Do statements have an intrinsic, unchanging truth value, even when currently unknown, or can they have different truth values at different times?

Question

Example:

I state that a coin will come up heads, then flip it. While the coin is flipping, does the statement 'the coin I just flipped will come up heads' have a truth value?

Based on my understanding, it's unknowable, so it doesn't have a truth value associated with it. I am not yet incorrect or correct.

But if I state that the coin comes up heads, flip it, and it comes up tails, the initial statement I made clearly doesn't match with reality, so its truth value is seemingly false.

From the perspective in the moment in time before the coin lands, to the moment after it lands, does the truth value retroactively change? Or would my initial perception (that the statement 'the coin I just flipped will come up heads' is one without a truth value) be fundamentally flawed, and the statement was always false, even though the information in question didn't exist yet?

Answer 1

Both, because propositions are expressed in language which is always both vague and ambiguous. Thus, a statement's truth value is dependent on the context of the discourse it finds itself.

Consider:

Today is Tuesday.

The proposition is true exactly one day every week, on Tuesday. But, we can make a similar proposition true by adding context:

'Today is Tuesday' is true only every Tuesday.

Now our proposition is true every day of the week. But, you might argue, you changed the proposition! True, but here's an alternative. Consider that you only, due to your religion, are allowed to utter 'Today is Tuesday' on Tuesday. Is the proposition always true? Sure, because at that point, you only utter it on Tuesdays, so the proposition because of a restriction of when it is uttered suddenly becomes always true when uttered.

But what if I read it on days other than Tuesday, you complain? Well, then it isn't always true. How exactly is that? Well according to some ways of thinking about truth, truth stems from having a judgement of truth, in this case of a proposition that purports to represent a truth condition about the state of affairs in the real world. So, now that you read it on days other than Tuesday, then the judgment you make about its truth will depend on the day you use it.

So am I saying that judgment is necessary to determine truth? Yes, very much so. This an important idea that goes back to at least Kant, but other philosophers have thought about it too. Consider Bretano's Theory of Judgment (SEP):

Judgements are one of the three basic kinds of intentional phenomena with which Brentano deals at great length in his Psychology. That is not to say, however, that Brentano’s theory of judgement is just concerned with psychological issues. Brentano also aims to show how an experience of judging, specifically the experience of judging correctly, can provide us with a basis for grasping concepts like existence, truth, and logical inference. Brentano’s investigation of the mental act of judgement promises therefore to advance logic, epistemology, and ultimately metaphysics.

So, if one is not an externalist in these matters, one simply can accept that the truth of a proposition relies on the judgment of the thinker. Since physical experience, rational thought, propositional content, one's truth-conditional semantics, propositional attitudes, and theories of truth all are relevant, it's easy to defend the notion that any truth-value of a proposition is highly-context dependent, an idea that particularly frustrates people who believe there is only way to think and believe.

Answer 2

To answer this question profoundly, we first need to introduce terminology.

In formal logic (gray area field between math and computer science), statements are separated from interpretations. A statement in this context may be something like "the ball is red", "Archimedes is a man", "if the tide is high, then it will be low six hours later", or whatever other logical statement you can come up with. So far, so good.

Now, an interpretation is a function that assigns values to the names in such statements. An interpretation may assign a European soccer ball to "the ball" in the first statement. Which will make the statement false in most cases. It may also assign an American foot ball to "the ball", and the statement will usually be true. Or it might assign a specific dance event to "the ball", which renders the truth value of "the ball is red" ill-defined. Whenever you are reading a statement, you are applying some interpretation to the statement in order to make sense of it.

This interpretation is usually implicit. You read a text, and you assume you know what the different words are referring to. And you are doing that by considering some context. When you read "the ball is red" in a British sports magazine, you are likely using a different interpretation for "the ball" than if you were hearing it in the context of a baseball game. And it is exactly this implicit nature of interpretations that leads to so many confusions. Mind you, we are not even able to write down almost all relevant interpretations, simply because they assign real world objects to the terms in the statement. And you can't put a specific ball into writing without resorting to some other terms that will need to be interpreted themselves with a real world object. You can only write down the names of things, not the things themselves.

