An Obvious Theory of Truth

Truisms are welcome in the theory of truth. Here is one: the sentence “London is rainy” if true if and only if the entity referred to by “London” has the property expressed by “rainy”. Generalizing, a sentence (or proposition) is true just in case the reference of the subject expression instantiates the property expressed by the predicate expression. This formula combines two concepts: a semantic concept of reference (denotation, expression) and the concept of instantiation understood as a non-semantic relation between objects and properties. Truth results when the entities denoted (objects and properties) stand in the instantiation relation. So we can say that truth consists of a combination of a semantic relation and a non-semantic relation: it is the “logical product” of these two relations. The analysis of truth is given by a “vertical” relation to the world and a “horizontal” relation between worldly entities. Thus “true” expresses a complex property comprising representation and instantiation—that is what the concept amounts to. Both are necessary for truth and together they are sufficient. Moreover, the formula is the most banal of truisms: of course a sentence is true if the things it talks about have the properties the sentence attributes to them. The sentence “snow is white” is true just if the stuff it refers to (snow) has the property the sentence ascribes to it (being white). How could this fail to be correct?[1]

Some minor wrinkles can be quickly ironed out. Is the theory (let’s call it that) ontologically committed to properties in some objectionable platonic sense? I stated it that way, but this is not integral to the theory (though metaphysically unobjectionable, in my view): we could state it in terms of concepts or even just predicates—as in the notion of an object falling into the extension of a predicate. Nor is the theory committed to sentences as truth-bearers: we can run it on propositions, statements, beliefs, what have you, so long as we have a relation like denotation to work with.  It might be thought that the theory is restricted to subject-predicate sentences and won’t extend to quantified sentences, but this limitation is easily remedied by adding that the objects referred to or quantified over should instantiate whatever is predicated of them. Whatever objects are semantically relevant are the ones that need to do the instantiating if the sentence is to be true. What about moral truths? Well, if there are such truths the theory commits us to the idea that moral sentences can be true only if there are moral properties (or concepts or predicates) for objects to instantiate—but this will presumably be so if there are moral truths to start with. What we don’t get are nonsensical truths, because there will be no objects and properties to stand in the instantiation relation (e.g. borogroves and mimsiness). We just have the commonsense thought that whether a sentence is true depends on what objects have which properties. If you say that an object has a property and it does, your statement is true; but if you say that an object has a property and it doesn’t, your statement is false. Clear?

What is surprising is that this theory, if we can dignify it with that word, has not been mooted (at least to my knowledge), since it seems blindingly obvious.[2] Some theories in its vicinity have been mooted, but not this theory exactly. It certainly carries the whiff of the correspondence theory, but it invokes no relation between whole propositions and facts, speaking instead of objects and properties and associated sentence-parts. The world comes into the picture, but not by way of a correspondence relation between facts and propositions. Nor is it a redundancy theory, since it defines truth as a complex property constituted by substantive relations; still less is the theory deflationary. It is also not the same as Tarski’s theory: the schema employed does not repeat on the right the sentence mentioned on the left (so it doesn’t satisfy Convention T) but rather embeds semantic vocabulary and the notion of instantiation. It is possible to universally quantify an instance of the schema and produce a well-formed result, whereas that is not possible for Tarski’s schema. We can say, “For all propositions x, x is true if and only if the objects referred to in x instantiate the properties expressed in x”, but we can’t say, “For all propositions x, x is true if and only if x”, because that is not well-formed (“x” being an individual variable not a sentence letter). Also, the definition proposed by the obvious theory is explicit, not inductive, and applies to any sentence in any language (we are not defining “true-in-L”).[3] The theory is closer to a formulation championed by P.F. Strawson: a statement is true if and only if “things are as they are thereby stated to be”. The spirit looks the same, but what are these “things”, and where is the reference to properties and their instantiation? It sounds a lot like saying, “if and only if reality is as stated”: but that is not the same as the formulation in terms of objects and properties. Perhaps the obvious theory could be read as a more explicit version of this type of theory; and indeed it looks very much like what people were driving at all along. For surely we want to say that the truth of a statement turns on the instantiation of properties by objects combined with suitable semantic relations to those objects and properties. To say something true you have to refer to an object and then assign a property to it that it actually has—obviously.

Consider the locution “true of”: what is its analysis? Obviously this: a predicate is true of an object if and only if the object has the property expressed by the predicate. This is the core of the obvious theory: truth itself is defined by reference to “true of” (as Tarski defines truth in terms of “satisfies”). We might say that “true of” is the basic notion in the theory of truth. We reach truth of propositions by plugging in a singular term: from “F is true of x” we derive “F is true of a” where “a” is a closed singular term (say a proper name). Thus the sentence “Fa” is true just if the predicate “F” is true of the object referred to by “a”. The other theories of truth remain neutral on the analysis of “true of”, which is a limitation in any attempt to define the concept of truth generally; but the obvious theory puts it at the center. To say something true you have to apply a predicate to what it is true of. And that is a matter of picking a predicate that expresses a property that applies to the object.

The OED defines “true” as “in accordance with fact or reality”. Fair enough, but what is “in accordance with” and what is “fact or reality”? The correspondence theory suggests some sort of isomorphism between propositions and complexes called facts. The obvious theory says that truth is a matter of identified objects instantiating assigned properties; so accordance is simply objects having the properties they are said to have. A statement is in accordance with reality just on the condition that it assigns properties to objects as they are actually distributed, i.e. as they are. Fact and reality are just objects having properties. This is a substantive definition of truth meeting standard conditions of adequacy: it defines truth in terms of notions severally necessary and jointly sufficient; it is non-circular; and it permits a universally quantified formula that captures our intuitions about truth. To repeat it in a slightly different language, a proposition is true if and only if its subject matter (objects and properties) exemplifies suitable instantiation relations. Truth is a matter of objects instantiating properties in the way alleged by a proposition. To understand the concept of truth, then, we need to grasp this complex of concepts: reference, object and property, instantiation. It is not simply a device of semantic ascent or essentially redundant or logically simple or merely a means of abbreviation. It is a thick analytically deep concept with a definite nature. Yet its nature is entirely (indeed painfully) obvious—not in the least bit surprising. The truth about truth is a true truism.[4]


[1] The same form of analysis can be applied to the concept of justification, which I take to be confirmation of the theory: a proposition is justified if and only if there are good reasons to believe that the objects referred to instantiate the property expressed. Likewise, we can say that it is a fact that p if and only if a certain object instantiates a given property, e.g. London instantiates being rainy (notice that no semantic relation is involved here).

[2] Why this should be is not clear to me: perhaps it is thought too obvious, or perhaps less obvious theories are confounded with it (correspondence theories).

[3] Devotees of Tarski’s theory will want to know how to provide recursion clauses for logical connectives. This is easily done: for example, “p and q” is true if and only if the objects and properties referred to in “p” stand in the instantiation relation and the objects and properties referred to in “q” stand in the instantiation relation; and similarly for “or” and “not”.

[4] Why is the truth about truth a truism while the truth about (say) knowledge is not? Because there is nothing more to the truth of propositions than objects instantiating properties combined with the fact that propositions stand for things. There is nothing hidden here, nothing to be discovered. Other theories purport to say something interesting, but the obvious theory is content with mere accuracy.

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