Existential Presuppositions and Uniqueness Presuppositions

  • Jaakko Hintikka
Part of the Synthese Library book series (SYLI, volume 29)


The meeting in the proceedings of which this paper appears was primarily devoted to presuppositionless logics, somewhat misleadingly known as free logics.1 (The term misleads because of the absence of any connection between these ‘free’ logics and the well-known free algebras.) The presuppositions which these logics dispense with are presuppositions of existence, typically presuppositions to the effect that certain free singular terms are not empty.


Modal Logic Actual World Singular Term Propositional Attitude World Line 
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  1. 1.
    The Irvine Colloquium in May 1968.Google Scholar
  2. 2.
    For further remarks on this point, see my paper, ‘Logic and Philosophy’ in Contemporary Philosophy - La Philosophie Contemporaine, vol. I (ed. by R. Klibansky), Florence 1968.Google Scholar
  3. 3.
    ‘Language-Games for Quantifiers’, American Philosophical Quarterly, Monograph Series, no. 2 (1968): Studies in Logical Theory, pp. 46–72.Google Scholar
  4. 4.
    On this subject, see my paper ‘On the Logic of Existence and Necessity I: Existence’, The Monist 50 (1966) 55–76. The present paper includes much of the material which I intended to include in the second part of that earlier paper.Google Scholar
  5. 5.
    There will be some overlap with my discussion note ‘Individuals, Possible Worlds, and Epistemic Logic’, Noûs 1 (1967) 33–62.Google Scholar
  6. 6.
    See e.g. ‘Knowledge, Identity, and Existence’, Theoria 33 (1967) 1–27; ‘Interpretation of Quantifiers’ in Logic, Methodology, and Philosophy of Science III, Proceedings of the 1967 International Congress (ed. by B. van Rootselaar and J. F. Staal), Amsterdam 1968, pp. 435–444; also ‘Quine on Modality’, Synthese 19 (1968–69) 147–157.Google Scholar
  7. 7.
    In order to prove this, it suffices to show that whenever Ω is a model system which satisfies the earlier conditions, we can adjoin new formulas to its members so as to obtain a new model system Ω’ which in addition to the earlier conditions also satisfies (C.N=). (Then the same sets of formulas will be satisfiable in either case.) This can be accomplished as follows: whenever μΩ, adjoin to μ all formulas p such that for some finite sequence of formulas P0 =P, P1, P2,…,P k and some suitable singular terms ‘a 1 ’, ‘b 1’, ‘a 2 ’, ‘b 2’,†‘a k ’, ‘b k’ (not necessarily different), ‘N ni (a i=b i)’∊μ or N ni (a i=b i)’= P i for j< i(i=1,…k) and p i and p i-1 are like except that a i and b i have been exchanged at some place or places where they occur in the scope of precisely n i modal operators. That Ω’ so constructed satisfies (C.N =) is immediately obvious. That it satisfies the other conditions can be proved by induction on the number of symbols ‘&’, ‘V’, ‘E’, ‘U’, ‘M’.Google Scholar
  8. 8.
    See e.g. my paper, ‘Modality and Quantification’, Theoria 27 (1961) 119–128.Google Scholar
  9. 9.
    Admittedly Quine also frequently mentions the failure of existential generalization as an indication of trouble in quantified modal logic. The impression he leaves, however, is that this is just another symptom of one and the same illness. We shall soon see that the question of the validity of the substitutivity of identity is largely independent of those changes in the quantifier conditions (C.E) and (C.U) which determine the fate of existential generalization.Google Scholar
  10. See e.g. W. V. Quine, From a Logical Point of View, 2nd ed., Cambridge, Mass., 1961, pp. 139–159; The Ways of Paradox, New York 1966, pp. 156–182; Dagfinn Føllesdal, papers referred to in note 6 above.Google Scholar
  11. 10.
    Alternatively, we may express the last part of this condition as follows:… and if ‘Q n1, n2,…(b)’ ∈μ, then p(b/x)∈μ Google Scholar
  12. 11.
    Special cases of this argument were given in Jaakko Hintikka, ‘On the Logic of Existence and Necessity’ (note 4 above) and ‘Individuals, Possible Worlds, and Epistemic Logic’ (note 5 above). In the latter, the generalization presented here was also anticipated.Google Scholar