So, with that out of the way, we can finally answer your question: Statements get their truth value from some interpretation. As long as you use the same interpretation, the truth value cannot change. But whenever you apply a different interpretation, the truth value can change. And that is precisely what happens when people interpret time dependent statements. You interpret the statement "the coin will come up heads" differently before and after throwing the coin. However, when you apply an interpretation that assigns one specific throwing of the coin to this statement, the statement is either always true or always false, depending on the actual outcome of the throw. The result may not be known, as is the case when the throw is still in the future. In that case, observing the actual result tells you whether the statement was true/false all along. However, if you always interpret the statement "the coin will come up heads" to refer to the next throw of that specific coin, you never know its truth value when it is said.

Answer 3

Statements can have truth values that change with time. The statement, 'It is the 29th of February today' is periodically true, but is not true now.

A prediction, such as 'It will rain tomorrow', does not have a known truth value, since it refers to an unknown future state.

Answer 4

The statement

The coin will come up head

is a sentence about a future event. After the coin came up, the statement is meaningless, because afterwards the coin will not come up any longer.

In 2-valued logic each statement is either true or false, even when we do not know the truth value. The problem is with future events. Your example is similar to Aristotle’s discussion about tomorrow’s see-battle. Aristotle concludes that future possible events do not necessarily have a truth value:

"Clearly, then, it is not necessary that of every affirmation and opposite negation one should be true and the other false. For what holds for things that are does not hold for things that are not but may possibly be or not be; with these it is as we have said." (Aristotle, On interpretation, Chap. 9)

For further discussion of the problem and different proposals for a solution see the Stanford encyclopedia.

Answer 5

I think you are confusing your state of knowledge about reality (in this case, the future of the coin) with reality itself. They will only agree if you know all relevant information about reality and you reason coherently from the information you have.

The motion of the coin is completely deterministic, it is not unpredictable in principle. The only thing stopping us from predicting it's trajectory reliably is lack of information. There is arguably no such thing as randomness in the macroscopic world, just ignorance/uncertainty, which we tend to model as "random chance". When we view it as our state of knowledge, the ambiguity/paradox is resolved.

Whether the coin will come down heads or tails has a constant truth value, we just don't know what it is. When we say "the coin will come down heads" we are making a statement about a model of reality, but we don't usually need to explicitly state that.

Answer 6

I can’t say anything of the following with confidence or definiteness, but I’ll try to give some perspective from what I myself have been learning lately.

