El Tribunal Constitucional y la exigencia del contenido

The main idea behind truthmaking is that truth supervenes on, or is grounded in, reality. A proposition is true because something in the world necessitates its truth. (Some (e.g. [Rea10], [Dod02], and [Lew01]) think it is better to formulate truthmaking in terms of supervenience on how things exist rather than onwhat things exist. That seems plausible for a good number of proposi- tions ordinarily considered, but it seems wrong for existential propositions (e.g. 〈Hesperus exists〉) and identities (e.g.〈Hesperus is Phosphorus〉. Probably it is best to formulate truthmaking in terms of both supervenience on what and how things exist, but I shall ignore this issue here.) What the necessitation condition (called ‘Necessitarianism’ in [Arm04] and ‘truthmaker essentialism’ in [Par99]) amounts to may be easy or difficult to specify depending on one’s view of (i) truthmaking and (ii) propositions. For example, if propositions make essential reference to worlds and times, then necessitation comes easy. For if the true proposition expressed by ‘Fluffy is brown’, relative to a given timet and worldwis at least as discriminating as〈Fluffy is brown attin w〉(where

t-slice-of-Fluffy-in-w, trivially necessitates the truth of the proposition. On the other hand, if propositions do not make explicit reference to worlds and times, as Kaplan and others have forcefully argued, spelling out what necessitation amounts to becomes an important problem in truthmaker theory.10

For a taste, here are the most popular proposals on the table. One takes the notion ofx’s necessitating the truth of a proposition_-A_.as primitive, another as equivalent to$(E!x_⇒A) (possibly without the$if_⇒already has strong enough modal force) where_⇒ is an entailment operation, e.g. relevant entail- ment, andE!xis a formalization of ‘x exists’, sometimes defined as_∃yy =x (though this definition is inadequate in a number of formal semantics for modal languages), and another as being reducible or explainable in terms of other, arguably non-modal, notions such as intrinsic properties or (more arguably non-modal, but see [Fin94]) essences. Significant worries arise for each of these accounts. Ultimately I reject Necessitarianism for the reasons discussed in section 5.7.

A given truth may have many truthmakers, always a maximal one and sometimes a minimal one. A truthmaker αis maximal for _-A_. when it is a truthmaker for_-A_.and no proper part ofαis also a truthmaker for_-A_., and it isminimal for _-A_.when it is a truthmaker for_-A_.and nothing of which it is a proper part is also a truthmaker for-A.(e.g. see [Arm04, pp. 19-20]). One equivalent way of formulating maximality is to say thatαis a maximal truth- maker for-A.when it is one that makes true any proposition made true by any other truthmaker for -A.. This definition does not rely on mereological prop- erties of parthood. However, no dual formulation of minimality is equivalent with the one initially given except, perhaps, for atomic propositions.11

10_{One such argument, essentially due to Kaplan [Kap78], is that there would be no con-}

tingent propositions if propositions make essential reference to worlds and times. For it is true at some world that ‘φis true atw’ iff (if and only if) it is true in every world, and likewise it is true at some time (and a given world) that ‘φis true at t’ iff it is true at every time. Alethic and temporal operators would then have no effect on the truth value of propositions and every proposition would be necessarily and always true. Typically no precise formulation of necessitation is given and instead the more cautious tactic of taking ‘necessitate’ as primitive is taken (see e.g. [Arm04]).

11_{The dual formulation of minimality would be:αis a minimal truthmaker for/A0when}

Some propositions have many minimal truthmakers and others may have none (under the assumption, e.g., that matter is indefinitely divisible). But every truth has a maximal truthmaker on the assumptions that (i) we have a suitably strong notion of mereological fusion at our disposal and (ii) Maximal- ism holds, i.e. that

Maximalism. For every true proposition-A.there is an objectαthat makes

it true.

I reject Maximalism but accept a version restricted to positive truths.12 _{We will} suppose for the moment that Maximalism holds since, for our purposes, what follows from Maximalism follows also from the version restricted to positive propositions.

Not only does it immediately follow that every truth has a unique maximal truthmaker, it follows that there is a unique maximal truthmaker that makes every truth true.

Proof. Consider all the true propositions. By Maximalism each such proposi- tion,_-A_., has a truthmaker. Take all and only the truthmakersαi (withi∈I

for some index I, e.g.I the class of all ordinals) for _-A_.. Then the αi taken collectivelyis a maximal truthmaker for_-A_., so there is a maximal truthmaker Φi for each truth -Ai.. Take the fusion %of each Φi. Then %is a maximal

truthmaker for each truth. For uniqueness, supposeβ is also a maximal truth- maker for-A.that is distinct from%. Thenβis one of theαi, so it is a proper

part of_%. This contradicts the maximality ofβ, so _%is unique.

made true byα. To see that the two formulations of minimality are not equivalent consider the proposition that cats exist. Then Fluffy and Blackie are both truthmakers for that proposition, and on the original formulation, minimal truthmakers, though on the second formulation neither is a minimal truthmaker since Fluffy makes true〈Fluffy exists〉 while Blackie does not.

