Wikipedia says:

In the same way, "all men are mortal" is unfalsifiable: even if someone is observed who has not died so far, he could still die in the next instant. By contrast, "all men are immortal," is falsifiable by the presentation of just one dead man.

The statement

P: All men are mortal.

is equivalent to

~P: No man is immortal.

So of course, "all men are immortal" is a different, but related statement. We seem to be able to logically assign truth values to all three. My first question is, how is falsifiability related to the logical possibility of assigning truth values?

To further illustrate, in economics, we make a distinction between positive and normative statements. Positive statements (facts) can have a truth value, normative statements (opinions) cannot. In other words, positive statements are propositions, normative statements are not. In order to illustrate the concept further, I've often employed falsifiability (testability). Facts are testable; opinions are not. So it seems, at the very least, that the universe of all propositions is a superset of falsifiable propositions.

Now consider

Q: A is A. = ~Q: ~A is ~A.

This classic tautology doesn't seem falsifiable since it can never be shown to be false. That is, we can logically assign a truth value (always true) to the proposition Q, but it isn't falsifiable. However, the related statement

R: A is ~A.

is always false (a contradiction?). Is R a proposition? Is something that is never true falsifiable? If so, this seems to violate the notion that falsifiability has nothing to do with actual truth values, on the logical possibility of their assignment.

Where am I confused?


2 Answers 2


There are several points of confusion here.

First, your examples are more complicated than they need to be because of the temporal aspect of the problem (immortality). We need to make a distinction between global statements that are falsifiable in practice (such as "All crows are black" which equals "No crows are white" which can be falsified by examining all crows, and which remains true even if a white crow is hatched tomorrow) and those which are not (such as "All men are mortal" which equals "No man is immortal", which cannot be tested as the test of immortality would require waiting until after the end of time).

If we set aside this problematic, we now come to an question of what we mean by truth. Some philosophical traditions make a distinction between observed truths and inferential truths; other argue that they have the same truth status. Pragmatism, on the other hand, argues that the "cash value" of truth is tied to its utility, so a statement can be considered to be "true" even if it cannot be rigorously and falsifiably verified.

All of this is orthogonal to your next problematic, which is known in the philosophy world as the "is-ought distinction", and was most famously raised by Hume. There's no need to drag normative statements into the discussion, as they have no bearing on truth and falsifiability.

Finally, you write:

This classic tautology [A = A] doesn't seem falsifiable since it can never be shown to be false.

That may or may not be the case, depending on how we are reading "A". We certainly can determine whether or not some given (sensible) entity is identical to itself, if we have stipulated the identity conditions for that entity. If we are dealing with A as an abstraction, we are beyond the scope of sensibility and are relying on pure reason.

In other words: there are differing notions of epistemology and truth in play. Falsifiability applies to empirical matters, but is not appropriate to mathematics or pure logic, where the canons of logic are applied to non-sensible abstractions. The process of determination of whether or not a given statement is "true" is going to vary based on the type of statement and the epistemological framework chosen.

  • In fact, the reason I brought up the tautology was something like whether or not "definitions" are falsifiable. I see now that the question, in that case, is a bit wrong. I'm still thinking its possible to create a hierarchy of these statements, but the boundaries are much clearer. Thanks for the great answer.
    – jrhorn424
    Nov 18, 2011 at 4:40
  • 1
    "All crows are black" is not equal to "No crows are white". It is equal to "No crows are not black". It can be falsified by examining a single crow that is not black. In particular, it is falsified if a white crow is hatched tomorrow. Putting these issues aside, you wrote interesting points about the different kind of truths.
    – Dominic108
    Jan 18, 2020 at 3:07

How is falsifiability related to the logical possibility of assigning truth values?

It's not. But clearly in the context of falling down and ceasing to function as a human body, we have a innate process of verification; that person fails to show at family functions or answer our phone calls (consistently...one would hope). And so the terms best apply to a context of verifiable events.

However if we are talking about a circle and "points on a plane equi-distant from a given point" the truth value is not established by sniffing out infinitessimal "points" and measuring distances and charting points.

Secondly, what is the use between determining a difference between positive and normative statements, if there is no recommendable difference in usage. You can hedge all you want, but in Hume's "Commit them to the flames" and in "Thou shalt not use normative statements like positive statements" there is the bulk force of a normative statement. You can call it what you want, "Best Practices", "more fruitful", "better controlled", whatever, how far do you get from Aristotle's repeated value: arete, when that can be translated as "expedience"?

And if a normative statement is just "your opinion" then you may not treat normative and positive statements as equal, but if I chose to treat opinion as just as valid as fact, what's that to you? We are allowed to differ on opinions, so shouldn't we?

We humans have a finite amount of time. (Oddly enough, this ties back to "All men are mortal".) The apportioning of finite or scarce resources is the defining attribute of Economics. Central to economics is the "Opportunity cost"; if you do X with your time, you can't do Y with it. These are pretty close to facts. From this arises the valid normative statement "Don't waste other people's time."

The family of stack-exchange sites owes its existence to the value of time.

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