1. There are many different things in modern philosophy, modern scientific knowledge, and modern society called “logic”. A subset of those things can be considered “formal systems”. I do not know a perfect or definitive definition of what a “formal system” is, and maybe there is not yet one, since having a “perfect definition” might imply being able to do so in some “perfect system of meaning”; but since formal logic, as I see it, is motivated by a desire to uncover what a “perfect system of meaning” would be like, we would not be able to define “formal system” definitively until we had determined a definitive formal system to express that idea in. It would be interesting to imagine how a perfect formal system would define what a “perfect formal system” is, but obviously, there are so many frontiers in research in logic, so it’s (arguably) not a concrete question to pursue. Assuming we can still make progress in understanding, with our intuitive ability to discern what things are like, without offering perfect definitions of them, I can approximate that a formal system tends to be a set of rules which are “unambiguous”, like some of the rules of mathematics. I leave the question of what “unambiguous” means for a later time.
2. In my opinion, it is way more modern to think of “logics” as formal systems, which means that there are as many different ones as humans can come up with. In other words, instead of asking if the nature of logic is such-and-such, the question is how a formal system could describe whatever phenomenon you have in mind well, and what kind. That is not to say that there are not some fundamental, universal laws of truth, but that whatever they are, we don’t know enough about it to ask a lot of questions about what it’s like, and we don’t need to consult with it to model the rules of systems we encounter in our daily lives. This is a suggested paradigm, not a truth claim I’m particularly attached to.
3. The above approach makes your question easier. Once you have studied different systems of logic, it may be easier to imagine how symbolic notations can be used to represent patterns and phenomena we encounter. Developing such a notation is not necessarily easy, as a new notational system sometimes amounts to the birth of a new theory. Physics is full of examples of this. (Richard Feynman invented a particular kind of diagram for describing quantum phenomena in physics, which were later studied for their mathematics properties in their own right. Such diagrams have been named “string diagrams”.) The important thing seems to be that the rules of your symbolic, representational system mirror the structure or behavior of the “real world”-thing you are experiencing.
4. Allowing yourself to freely create any symbolic-representational system invites one to ask if there is any real boundary between fields traditionally known as “logic” and “ontology”. Take modal logic for an example. Modal logic built on pre-existing logics by allowing a symbol to represent the conceptual idea of “possibly” and “necessarily”. From there, modal logic has seemingly rapidly expanded to encompass almost any imaginable way of semantically inflecting truths, and instituting a symbol to reflect it - I can make an operator that conveys “knowability”, as in, “this proposition is known”, or an operator that conveys “obviousness”, as in, “this proposition is obvious”. I think the idea that “pure logic” and “human conceptual meaning” are incompatible “layers” caused some confusion until it became clearer that they were not. In linguistics, notational systems have been developed to abstract away “conceptual meaning” from “logical structure” (for example, P(x) is a predicate that means “red” - but quantification of that predicate over an entity is apparently purely mathematical, encoded in the underlying logical system, not in the “conceptual” predicates). Modal logic is just one example that shows how the structure of concepts themselves can actually be represented by “formal” structures; the formal systems that come close to behaving like human conceptual meaning are just bigger and have more rules. That is how modern language-based AI works: they have learned patterns of human semantics and are able to model those rules in computer circuitry which ultimately reduces to very elementary mathematics (binary arithmetic, etc.)

Therefore, I guess there are two approaches to the question: what is the nature of “knowing” or “truth”, itself, in our world (which is definitely useful and interesting); or, what I find more inviting, how could I model what I observe as the patterns of some system, in symbols? There are tons of logics developed for those kinds of purposes, like temporal logic, dynamic logic, imperative logics, erotetic logics, dialethic logics, and others that I don’t know of.

One framework I can pass on a recommendation for is David Spivak’s Temporal Type Theory. While I believe intended for the modeling of temporal systems, since it presumably includes a concept of “truth”, it could maybe be used to model “the truth of a proposition at a certain time.” (In my opinion, David Spivak is a genius who has changed the world by more than anyone thrusting category theory into real-world domains outside of mathematics, as a “universal modeling language”, in the field of applied category theory. In fact, I worship him.)

Answer 7

Do statements always have the same truth value, and that truth value is just revealed, or can they have different truth values at different times?

It is trivial that if a statement is true (or false), it is true (or false) of the real world, and that each statement has to be interpreted in context. The statement "Donald is a criminal" may be true in a number of contexts and false in others, it all depends on which Donald the statement is referring to.

It would be absurd to assert that a statement has no truth value because it is sometimes true and sometimes false. If that was the case, we would have to say that the statement "the statement has no truth value" has itself no truth value because it would have different truth values according to the different truth values of the statement. Thus, asserting "the statement has no truth value" would then be both asserting that the statement is true and that it has no truth value, which is absurd.

So, a statement is only a statement in context. What this means is essentially that we have to interpret what the statement is used to mean according to the context of its utterance. We all do that all the time and there is no problem.

The implicit fallacy in the question is to pretend that it is the same statement irrespective of context.

I state that a coin will come up heads, then flip it. While the coin is flipping, does the statement 'the coin i just flipped will come up heads' have a truth value?

Yes, it has.

You don't know which truth value it is yet, but you will if you wait long enough.

Whether you are here or not to verify the result, it will be empirically true or empirically false that the coin you just flipped has come up heads, and it is already true or false now that it will or will not.

