# Can a proposition change its truth value?

According to a modern conception of the nature of the proposition, no proposition can be at one time true and another time false

However my understanding of propositions is that some of them can change their true value. For instance:

The rain in Spain falls mainly on the plain

is true (for the sake of argument) at all times. However

Today it is raining

might be true on the 18th May 2014 but false the day afterwards. So it's truth value can change.

So what have I done wrong? Have a misunderstood the nature of a proposition or truth value? Or is there more than one 'modern conceptions' of a proposition?

As ever, many thanks for everyone's expertise.

• You should take a look at dynamic semantics plato.stanford.edu/entries/dynamic-semantics
– sjmc
May 18 '14 at 17:21
• @sjmc: I don't think the debate has anything to do with dynamic semantics (provided you mean the DPL tradition inlcuding Groenendijk et al.). The debate presupposes a static conception of sentential meaning or proposition conceived as a vehicle to represent the world in a certain way, a notion still predominant in philosophy. Dynamics, on the other hand, consider meanings not to be mere representations but rather 'information state changers' or functions from states to states. May 18 '14 at 18:57
• The rain in plain falls mainly on the plain is a tautology. Did you mean The rain in Spain falls mainly on the plain?
– TRiG
May 19 '14 at 9:36
• @Crab: I think one can easily resolve the problem without bringing up the big guns: The sentence "Today it is raining" changes its meaning because the term "today" is not a constant but a variable. Each day "today" has a different value. As a consequence, the different propositions, which result from he different values of "today", may have different truth values. Jul 30 '15 at 15:54
• @JoWehler How do we know that each statement like P it must be either true XOR false? Law of excluded middle and law of non-contradiction relate the truth value of a statement and its negation but don't explicitly state that P has exactly one truth value. Sep 17 '20 at 15:42

There are two main views on the semantics of propositions: tensed vs tenseless. Quoting Markosian:

Tensed view: Propositions have truth values at times rather than just having truth values simpliciter. [This makes it] possible for a proposition to have different truth values at different times.

Tenseless view: Propositions have truth values simpliciter rather than having truth values at times. [This makes it impossible] for a proposition to have different truth values at different times.

The 'modern conception' that Kenny is referring to is the one inherited from mathematics, where sentences don't include such locutions as 'I', 'now', 'yesterday' and so on, and thus the need to make sentences temporally unstable (to use Rescher's phrase) doesn't arise.

The tenseless view of propositions is still prevalent in the mathematical practice, but it seems a little too strong to claim that it's the modern conception of the semantics of propositions. The alternatives are out there, and philosophers of time, logicians interested in the temporal modalities, and others in linguistics and computer science departments are debating the pros and cons of each view. So yes, there is more than one modern conception of the semantics of propositions.

Further Reading. I would recommend reading the aforementioned SEP article on Time in its entirety. If you're interested in a more formal treatment you can look at van Benthem's Modal Logic for Open Minds, chapter 18, and/or Goldblatt's Logics of Time and Computation, chapter 6, both from CSLI.

Just to add some more relevant literature on the debate between eternalists (propostitions don't change their truth-values) and temporalists (eternalism's negation), which at its heart is a metaphysical rather than a formal discussion: Proponents of temporalism include:

• Arthur Prior: Past, Present and Future. Oxford 1967.
• Prior: Papers on Time and Tense. Oxford 1968.
• David Kaplan: "Demonstratives". In Themes from Kaplan ed. Almog et al.. New York 1989.
• Francois Recanati: Perspectival Thought. New York 2007.
• Berit Brogaard: Transient Truths. New York 2012.

Since eternalism has been the orthodoxy until recently there are only few comprehensive defenses of that position. But you may read:

• (+) Awesome selection May 18 '14 at 18:57

Truth functional temporalism, the idea that a proposition's truth value is affected by its relative position in a compound sequence even if no overt tense differentiation is made, can be invoked to resolve certain paradoxes. The barber who decides to shave today all and only those who didn't shave themselves yesterday will shave himself today if he didn't yesterday either, but won't if he did. End of problem. (Ditto mutatis mutandi for the Russell set paradox.)