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10. Modality / A. Necessity / 2. Nature of Necessity

[understanding the concept of necessity]

23 ideas
Necessity makes alternatives impossible [Aristotle]
     Full Idea: Necessity is what makes it impossible for something to be other than it is.
     From: Aristotle (Metaphysics [c.324 BCE], 1015b03)
     A reaction: Note that necessity here seems like an active force, rather than a mere description of a logical or metaphysical state of affairs. The underlying idea seems to be that essences enforce necessities, but it doesn't say that here.
What is necessary cannot be otherwise [Aristotle]
     Full Idea: What is necessary cannot be otherwise.
     From: Aristotle (Posterior Analytics [c.327 BCE], 88b32)
     A reaction: If the next interesting question is the source of necessity, then the question seems to be 'what prevents it from being otherwise?'.
Every necessary proposition is demonstrable to someone who understands [Leibniz]
     Full Idea: Every necessary proposition is demonstrable, at least by someone who understands it.
     From: Gottfried Leibniz (De arcanus motus [1676], 203), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6
     A reaction: This kind of optimism leads to the crisis of the Hilbert Programme in the 1930s. Gödel seems to have conclusively proved that Leibniz was wrong. What would Leibniz have made of Gödel?
Necessary truths are those provable from identities by pure logic in finite steps [Leibniz, by Hacking]
     Full Idea: Leibniz argued that the necessary truths are just those which can be proved from identities by pure logic in a finite number of steps. ...[232] this claim is vindicated by Gentzen's sequent calculus.
     From: report of Gottfried Leibniz (works [1690]) by Ian Hacking - What is Logic? §01
     A reaction: This seems an odd idea, as if there were no necessary truths other than those for which a proof could be constructed. Sounds like intuitionism.
Necessity is what will be, despite any alternative suppositions whatever [Mill]
     Full Idea: That which is necessary, that which must be, means that which will be, whatever suppositions we may make in regard to all other things.
     From: John Stuart Mill (System of Logic [1843], 3.06.6)
     A reaction: [Mill discusses causal necessity] This is quoted by McFetridge. This slightly firms up the definition as 'what has to be true', though it makes it dependent on our 'suppositions'. Presumably nothing beyond our powers of supposition could matter either.
Necessity can only mean what must be, without conditions of any kind [Mill]
     Full Idea: If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be whatever supposition we make with regard to other things.
     From: John Stuart Mill (System of Logic [1843], p.339 [1974 ed]), quoted by R.D. Ingthorsson - A Powerful Particulars View of Causation 5.3
     A reaction: 'It is necessary to leave now, if you want to catch the train' is a genuine type of necessity. Mill's type is probably Absolute necessity, to which nothing could make any difference. Or Metaphysical necessity, determined by all things.
Nothing necessary can come into existence, since it already 'is' [Kierkegaard]
     Full Idea: Can the necessary come into existence? That is a change, and everything that comes into existence demonstrates that it is not necessary. The necessary already 'is'.
     From: Sřren Kierkegaard (Philosophical Fragments [1844], p.74)
     A reaction: [SY]
Something can be irrefutable; that doesn't make it true [Nietzsche]
     Full Idea: Something can be irrefutable; that doesn't make it true.
     From: Friedrich Nietzsche (Writings from Late Notebooks [1887], 34[247])
     A reaction: This is a warning to rationalists who are looking for strategies to demonstrate necessities a priori.
'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell]
     Full Idea: 'Necessary' is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments. Thus 'If x is a man, x is mortal' is necessary, because it is true for any possible value of x.
     From: Bertrand Russell (On the Notion of Cause [1912], p.175)
     A reaction: This is presumably the intermediate definition of necessity, prior to modern talk of possible worlds. Since it is a predicate about functions, it is presumably a metalinguistic concept, like the semantic concept of truth.
Modal terms are properties of propositional functions, not of propositions [Russell]
     Full Idea: Traditional philosophy discusses 'necessary', 'possible' and 'impossible' as properties of propositions, whereas in fact they are properties of propositional functions; propositions are only true or false.
     From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §V)
     A reaction: I am unclear how a truth could be known to be necessary if it is full of variables. 'x is human' seems to have no modality, but 'Socrates is human' could well be necessary. I like McGinn's rather adverbial account of modality.
Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]
     Full Idea: C.I.Lewis's S4 system develops a sense of necessity as 'provability' in some fairly informal sense.
     From: report of C.I. Lewis (works [1935]) by Stephen Read - Thinking About Logic Ch. 4
Necessity can attach to statement-names, to statements, and to open sentences [Quine]
     Full Idea: Three degrees necessity in logic or semantics: first and least is attaching a semantical predicate to the names of statements (as Nec '9>5'); second and more drastic attaches to statements themselves; third and gravest attaches to open sentences.