But, if I state that the coin comes up heads, flip it, and it comes up tails, the initial statement I made clearly doesn't match with reality, so it's truth value is seemingly false.

The prediction that the coin will come up heads implicitly concerns the next time that the coin lands. Statements have to be interpreted in context.

Answer 8

Any claim to know about a future event when one doesn’t is surely invalid whether or not it turns out to be correct. Here the exact phrasing matters; ‘the coin will come up heads’ is invalid if the speaker doesn’t know, but ‘I predict that the coin will come up heads’ is valid because the speaker is free to make predictions. Whether the prediction turns out to agree with the coin is a separate matter.

Answer 9

Tl; dr: Absolute statements about the future have no definite truth value. All we can do is make probabilistic statements.

The future is categorically unknown; quantum physics is one of the two great fundamental shifts in our understanding of nature brought about in the 20th century (the other one being that time and space differ in different reference systems). It effectively killed Laplace's demon.

Quantum physics posit that on the microscopic level, future events are not only unknown but unknowable. Each one of a plethora of possible micro-events (e.g. the spontaneous splitting of an unstable nucleus; the transition of an electron to a lower orbit, emitting a photon) is assigned a probability to happen in a given interval in space and time. It may be more likely to happen at time T1 and location L1 than at some other T2/L2 location, but we really do not and cannot now where it will actually take place.

This principle unknowability caused intense debates at the intersection of physics and philosophy. Famously, Einstein, one of the main proponents, could not accept the "Copenhagen interpretation" which essentially embraces the unknowability, saying "Der Alte würfelt nicht.". I think most physicists today would disagree, even though no proper consensus has been found about what it all means then.

For macroscopic aggregates of particles, these probabilities usually equal out and coalesce to a predictable future, which is why engineering works: Houses do not collapse, bullets hit their targets.

But the fundamental microscopic uncertainty underlying the macroscopic state prevents an entirely known future. Even worse, on the microscopic scale, several possibilities can overlay into a state called "superposition": Even the present time contains more than one possible state; reality proper is indeterminate.

It should be clear that any attempt to assign absolute truth values to future events is laughable. The future is unknowable. For statistical reasons, many macroscopic events are very likely; but the uncertainty creeps in through random effects of microscopic events in non-linear systems (like the coin toss) and through "error accretion" over long time spans.

Does a prediction then change its truth value? I would indeed think that a three-valued logic is necessary to properly reason about predictions, and that yes, the truth value of most predictions changes after the event they predicted happened or not. The exceptions are predictions about — usually microscopic — events which are still part of a superposition, like Schrodinger's cat; the prediction that the cat will be dead at a time T1 in the unopened box has the value "unknown" (or, more precisely, a certain probability) before T1; it retains this "indeterminate" value even after T1 until the box is opened.

Answer 10

Truth values are strongly associated with logical contexts, the object of study of Epistemic Contextualism.

To put it in simple words, Aristotle's three laws of reason (e.g. Law of Identity) depend on an epistemic context. If you tell a story about Einstein existing to the moon, the statement "Einstein exists on the moon" is true: but ONLY in a certain epistemic context. And it is true as long as the story is told, imagined, used. Outside such context, in any new context, truth is relative (the statement can be false or true, depending on the new context).

With more rigor, epistemic contexts depend on several elements: language, semantics, environment, amount of subjectivity and objectivity, etc. In addition, epistemic contexts allow certain levels of dynamics (that is, breaking the law of identity in the context): e.g.

...

- But men arrived to the moon after Einstein died!

- So, Einstein existing on the moon is necessarily false; it can't be true anymore.

...

Answer 11

I state that a coin will come up heads, then flip it. While the coin is flipping, does the statement 'the coin I just flipped will come up heads' have a truth value?

This sounds like a restatement of Schrodinger's cat.

While the coin is flipping it is simultaneously Heads and Tails until it lands like Schrodinger's cat is simultaneously Dead and Alive until the box is opened. So the prediction about the final state of the coin is also simultaneously True and False until the coin lands.