Real Logic (Formal 'Logic': Dispensable)

Types (or 'sources', or 'grounds', or ...) of necessity

[under development]

Necessity

That something 'is necessary', in philosophers' jargon, means that it could not fail to exist, or occur, or happen. That something is necessarily true means that it could not fail to be true, for some or the other reason.

Some bearers of necessity

Within philosophy, 'necessity' mostly ascribed (a) to states of affairs, or (b) to the truth or falsity of intensions (judgements, statements, propositions). Examples:

(a) Necessarily, bachelors are unmarried. Necessarily, when the sun shines it gets warmer.

(b) Necessarily, 'Bachelors are unmarried' is true. Necessarily, 'Some bachelors are married' is false.

Sometimes, philosophers ascribe 'necessity' directly to things—meaning that these things could not fail to obtain. Example:

Potential definitions of necessity

A sentence of the form 'Necessarily, (if q then) p' means that (if q then) non-p is impossible. Thus, necessity may be defined as impossibility of absence (a definition along these lines treats the notion of impossibility as more basic). Also, that something is necessary means that any alternative to it is impossible.

Definitions of necessity in terms of possible worlds enjoy large popularity and sound very learned; yet their avail is dubious. Above all, the notion of a 'possible world' itself is largely unclear (What sense does it make to use it in the definitions of a term which seems actually to be less unclear?). What are the restrictions on being a 'world' (in the relevant sense)? And what are the restriction of a world's being 'possible' in the relevant sense? That means, what exactly is the definition of a world's 'impossibility'? And does the definition of 'world' admit of 'impossible' instances? What exactly does it mean that 'there is' a world which is possible but not real (what exactly would it be for this world not to 'be there')?

NB. On the assumption that x exists (occurs, happens) necessarily, it is strictly excluded that p does not exist (occur, happen). Hence, for example, 'moral ought' and the 'ought' of rationality cannot be subsumed under 'necessity', for that something ought to be the case does not mean that it cannot fail to exist (occur, happen).

Varieties of necessity

Many of the problems necessity seems to raise are due to the widespread (mistaken) assumption that there be one unitary phenomenon worth calling by the term 'necessary'. For in fact, the term 'necessity' is rather general (or perhaps underdetermined, or ambiguous, or vague): it can be applied in different connections and be used to refer to rather different things.

To start with, within philosophical debates, the notion of necessity comes in two general varieties, which we may call 'extensional' and 'intensional' necessity. [@~Carnap.]

(a) Intensional necessity applies to the truth or falsity of an intension. It occurs when the relevant truth or falsity could not fail to obtain.

(b) Extensional necessity (given certain conditions) applies to worldly states of affairs—it occurs when the relevant state of affairs could not fail to obtain (given those conditions). (It would be intuitive to use the term 'metaphysical necessity' for this variety; however, such usage would tend to be misleading, because unfortunately, the term 'metaphysical necessity' was repeatedly used for varieties of intensional necessity—among others, by Kripke).

That (a) and (b) refer to different varieties of 'necessity' may be defended by saying that the bearers of necessity are categorically different kinds of entity in the two cases —intensions, or judgements, in the one case, states of affairs in the other. (Many philosophers neglect necessity in the (b) sense entirely.)

Intensional necessity, too, comes in different possible* varieties (or comes with different backgrounds, or has different possible reasons or 'causes', or 'sources', or 'grounds').** Here are some examples.

(a.1) Logical necessity (necessity by virtue of logic, as, for instance, in the case of 'Necessarily, either p or not p');

(a.2) Semantic necessity (necessity by virtue of meaning, as, for instance, in the case of 'Necessarily, all bachelors are unmarried')

(a.2-i) Analytic semantic necessity (as, for instance, in the case of 'Necessarily, "bachelors" are [given the common usage of that word] unmarried men');

(a.2-ii) Stipulative semantic necessity (as, for instance, in the case of 'Necessarily, "illocutionary acts" are [stipulatively defined as being] conventional acts');

(a.3) Formal necessity (as perhaps, for instance, in the case of 'Necessarily, 1=1').

(According to this terminology, 'analytic', 'formal' and 'logical' truths are different subtypes of necessary truth.)

Likewise, there are different possible* varieties of extensional necessity (or necessity going back to different 'sources'):

(b.1) The necessity involved in causality (cf. 'Necessarily, when the sun shines it becomes warmer');

(b.2) The necessity involved in the case of natural laws (cf. 'Necessarily, the state of these atoms correlates with their energy level');

(b.3) The necessity of 'constitutive identification' (cf. 'Necessarily, this glass of water contains H2O');

(b.4) Magical necessity [😁].

[*Again, perhaps not each of these varieties would stand close scrutiny; furthermore, some of these varieties may be reducable to others.]

[xxx under development]

It is one of the most frequent errors in philosophy, committed by prominent philosophers such as Quine, Kripke and Lewis no less than by rookies, to take the lack of necessity of one variety as a reason to conclude to contingency. [In the final version, some examples will here be given.] 'Contingency', quite clearly, is the absence of any variety of necessity.

Given the variety of phenomena to which the term 'necessity' can be applied, it is an important requirement on any writing about 'necessity' that before starting, a clear definition is given of the variety of 'necessity' under consideration. Unfortunately, authors often fail to give such a definition; and in some of these cases, the different senses of 'necessary' are either mingled up, or confused. [In the final version, examples will here be given.]

o Kripke uses the rather unfitting term 'metaphysical necessity' for a variety of intensional necessity; this leads to a corresponding mistake in his argument.

*Perhaps not each of these varieties would stand close scrutiny.

** These formulations tend to be too vague, or general, or indeterminate, to assess their suitability.