     From: Willard Quine (Three Grades of Modal Involvement [1953], p.158)
Kripke says his necessary a posteriori examples are known a priori to be necessary [Kripke, by Mackie,P]
     Full Idea: Kripke claims that all of his examples of the necessary a posteriori have the characteristic that we can know a priori that if they are true, they are necessarily true.
     From: report of Saul A. Kripke (Naming and Necessity lectures [1970], 159) by Penelope Mackie - How Things Might Have Been 1.4
     A reaction: That is, it seems, that they are not really necessary a posteriori! The necessity seems to only arrive with the addition of a priori judgements, thus endorsing the traditional view that necessity is only derivable a priori. Hm.
What reduces the field of the possible is a step towards necessity [Harré/Madden]
     Full Idea: Whatever reduces the field of the possible is a step towards necessity.
     From: Harré,R./Madden,E.H. (Causal Powers [1975], 7.IV)
     A reaction: This is a deeply stirring idea, because it suddenly opens up a research project of narrowing the possibilities, with a stunning Holy Grail at the end of it. Sherlock Holmes said this first, of course.
Statements about necessities need not be necessarily true [Pollock]
     Full Idea: True statements about the necessary properties of things need not be necessarily true. The well-known example is that the number of planets (9) is necessarily an odd number. The necessity is de re, but not de dicto.
     From: John L. Pollock (Epistemic Norms [1986], 'Nat.Internal')
     A reaction: This would be a matter of the scope (the placing of the brackets) of the 'necessarily' operator in a formula. The quick course in modal logic should eradicate errors of this kind in your budding philosopher.
Absolute necessity might be achievable either logically or metaphysically [Hale]
     Full Idea: Maybe peaceful co-existence between absolute logical necessity and absolute metaphysical necessity can be secured, ..and absolute necessity is their union. ...However, a truth would then qualify as absolutely necessary in two quite different ways.
     From: Bob Hale (Absolute Necessities [1996], 4)
     A reaction: Hale is addressing a really big question for metaphysic (absolute necessity) which others avoid. In the end he votes for rejecting 'metaphysical' necessity. I am tempted to vote for rejecting logical necessity (as being relative). 'Absolute' is an ideal.
Equating necessity with truth in every possible world is the S5 conception of necessity [Read]
     Full Idea: The equation of 'necessity' with 'true in every possible world' is known as the S5 conception, corresponding to the strongest of C.I.Lewis's five modal systems.
     From: Stephen Read (Thinking About Logic [1995], Ch.4)
     A reaction: Are the worlds naturally, or metaphysically, or logically possible?
We may be sure that P is necessary, but is it necessarily necessary? [Melia]
     Full Idea: We may have fairly firm beliefs as to whether or not P is necessary, but many of us find ourselves at a complete loss when wondering whether or not P is necessarily necessary.
     From: Joseph Melia (Modality [2003], Ch.2)
     A reaction: I think it is questions like this which are pushing philosophy back towards some sort of rationalism. See Idea 3651, for example. A regress of necessities would be mad, so necessity must be taken as self-evident (in itself, though maybe not to us).
A sentence is necessary if it is true in a set of worlds, and nonfalse in the other worlds [Hanna]
     Full Idea: On my view, necessity is the truth of a sentence in every member of a set of possible worlds, together with its nonfalsity in every other possible worlds.
     From: Robert Hanna (Rationality and Logic [2006], 6.6)
Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach]
     Full Idea: Should necessity be treated as a predicate rather than (as in modal logic) as a sentential operator? It is odd to assign different status to necessity and truth, hampering their interaction. That all necessities are true can't be expressed by an operator.
     From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2)
     A reaction: [compressed] Halbach and Horsten consistently treat truth as a predicate, but maybe truth is an operator. Making necessity a predicate and not an operator would be a huge upheaval in the world of modal logic. Nice move!
Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
     Full Idea: The link between time and modality was severed by Duns Scotus, who proposed a notion of possibility based purely on the notion of semantic consistency. 'Possible' means for him logically possible, that is, not involving contradiction.
     From: Michal Walicki (Introduction to Mathematical Logic [2012], History B.4)
The modern revival of necessity and possibility treated them as special cases of quantification [Vetter]
     Full Idea: Necessity and possibility had a revival with the development of modal logic, treating them as special cases of the existential and universal quantifiers, ranging over an infinity of possible worlds.
     From: Barbara Vetter (Potentiality [2015], 1.1)
     A reaction: The problem seems to be that possible worlds offer a very useful and interesting 'model' of modality, but say nothing at all about its nature. Any more than a weather map will show you what weather is.
It is necessary that p means that nothing has the potentiality for not-p [Vetter]
     Full Idea: Necessities mark the limits of the potentialities that objects have. More precisely, it is necessary that p just in case nothing has, or had, or will have a potentiality to be such that not-p.
     From: Barbara Vetter (Potentiality [2015], 6.2)
     A reaction: [See Vetter's other ideas for her potentiality account of modality] If we wish to build a naturalistic account of modality (and if you don't want that then your untethered metaphysics will drift away in logical space) then this is the way to go.