Usucapión Especial Agraria

We can now move on to consider Shalkowski’s more general challenges against the anti-essentialist. First, he presents a general problem for any view which takes only logical necessity to be (richly) absolute or which seeks to give an account of metaphysical necessity in terms of logical neces- sity. Such a project requires one to provide an account of logical modality and, it is argued, any successful such account will have to make reference to metaphysical considerations, drawing on a prior notion of metaphysical modality. Therefore, the account of metaphysical necessity will fall foul of vicious circularity.

The problem starts with a standard model-theoretic understanding of logical consequence and logical necessity. This requires making use of a do- main or class of models. However, one needs to give an account of what models there are. What counts as a genuine model? What makes some candidate models admissible and some inadmissible? Shalkowski considers several alternatives open to the anti-essentialist. First he considers Platon- ism, by which models are abstract objects. However, it is difficult for the Platonist to show why these actual abstract objects should have any bearing on logical possibilities and necessities.

So far, all the Platonist has told us is that the actual world con- tains some abstract objects in addition to the concrete objects recognized by the nominalist. With respect to understanding modality this is no more illuminating than being told that there are extraterrestrial objects such as planets and comets in addi-

tion to the terrestrial objects we all know and love. (2004, p. 67)

Two further assumptions are needed.

(i) every model represents a possibility. . .

(ii) all possibilities are represented by some model. (2004, p. 68)

Shalkowski has a number of objections against “Modal Platonism”, but the most important is that it cannot justify (i) and (ii) without making problematic metaphysical commitments.

There is nothing, though, in standard model theory that can count as justifying the two modal constraints that modal platon- ism requires. It is not as though model theorists have exhaus- tively examined objectively existing entities, catalogued their structures and their representational capacities, compared the results of this examination with considered judgments about the modal facts, and then reported back to the rest of us. (2004, p. 70)

Why think that a certain class of abstract objects succeeds in representing all and only possibilities? We cannot rely on logical principles to justify the claim, as the question is precisely whether our logical principles yield the right domain of models for modalizing. Rather

Some other necessity [other than logical] must be taken as basic to provide for some appropriate constraints on the existence and nature of the class of objects that are thought to underwrite logical necessity, such as abstract models. (2004, p. 81)

Shalkowski of course makes the additional point that this justification can be given using metaphysical considerations. We can frame the appropri- ate constraints in terms of the metaphysical necessities and possibilities for, arising from the essence of, logical objects. We can ensure that the models or the truth-tables of logic are relevant for necessity and possibility by taking them to encode essential truths about logical objects, such as propositions, or logical constants, and so on.

What the anti-essentialist takes to be modally innocent seman- tic facts involving models, the essentialist sees to be closet es- sentialism about peculiar sorts of entities. . . . If the truths of logic as specified by truth tables are to be useable in our rea- soning about contrafactual situations, then the semantic infor- mation contained in truth tables must represent not just the ac- tual facts about propositions but also modal information about

propositions (or some other favoured truth bearers). This modal information, if it is to be useful in reasoning across the full range of the possibilities, must be information about the essence of propositions. Implicit in truth tables, then, is the thesis that what the tables represent are all and only the relevant possibili- ties for propositions. Conditions (i) and (ii) resurface as hidden assumptions in all elementary logical semantics. (2004, p. 78)

Logical modality is a matter of the essences of a certain class of logical objects, and associated metaphysical necessities and possibilities for those objects. In order to fix on an account of logical modality, one must ad- dress certain metaphysical issues concerning the natures of certain objects. Therefore, one cannot give an account of metaphysical modality in terms of logical modality, as this will lead to circularity; any successful account of logical modality will have made prior recourse to metaphysical necessities and possibilities for logical objects.

In response, one might ask why truth tables contain only some infor- mation about the essence of propositions, and how the line is drawn be- tween information which is and is not included. E.g., one might think that propositions are essentially abstract entities, or essentially intentional (about things), or essentially such that they can be the objects of certain attitudes such as belief, or perhaps even essentially logical entities. But none of this appears to be encoded in the truth tables of propositional logic. The same point applies if one abandons the idea that these encode the essence of propositions, in favour of taking them to encode the essence of the log- ical constants, such as conjunction and negation. These will still arguably have essential properties which fail to be encoded, such as being essentially abstract. This is an instance of a general problem: the essentialist needs to distinguish between what is true in virtue of the nature of logical entities, and a proper sub-class which covers our standard notion of logical necessity.3 Shalkowski owes us an explanation of why only some essential truths about logical entities are relevant for what models there are.