12_{Lewis [Lew03, p. 29] says “[s]ome philosophers hold [Maximalism]: they say that every}

truth must have a truthmaker. That is, all propositions are positive.” So he thinks Max- imalism is equivalent to the claim that all propositions are positive. But Lewis does not think positivity and negativity are mutually exclusive, whereas I (and most) do. In fact, he thinks every proposition is both positive and negative. That is why Maximalism restricted to positive propositions does not amount to “Maximalism unrestricted” on my picture.

(The proof does not go through if ‘taken collectively’ does not mean ‘fused’ so that ‘theαi taken collectively’ may refer to a plurality rather than a single

individual. This would require giving up maximal truthmakers and revising Maximalism to state that for every true proposition there are some objects, rather than always a single one, that make it true. One might also reject the principle ofunrestricted fusion—viz. that for any thingsxthere is a (unique) fusion of those things—either because the principle is claimed to bear onto- logical weight, restricted or not, or because it ought to be restricted for other reasons, e.g. out of considerations of the individuation of ordinary objects. In regard to the former, it is not clear the principle does indeed bear ontological weight. Weak composition-as-identity theses, one version of which is defended in [Lew91], support the “ontological innocence” of the principle. If we assume unrestricted fusion, as I shall from hereon, Maximalism and its pluralized ver- sion (viz. for every true proposition-A., thereare some objectsαi that make

it true) turn out equivalent in which case the proof goes through regardless of whether Maximalism or the pluralized version is assumed.)

That there is a unique maximal truthmaker for every truth does not imply what Restall [Res96, p. 334] calls ‘truthmaker monism’, viz. that every truth- maker makes every truth true, for that requires further assumptions such as the classical entailment thesis. Nor does it trivialize the truthmaking enterprise. One of the main interests of truthmaking is to ground truth inminimal—or at least sufficiently small—truthmakers, the existence of which are not ruled out by the existence of maximal truthmakers. Similarly the fact that every expla- nation can be embedded in a stronger explanation (just conjoin a truth to the original explanation) does not trivialize explanations. Finally there is nothing like a slingshot argument available as an immediate consequence of UMT if the conclusion of that argument is that there is precisely one proposition. For propositions on the present account are structured entities, not truth values.13 13_{If the conclusion of the slingshot argument is that every truth corresponds to the same}

fact and ‘fact’ is understood as ‘maximal sum’ then the slingshot argument follows. But the slingshot argument is not typically understood this way because facts are not typically

On many accounts of propositions and truthmakers there is at least a proper class of propositions but far fewer truthmakers. If one is a nominalist about abstract objects, then there are only as many truthmakers as there are concrete objects and compositions of those objects.14 _{So we do not need to come up} with an incredible amount of truthmakers for so many true propositions. Even fewer truthmakers may be posited if “the ‘logical constants’ are not represen- tatives” ([Wit21, 4.0312]), i.e. if one holds an atomist theory of truthmaking. There is nothing problematic about providing truthmakers for certain com- pound propositions, such as conjunctions. The only problematic case involves negative propositions. One conclusion to draw from all of this is that the only constant thatmust notbe a representative is negation and that one may, if one wishes, remain neutral as regards the others (assuming that from the others, taken together, negation is indefinable).

From what has been said about truthmaking so far, a proposition is true iff it has a truthmaker, iff it is made true by the maximal truthmaker. Thus being true and being made true by the maximal truthmaker are extensionally equivalent. If we restrict maximalism to positive propositions, there will be more to truth than being made true by the maximal truthmaker; in particular, negative truths will be true in virtue of lacking a truthmaker (or equivalently, lacking the maximal truthmaker). On the other hand suppose_-¬A_.is a nega- tive truth. Then_-A_.is a falsity on a standard-going definition of falsity. So if we discard all talk of negative truths in favor of talk of falsities then it remains true that all there is to truth is being made true by the maximal truthmaker (and all there is to falsity is lacking the maximal truthmaker).

Now if there is nothing more to truth than being made true by the maximal truthmaker, it follows that

understood this way; they are not mere sums of objects, they are more like structured propositions.

14_{Whether or not the fusion of some objects is to be counted as an additional object is often}

thought to be a matter of whether certain forms of composition-as-identity hold. However, Baxter [Bax88] provides an argument against fusions counting as additional objects over their parts without even invoking composition-as-identity.

Fundamental thesis. There is but one truth value, truth, i.e. the maximal truthmaker.

Truth is what Frege called the circumstance that a truth, any truth, is true. Having sympathies with Frege, we may think of ‘α makes true -A.’ meaning nothing more than ‘αis the circumstance that -A.is true’ or even (and less circularly, since no reference to truth is made) ‘αis referred to byA’.

Is there anything analogous to the circumstance that a falsity is false, such as the maximal falsitymaker? It is often supposed thatαis a falsitymaker for a proposition iff it is a truthmaker for its contradictory. On the present view this must obviously be rejected since then the maximal falsitymaker is identical to the maximal truthmaker, in which case the absurdity that a sentence is true iff it is false follows. But that is what we would expect on the present account: there are no such things as falsitymakers and a negative proposition -¬A.is not made true by-A.having a falsitymaker, it is made true wholly in virtue of lacking a truthmaker.15

I have sketched a view of the ontology of truth values which requires a rejection of Maximalism and an account of positive propositions. I take up each task in turn.