed place).

• But if it is not Monday at that place, then the statement "today is Monday" does not make sense. I guess I was trying to say that there is no option, it just is the case. Perhaps "Truth" was the wrong word to use. "Fact" does not seem to fit either. I am saying that "what is" is not about statements, it just is.
– user16869
Feb 9, 2016 at 3:41
• @no comprende But what do you mean for a statement "to fit" with what is? How can something lasting fit something fleeting, something made of words something concrete? Or do you mean by "delta function" that this fit is only instantaneous? How then would it be established? Feb 9, 2016 at 4:00
• "This tells us that truth can be subjective." I'm not sure that follows, or at least not what one normally means by saying truth can be subjective. Saying "Today is Monday" has implied "...where I am speaking right now." Compare that to "That object is 2 meters long" or "That book has 200 pages." The book couldn't suddenly have 250 pages for someone else. Feb 9, 2016 at 12:10
• @Conifold I think that ALL truth is subjective. Without a subject, it is not known. There would be no correspondence with anything. It is true now. The next moment, whatever is, is true, now. The experience of it makes it true. You can't experience something that is not.
– user16869
Feb 9, 2016 at 13:05

One has to discriminate between a state of affairs or fact, which belongs to the real world, and a proposition, which is a linguistic entity belonging to the realm of mind.

A state of affairs happens or does not happen. On the opposite, a proposition is true or false.

In order to discriminate both, I recommend: If P denotes a state of affairs, e.g. it rains on 1.1.2016 in Manhattan, then "P" (enclosed in quotation marks) is the proposition "it rains on 1.1.2016 in Manhattan".

A proposition does not change its truth value: For the sake of the argument let's assume that it rains on 1.1.2016 in Manhattan. Then the proposition "It rains on 1.1.2016 in Manhattan" is true all days, even on days where it does not rain in Manhattan.

On the opposite, a sentence like "Today it rains in Manhattan" is true on some days and is wrong on other days. But the sentence is not a proposition, because it contains the unbound variable "today".

Hence what changes in time, are the states of affair - not the truth value of a proposition.

Aside: Dirac's delta-"function" is not a function at all. It is a distribution, i.e. a continous linear operator on a certain space of functions. The Dirac distribution does not have the form of an integral with a certain function as kernel. Hence I agree with Conifold that instead you mean an indicator function. Nevertheless I do not think that the issue of your question becomes more transparent when linked with mathematical terms.

• Thank you. I answered with a comment, then moved it in to my question. We are getting somewhere now.
– user16869
Feb 9, 2016 at 13:23