One might also accuse Shalkowski of assuming an essentialist account of modality in his argument. He moves immediately from the thought that models must represent ‘modal information about propositions’, to the claim that this modal information ‘if it is to be useful in reasoning across the full range of the possibilities, must be information about the essence of proposi- tions’ (2004, p. 78). But this only follows given an antecedent commitment to an essentialist account of this modal information. An alternative move could take the modal information to arise from the limits of how we think about propositions, or even from the behaviour of counterpart propositions in other possible worlds.4 Note also, even if we need information about

3_{See e.g. Correia (forthcoming, §5).} 4

‘the full range of the possibilities’ it is not clear that information about the essence of propositions will do that. Suppose you take essence to pro- vide the source of metaphysical possibility, but that you nevertheless take mere logical possibility to be a genuine kind of possibility. The essence of propositions is only going to tell you what is metaphysically possible for propositions, but surely, for the purposes of logic, we want to count what is logically possible as well?

Two variants of this argument are presented by Vaidya (2006). He starts with the fact that there are many different formalizations of logic to choose from when giving an account of logical modality.

1. P is logically necessary only if P is either an axiom or deductive con- sequence of the axioms of the correct logical system.

2. There are multiple formalizations of logic that are plausible. . . . 3. There are three plausible domains one can appeal to in order to deter-

mine which formal system correctly captures logic: logic, metaphysics, or physical theory.

4. Appealing to different formalizations of logic to determine which for- mal system is correct is circular. Moreover, one cannot appeal to facts about a first-order classical system to argue that a paraconsistent sys- tem is not adequate. The facts appealed to must be external to the formalization.

5. Appealing to physical theory to determine which formal system is cor- rect would commit the naturalistic fallacy.

6. Consequently, the domain one must appeal to in determining which formalization of logic is correct is metaphysics.

7. Therefore, some metaphysical truths about the scope and nature of logic determine whether P is logically necessary. (2006, pp. 179–180) In short, in order to fix on a unique account of logical necessity, we need to fix on a unique underlying logical system. The only way to settle on the correct logic for logical necessity is to appeal to metaphysical considerations. Therefore, metaphysical considerations in part determine whether a given proposition is logically necessary.

This argument suffers from a circularity problem. Regardless of the conclusion, one is using logical reasoning to come to the conclusion that such-and-such is the correct logic.5 Even if we don’t endorse this particular argument, it seems likely that in arguing that one logic is correct, we will engage in logical reasoning, and thus presuppose some underlying logical

principles. It looks like one will have to appeal to something non-logical to get off the ground justifying one logic over another. But it also looks like logic is always going to appear in the picture somewhere.

Vaidya’s second argument is more specific about what metaphysical con- siderations he takes to be relevant to logical necessity, namely, the nature or essence of logical constants. What propositions are logically true depends upon which propositions are true under substitution of their non-logical con- stituents. This, in turn, depends upon what the logical constituents are, i.e. what the logical constants are. We need to be right about the distribution of the fundamental kind property of being a logical constant in the world in order to be right about the logical truths and logical necessity.

[L]ogical necessity is metaphysically determined by the logical constants. . . . A proposition P is a logical truth just in case P is true under every replacement of constituents of P that are not logical constants. Consequently, the logical truths are deter- mined by what the logical constants are. . . .

One distinctively metaphysical principle is the essentiality of fundamental kind. In general, the fundamental kind of thing x is, is a property x cannot fail to have. The properties that individuate an entity at its most fundamental level are essential to that entity. These properties speak to the issue of what kind of thing x is. The suggestion here is that being a logical constant is a fundamental kind property. . . . What things are taken to be logical constants can vary across various formalizations of logic. However, for a system L to be the correct logical system is for it to capture the essential nature of the logical constants. Consequently, there is a metaphysical foundation to logic. (2006, pp. 180–181)

This argument rests upon the principle of the essentiality of fundamental kind. So one can only accept Vaidya’s conclusion if one is also prepared to accept the truth of this principle, and that it applies to entities such as logi- cal constants. The argument also leaves open some important details of how this principle is to be used. Vaidya appeals to the idea that being a logical constant is an essential property, such that logical necessity stems from a fixed class of logical constants. However, it also seems natural to expect that, on this view, the nature of each logical constant would be relevant. E.g., one might take one difference between Classical and Intuitionistic logic to be that they attribute different properties to negation. One way to decide between the logics might be to inquire into the nature of negation, e.g. if an essential property of negation is that, for all p, ¬¬p iff p, then Intuitionistic logic is wrong because it gets the properties of negation wrong. Vaidya might reply that intuitionistic negation and classical negation are different entities, one of which, say, is essentially of the kind logical constant, one of which is not.

