With the exception of logical necessity, I have avoided reference to specific kinds of alethic modality. My aim has been to explain a notion of absolute necessity which leaves it open which specific kinds of alethic necessity are absolute. If it is agreed that logical necessities must be true at all possibilities, then the semantic argument discussed in the preceding section establishes that logical necessities are absolute.
If we also accept 20 that there are no logical necessities whose negations are metaphysically possible—i. If we assume that logical possibility is not just weaker than metaphysical, but weaker than any other kind of possibility, one picture of the space of possibilities we might adopt has the whole space filled by logical possibilities, and a proper subspace filled by metaphysical possibilities:.
It involves seeing metaphysical necessities as holding, not at all possibilities whatever, but only throughout a restricted class of them. The picture is indeed inevitable, if we think of the points in the space of possibilities as logical possibilities—for then our assumption that it may be metaphysically but not logically necessary that p, or logically but not metaphysically.
However, we could instead think of the difference between logical and metaphysical modalities in a quite different way. For we are not forced to understand the difference in terms of different more or less inclusive kinds of possible situations in which logical and metaphysical necessities and possibilities are true. Instead, we could think of necessities of both kinds as being true throughout the whole space of possibilities, and view the difference between them as like the difference between broader and narrower kinds of logical necessity, rather than like that between, say, logical necessity and some kind of merely relative necessity such as biological or technical necessity.
What is biologically necessary is, roughly, what must be so, given the actual laws of biology, or the nature of living organisms. What is biologically impossible may well be logically possible.
So the right picture, in terms of possibilities, identifies the biologically necessary as what holds true throughout only a restricted range of possibilities. But with logical necessity a different picture seems appropriate. We can distinguish between narrower and broader kinds of logical necessity. There are, for example, the logical necessities of propositional logic, those of first-order logic, and so on. One might think of logical necessities as those necessary propositions which can be expressed making essential use of just logical vocabulary.
Alternatively, one might adopt a broader, more generous conception which encompasses what might otherwise be classed as analytic or conceptual necessities, and so recognises as logically necessary truths whose expression essentially involves non-logical vocabulary.
There is no need to resolve that issue here. Even if one restricts logical necessities to truths whose expression essentially involves only logical vocabulary, there are broader and narrower classes of logical necessities. But it does not seem correct to think of the necessities of propositional logic as holding true throughout a more extensive class of possibilities than those of first-order logic which depend on their quantificational structure.
Rather, we should surely think of necessities of both kinds as holding throughout the whole space of possibilities. The difference between the necessities of propositional logic and those of first-order logic is not a difference in the ranges of possibilities throughout which they hold. At the linguistic level, it is simply a difference in the kind of vocabulary required for their adequate expression.
At what one might think of as a more fundamental—ontological or metaphysical—level, it is a difference in the range of entities essentially involved in explaining why these different kinds of necessities hold.
Logical necessities are properly included among metaphysical necessities, just as the necessities of propositional logic are properly included within those of first-order logic. But logical and metaphysical necessities alike may be true throughout the whole space of possibilities.
In particular, there may be no possibilities at which some metaphysical but non-logical necessities fail to be true. A full exposition and defence of this theory lies well beyond the scope of this paper.
Here I shall be able to give only a brief outline of the main ideas. Some philosophers—most famously David Lewis—have answered: There are many possible worlds besides the actual world. Necessity is simply truth in all of them, and possibility truth in at least one. Other philosophers, mainly before Lewis, have said: Necessity is just truth in virtue of meaning. It is not in the world apart from us, but is simply the product of our conventions for using words.
The essentialist theory rejects both these answers, and says: Necessity has its source in the natures of things. Anything we can talk about is a thing. This is what is given by a definition of the thing. For example, the definition of circle is: set of points in a plane equidistant from some given point. The definition of mammal is: air-breathing animal with a backbone and, if female, mammary glands.