  13. 12.
    Again, (C.U1) may be formulated as follows: … and if‘(Ex)(N n 1(x = b) &N n 2(x = b)&…)’ ∈μ, then p(b/x)∈μ. Here instead of ‘(Ex)(N n 1(x = b)&N n 2(x = b)&…)’ we may have any formula obtained from it by the following operations: changing the order of conjunction members and/or identities; replacing the bound variable everywhere by another one.Google Scholar
  14. 13.
    Here we see especially sharply the difference between questions pertaining to the substitutivity of identity and questions pertaining to existential generalization. In the former, the question is whether two singular terms pick out the same individual in each possible world in a certain class of possible worlds (considered alone without regard to the others). In the latter, we are asking whether a given singular term picks out one and the same individual in all possible worlds of a certain kind (when they are compared with each other).Google Scholar
  15. 14.
    See e.g. my paper ‘Modality and Quantification’ (note 8 above).Google Scholar
  16. 15.
    The general validity of (26) presupposes that any actually existing individual also exists in all the alternatives to the actual world. The following model system Ω provides a counter-example to (26): Ω consists of μ and v, the latter of which is an alternative to the former. Here\(\mu = \left\{ {\left( {Ex} \right)Np,} \right.\;Np\left( {a / x} \right),\;\left( {Ex} \right)\left( {x = a} \right),\;p\left({a / x} \right),\;M\left( {Ux} \right) \sim p\); \(v = \left\{ {\left( {Ux} \right)\; \sim \;p,\;p\left( {a / x} \right)} \right\}.\)We could not have this counter-example, however, if ‘(Ex)(x=a)’ ∈μ entailed‘(Ex)(x=a)’∈v, i.e. if we could ‘move’ an existence assumption concerning a from a possible world to its alternatives.Google Scholar
  17. 16.
    Thus the elimination of existential presuppositions helps us to dispense with unwanted assumptions concerning the ‘transfer’ of individuals from a possible world to its alternatives.Google Scholar
  18. 17.
    This is one of the many places where one is easily misled if one trusts uncritically the superficial suggestions of ordinary language. Surely there are circumstances in which someone knows who is referred to by ‘a’ is and also knows who is referred to by ‘b’ is while in reality ‘a = b’ is true, apparently without thereby knowing that the references ofaandbare identical, contrary to what (C.ind.=0) requires. However, one has to insist here very strongly that in the two cases of a and b, respectively, precisely the same sense (same criteria) of knowing who must be presupposed. This is not the case, it seems to me, in any of the apparent counter-examples that have been offered.Google Scholar
  19. 18.
    In his paper, ‘Some Problems about Belief’ Synthese 19 (1968–69) 158–177, esspecially pp. 168–169, Wilfrid Sellars claims in effect that the validity of (C.ind=0) is ruled out by the interpretation of quantifiers which I propose in my Knowledge and Belief Ithaca, N.Y., 1962. This argument completely misconstrues my intended interpretation, however, for reasons I can only guess at, and hence fails to have any relevance here. Although (C.ind = 0) was not mentioned in Knowledge and Belief there is nothing there that rules this condition out for syntactical or for semantical reasons. Nor is there anything in Knowledge and Belief that is affected by the adjunction of this new condition.Google Scholar
  20. 19.
    A few additional comments are presented in my paper, ‘Semantics for Propositional Attitudes’ in Philosophical Logic ( J. W. Davis, D. J. Hockney and W. K. Wilson), D. Reidel Publishing Company, Dordrecht 1969.Google Scholar
  21. 20.
    Cf ‘Semantics for Propositional Attitudes’ (note 19 above).Google Scholar
  22. 21.
    See R. Sleigh, ‘On Quantifying into Epistemic Contexts’, Nousû 1 (1967) 23–32.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1970

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  • Jaakko Hintikka

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