Suppose the logical constant is classical negation. What kind of thing is in- tuitionistic negation then, if not a logical constant? Perhaps, then, classical negation and intuitionistic negation are both logical constants, but different kinds of logical constant. However, this would undermine Vaidya’s point. He suggests that for a logical system to be “the correct logical system is for it to capture the essential nature of the logical constants” (my emphasis). But if both kinds of negation are logical constants, albeit different kinds of logical constant, then a logical system must include both kinds. But it can’t be that both ∀p(p ⇔ ¬¬p) and ¬∀p(p ⇔ ¬¬p). One could reply that the correct logical system has to capture the essential nature of logical constants of a particular kind. But then one will need to argue why one kind, e.g. the classical constants, should be favoured over another, e.g. the intuitionistic constants. But this returns us back to the debate over what is the correct logical system—essentialist considerations have not helped us. Alternatively, one could claim that a correct logical system has to capture the essential nature of logical constants of a kind, but that there can be many such correct systems. But this would be (a) to reject the assumption behind Vaidya’s first premise, that there is such a thing as the correct logical system, and (b) to engage again in debates concerning logical pluralism vs. logical monism. Again, essentialism has not helped us avoid these debates. The advantage of talking in terms of “capturing the essential nature of the logical constants” has been lost. We are left with the same, familiar debates. An additional matter concerns how we are supposed to discover what the right logic is. It may be well and good to claim that logical necessity is deter- mined by metaphysical necessities stemming from the essence of the logical constants (or from the essentiality of being a logical constant ), however, it remains unclear how we may be able to discover these essences.

The final point of Shalkowski’s that I wish to highlight suggests where the problematic metaphysical commitments of the anti-essentialist may lie. The argument is, roughly, that logical modality, in allowing all and any com- binations of properties, and in claiming to be metaphysically significant, is committed to the Humean metaphysical position that there are no necessary connections between distinct existences, i.e. no combinations of primitive properties are ruled out by the relations between them.

If logical necessity is supposed to be a metaphysically significant necessity in the sense explained, that is, that the T-axiom holds for logical necessity, then one adopting classical logic as encom- passing all and only the fundamental necessary truths must face the fact that defending this commitment requires defending a substantial Humean metaphysical view. If the only necessities are austere logical truths expressed in primitive predicate nota- tion, then whatever is not ruled out by those truths is possible; whatever is not contradictory is possibly true. This is simply

a way of expressing in terms of grammatical form the meta- physical thesis that all logically possible combinations of basic properties are genuinely possible; there are no necessary connec- tions between primitive properties. The problem here is not that the anti-essentialist will find this Humean metaphysics unattrac- tive, but rather that the modal doctrine, the anti-essentialism, is hostage to a particular metaphysical program. This conflicts with the common perception that logic and its correlated modal- ity are free of metaphysical commitment in a way that essential- ism is not. (Shalkowski, 2004, pp. 73–4)

Note that the passage ends with a point about the dialectic between essen- tialists and anti-essentialists. Both bear significant metaphysical commit- ments. The problem for anti-essentialists, however, is that it seems that their account of modality requires that there be no such metaphysical commit- ments. Essentialists have no such constraint, and thus gain the advantage here.

This argument rests on the idea that the anti-essentialist takes logical modality to be genuine, and thereby takes it to be metaphysically significant. But this just seems wrong. The point of having a notion of logical possibil- ity wider than metaphysical possibility is clearly completely undermined if one also claims that all logical possibilities are “metaphysically significant”, where “metaphysically significant” would appear to mean “metaphysically possible”. In taking a certain stance on what it takes for a possibility to be genuine or real, and dismissing all weaker kinds of possibility as no good, Shalkowski is clearly favouring his essentialist view. Of course mere logical possibilities are not metaphysically possible, but the relative modality the- orist does not want to claim that they are. They want to be able to say both that some logical possibilities are not metaphysical possibilities and that mere logical possibility is still genuine possibility. Shalkowski’s argu- ment that taking logical modality to be “genuine” commits one to Humean metaphysics, depends crucially on understanding “genuine” to mean some- thing like “metaphysically significant”. But someone who takes the realm of logical possibility to be wider than the realm of metaphysical possibility would precisely not take logical possibility to be metaphysically significant, although they may have another way to cash out the idea that logical pos- sibilities are not mere possibilities “in name only”.