On Truths vs. truths

By Adam J. Pearson

When I consider the matter carefully, I do not find any absolute, capital ‘T’ Truths in the world; I find only relative, lowercase ‘t’ truths. Relative truths are dependent on relationships between sentences and states of affairs (ways things are) in the world. Since most states of affairs in the world change, most truths are, therefore, themselves subject to change. A true statement can become false over time.

For example, the statement “there is an apple on the table in my kitchen” might be true right now if there is such an apple on the table. Imagine, though, that I am in a hurry to leave my house and run out with the left wide door open. I return home a few days later and find that a deer has stolen off my apple (and there are delightful deer droppings all over the house)! In this situation, the statement “there is an apple on the table on the table in my kitchen,” which was once true, is now false. This is because its truth depends on its relation to what’s actually present on my table; once the apple leaves that table, the sentence turns from true to false.

Not even mathematical statements can claim the status of absolute Truth because their truth is relative to particular axioms. In geometry, for instance, the truth of the statement “the interior angles of a triangle add up to 180 degrees” depends on the kind of geometrical space you are working within. On a flat Euclidian plane, the statement is true (see Fig 1.1).


Fig 1.1A triangle in a flat Euclidian plane – its interior angles add up to 180 degrees.

In contrast, on a spherical, non-Euclidian plane, the statement is false; the internal angles of a triangle mapped on to a sphere add up to more than 180 degrees (see Fig 1.2).


Fig 1.2A triangle mapped on to a spherical surface – its internal angles add up to more than 180 degrees.

On a hyperbolic saddle-shaped plane, the statement is also false; the internal angles of a triangle mapped onto a saddle-shaped surface add up to less than 180 degrees (see Fig 1.3).


Fig 1.3A triangle mapped on to a saddle-shaped surface – its interior angles add up to less than 180 degrees. 

As the case of the triangle mapped on to different shapes of geometrical surfaces shows, even in mathematics, the truth of a statement depends on the context in which we are considering it and the ways we define its key terms. Within a given system, exactitude and certainty can be established, but the same statement considered in different geometries can have different truth-values. This, as we saw, is the case for the internal angles of the triangle, which add up to exactly 180 degrees on a flat surface, more than 180 degrees on a spherical surface, and less than 180 degrees on a saddle-shaped surface.

Even simple arithmetical statements and simple geometrical statements like a “triangle has three sides” ultimately depend on basic axioms and definitions.  Outside of the realm of pure mathematics, when we are speaking about conditions and types of things and states in the physical universe, the relative nature of truths is all the more apparent. There are scientific laws that hold at certain length-scales, but that break down at the level of the really large (cosmological level) and the really small (quantum level).

The point I am making here is not that ‘no statement is true,’ but that statements are true relative to states of affairs (ways things are) in the world. When the states change, the truth-value of the sentences that depend on them also change. This fragile relativity of truth is an epistemological consequence of the changing nature of our physical universe.

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