So consider first the propositions:. I claim that these are necessarily true, and indeed absolutely necessary. Why is that? The essentialist answer is that the first is necessary because true in virtue of the nature of the natural numbers 1 and 2, and of the relation of being less than —to be the number 2 just is to be the natural number which immediately follows 1, and for a natural number x to be less than a natural number y is just for y to follow after x in the sequence of natural numbers.
Similarly, the second is necessary because true in virtue of the nature of the numbers 1 and 2 and of the operation function of addition: addition of natural numbers is that function of two natural numbers x and y whose value is the natural number z iff z is the y th successor of x. Here is another example. Consider the proposition:.
If a conjunction of propositions A and B is true, A is true. I claim this too is absolutely necessary. The essentialist answer is very simple: it is necessary because it is true just in virtue of the nature of conjunction.
Conjunction just is that function of two propositions which has a true proposition as its value for those propositions as arguments if and only if both arguments are true. These are the purely logical necessities. Other necessities depend upon the natures of non-logical entities—just as in my earlier examples, which depend upon the natures of certain mathematical entities.
The essentialist theory is a kind of obvious generalisation of these claims. Things of all kinds have natures. That is, it is metaphysically necessary that p iff there are some things X 1 , A fuller explanation would need to say much more about the structure of the theory, and about the kind of explanation it provides.
This would require a defence of the notion of essence or nature against the charge that these notions are unintelligible, or at least too unclear to be used for philosophical purposes. There need to be limits, or restrictions, upon what counts as belonging to the nature of a thing—if just any necessary truth about a thing counts as part of its nature, the theory becomes explanatorily vacuous. Among the questions that we shall need to answer are: Can the theory account for all metaphysical necessities?
Are all metaphysical necessities absolute? The first point to be clear about is that this question is distinct from the question whether the essentialist can explain all metaphysical necessities.
It is plausible that all absolute necessities are metaphysical, so that an affirmative answer to the latter question requires an affirmative answer to our present question.
But the converse does not hold. Metaphysical necessities—or at least what are commonly taken to be metaphysical necessities—may not all be absolute. According to post-Kripkean orthodoxy, these are metaphysical necessities. But they are surely not absolute. If an essentialist explanation is correct, the explanandum —the necessity to be explained—depends upon the explanans —the relevant facts about the nature of the entities involved.
It follows that, if the necessity explained is to be absolute, the explanans must not itself be contingent—so that in particular, it must involve no commitment to any entity whose existence is a matter of contingency. Our question is, in part, whether every absolute necessity can be given an essentialist explanation that meets this condition. Every essentialist explanation appeals to the nature of at least one entity, and so requires at the very least that certain natures exist.
Thus if an essentialist necessity is to be absolute, the relevant nature s must exist of necessity. I hold that the nature of a thing is always a property, 27 so we should begin by seeing how the existence of certain properties can be necessary.
To avoid complications afflicting predicates which involve reference to contingently existing objects, I shall focus on purely general predicates, by which I mean predicates entirely free of any devices of singular reference.
Correspondingly, by a pure property or relation, I mean a property or relation which is or could be the semantic value of a purely general predicate.
On the modest, deflationary theory of properties, the actual existence of a suitably meaningful purely general predicate suffices for that of a corresponding pure property or relation.
For we should surely allow for the existence of properties and relations for which, as a matter of contingent fact, no actual language provides suitable predicates. The most that can properly be required, for the existence of a property or relation, is that there could be a suitable predicate—i. In particular, it is sufficient for the existence of a pure property or relation that there could be a suitably meaningful purely general predicate. But the possibility in question here—whether or not there could be a predicate with a certain meaning—is surely absolute.
That is, if it is indeed possible that there should be a suitable predicate, that is itself necessarily so— i. But if that is right, then the existence of any pure property or relation is always a matter of necessity.
