Rescher_PresuppositionLogic_1961

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On the Logic of Presupposition Author(s): Nicholas Rescher Source: Philosophy and Phenomenological Research, Vol. 21, No. 4 (Jun., 1961), pp. 521-527Published by: International Phenomenological SocietyStable URL: http://www.jstor.org/stable/2105021Accessed: 27-10-2015 23:33 UTC

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ON THE LOGIC OF PRESUPPOSITION

"Every question involves a presupposition."

R. G. COLLmIGWOOD

I. Introduction. My object here is not to examine some particular set of presuppositions

for particular presuppositions must relate to a specific subject-matter, and the question I mean to attack in this paper is not substantive, but logical. I want to enquire into the kinds of presuppositions that there are, and to examine their abstract logical characteristics. In this way, I hope to be able to shed some light upon the scope and the meaning of the concept of a presupposition.

The ultimate purpose of this enquiry is philosophical. In a series of highly suggestive and original books, Collingwood has propounded the thesis that the primary aim of philosophy is the study of irreducible or "absolute" presuppositions. We need not, of course, endorse so sweeping a claim regarding the thorny question of the nature of philosophy. But there is no denying the more conservative view that at least one of the central tasks of philosophy is to render explicit and to clarify the presuppositions of our scientific and of our common-sense knowledge of the world. Clearly, an analysis of the nature of presuppositions is an indispensable preliminary to this task, and the present inquiry may therefore offer a useful contribution to its effective discharge.

II. Propositional Presupposition. It is apparent that one proposition can "presuppose" another. This is

the case whenever a proposition serves as an essential precondition for the truth, or even for the very possibility of another. Examples of this are:

Example 1. "Saylor killed Taylor" presupposes that "Taylor is dead."

Example 2. "Black infers that Brown is present" presupposes that "Black has evidence for Brown's presence."

Example 3. "Robinson denied his guilt and Jones believed him" presupposes that "Jones was aware that Robinson denied his guilt."

521



522 PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH

These examples are instances of the paradigm, "To assert that p presupposes that q" or more simply "p presupposes q." We can conveniently represent this relationship by the symbolic abbreviation: pre (p : q).

The fundamental point to be made regarding this concept of propositional presupposition is that it is equivocal, and covers several distinct, though related concepts of presupposition. To see that this is so, let us examine what happens when a presupposed condition fails to be satisfied, that is, when we have that pre (p: q) but also that q.

Take, for instance, the foregoing Example 1, and consider the statement "Saylor killed Taylor" when, in fact, "Taylor is alive" is true. Then, clearly, "Saylor killed Taylor" must be false. Or again, consider,

Example 4. "Smith knows French" presupposes that "Smith knows the meaning of some French words."

Here again when the presupposed statement is false, the falsity of the presupposing statement is a consequence. We thus have one sense of propositional "presupposition," symbolically "prei," which is governed by the rule:

Rule 1. [prej (p : q) & q] p.

By contrast, consider such a presupposition as is represented by,

Example 5. "The number m is a prime number" presupposes that "The number m is an integer."

Here, when the presupposition is not satisfied - say when m is a or V2 or some other noninteger - then the presupposing statement "m is a prime" is not simply false, but is in fact impossible. Again, consider,

Example 6. "The act A is morally obligatory in circumstance C" presupposes that "The act A is a possible action in circumstance C."

If A is not a possible action in the circumstance C, then it is not simply false, but actually absurd (impossible) to hold that A is obligatory in C. From examples such as these, we obtain a second sense of propositional "presupposition," symbolically "pre2" which is governed by the rule:

Rule 2. [pre2 (p : q) & q] O p.

I shall term these two cases the "weak" and the "strong" senses of (propositional) presupposition, respectively. In the "weak" sense, the falsity of the presupposition entails the falsity of the presupposing state-

1 Here (and throughout) the arrow represents logical entailment, and must not be construed as material implication.



ON THE LOGIC OF PRESUPPOSITION 523

ment; in the "strong" sense, it entails the impossibility of the presupposing statement.