For let P be any pure property or relation. Necessarily, P exists iff there could be a predicate having P as its semantic value. But since the logic of absolute modality is S5, it is necessary that there could be a predicate having P as its semantic value iff necessarily there could be such a predicate. It follows that if P exists, then necessarily P exists.
It is clear that if an essentialist explanation appeals only to pure properties and relations, there is no reason why the necessity explained should not be absolute. For there is, in the definition of the relevant entities, no presupposition of existence of any objects at all, and so no presupposition of any objects whose existence might be a contingent matter. However, it is plausible that there are absolute necessities which cannot be explained by appeal only to the natures of things which are pure properties or relations.
It seems quite clear that if these necessities can be explained on the essentialist theory at all, it must explain them, much as I have suggested already, by appeal to the nature of the numbers 1 and 2, the relation of being less than, and the operation of addition. But in that case, the essentialist explanation would not appeal only to pure properties and relations, for the definitions of these entities essentially involve reference to particular objects.
They presuppose the existence of the natural numbers, and in particular, of the number 0. But it does bring to the fore a crucial question. For since these necessities require the existence of certain objects, they can be absolute only if the existence of those objects is itself absolutely necessary. The crucial question, therefore, is: How, if at all, can the essentialist theory explain the necessary existence of those objects? I shall argue that the essentialist can do better—that he can provide an explanation why the natural numbers, for example, exist as a matter of necessity.
We start with the fact that pure properties and relations necessarily exist. I contend that this fact can be explained in essentialist terms. The essentialist does not claim that existence is simply and irreducibly part of what it is for something to be a pure property or relation.
What he claims is that a pure property or relation just is one for the existence of which it is sufficient that there could be a suitable predicate—that is, in the case of a first-level property or relation, a predicate expressing the condition objects must meet, if they are to have that property or bear that relation to one another, and similarly for higher-levels.
That is what is true, in virtue of the nature of a pure property or relation. The possibility involved here, of the existence of a suitable predicate, consists simply in its not being ruled out by any absolute necessities. Hence it is an absolute possibility. But what is absolutely possible is absolutely necessarily possible. Since it is clear that there are indefinitely many meaningful purely general first-level predicates, this implies the existence, and indeed necessary existence, of a large range of pure first-level properties and relations.
This includes many pure sort al properties—i. It might at first appear that no extension of the argument is required. For functions, as usually treated in set theory, are just a special subclass of relations. But matters are not quite so straightforward. This may be a matter of law, or it may be just a matter of chance. Either way, it is clearly a contingent matter—nothing in the notion of marriage as such precludes polygamy or enforces heterosexuality.
My earlier argument does not, accordingly, establish the necessary existence of such a function. At most, it establishes the necessary existence of a certain binary relation— being married to —which may, but need not, be a function.
And the point clearly generalises. That is, the general argument cannot, by itself, establish the necessary existence of any function; it may establish the necessary existence of a relation, but it cannot show that any relation is functional. How, then—if at all—can the necessary existence of any functions be established? As a simple illustration, consider the successor relation of addition among numbers, xSy. By the general argument given already, this relation necessarily exists.
What we want to see is that it is, also as a matter of necessity, a functional relation. It will then follow that the existence of the successor function is necessary. I shall assume, with Frege, that a number 34 is essentially the number of things of some kind. We can define the successor relation among numbers— n follows directly after m —again with Frege, 35 as follows:.
See essence , -al 1. See necessary. Essential, inherent, intrinsic refer to that which is in the natural composition of a thing. Essential suggests that which is in the very essence or constitution of a thing: Oxygen and hydrogen are essential in water. Inherent means inborn or fixed from the beginning as a permanent quality or constituent of a thing: properties inherent in iron.
Intrinsic implies belonging to the nature of a thing itself, and comprised within it, without regard to external considerations or accidentally added properties: the intrinsic value of diamonds.
Words nearby essential esse , Essen , essence , essence d'orient , Essene , essential , essential amino acid , essential dysmenorrhea , essential element , essential fatty acid , essential fructosuria.
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