It is important at this point to take note of a fundamental ambiguity in the ordinary-language characterization of a statement as "impossible." Such a designation may be construed either as asserting the impossibility of what the statement asserts (its is in this sense that the statement "That parallelogram has three acute angles" is impossible), or as asserting the impossibility of the very statement itself as gramatically or semantically meaningless (in the sense that the statement "Left blue is quick-witted" is impossible). On the first interpretation of the "impossibility" of a statement p, what p affirms is impossible, although p itself is an entirely proper statement, having as good a title to validity as any other. But on the second interpretation, it transpires that p itself is impossible, i.e., is not a proper statement at all, and is meaningless. This distinction gives rise to two corresponding senses of propositional presupposition. On the accepted practice of modal logic, the notion of "impossibility" is construed in the first sense (it being assumed that all of the statement at issue are proper and meaningful). In this manner we obtain "pre2" as above. But it should be noted in at least a passing way that we must recognize also the existence of a concept of (propositional) meaning-presupposition, symbolically " pre3," for which the presupposition-protasis is required to assure the very meaningfulness of the apodasis. This mode of presupposition is instantiated by examples such as the following:

Example 7. (The meaningfulness of the sentence) "The dog x-y-z the man" presupposes (that) "The dummy- expression 'x-y-z' stands for a verb."

In view of the fact that Rule 1 is intended to characterize weak (propositional) presupposition, we see that this type of presupposition can be represented by an explicit definition:

Definition 1. prel (p: q) =Df P -i q.

Thus weak (propositional) presupposition is not actually a distinctive logical concept in its own right; it amounts simply to the familiar concept of a necessary condition. Moreover, we can also define strong (propositional) presupposition by the analogous definition:

Definition 2. pre2 (p: q) =Df > p -A q.

But this concept is, as it were, a "new" idea, and represents distinctive logical conception. It is important to note that we have,

(1) pre2 (p: q) -?pre, (p: q),

to justify our terminology of "weak" and "strong" presupposition. Our




third sense of propositional presupposition, "pre3," cannot, of course, be represented by any comparable definition-schema.

III. Property Presupposition Properties, as well as propositions, can "presuppose" one another, for

the possession of one property may serve as a requirement for that of another. Instances of this are:

Example 8. "The person x is a minor" presupposes that "The person x is under 21 years of age."

Example 9. "The person x is a spinster" presupposes that "The person x is a female."

Thus in Example 8, it is asserted, in effect, that the property of being-a- minor presupposes that of being-under-21, and in Example 9 that spinster- hood presupposes feminity.

Our examples are therefore instances of the paradigm, "To assert that an object possesses the property b presupposes that it also has the property VI or more simply "o presupposes V.." We can conveniently represent this relationship by the symbolic abbreviation: pre (0, Vp).

It is readily seen that property presupposition is also equivocal as between two distinct conceptions. The one sense, prel is governed by a rule analogous to Rule 1 above:

Rule 3. [prel (s, Vp) & ipx] Ox bx.

This rule will characterize the "weak" sense of property presupposition. The second, "strong" sense, pre2, is governed by the rule:

Rule 4. [pre2 (0, Vy) & "'-' x] --x t Ox.

An instance of weak property presupposition is afforded by Example 8 above. If a person is past 21, it is simply false to assert that he is a minor. An instance of strong property presupposition is given in Example 9. If a person is a male, it is (not merely false but) actually impossible that this person could possess the property of being a spinster.

Property presupposition is not a primitive idea, but is definable in terms of propositional presupposition by the use of propositional functions. That is to say, we can give the following two definitions:

Definition 3. pre1 (0 : V) _Df (X) prel (ox: wpx). Definition 4. pre2 (b : V) Df (X) pre2 (OX: X):

Given Rules 1 and 2, these definitions are seen to be adequate in the sense that they have the consequence that the relationships defined by them indeed satisfy the appropriate rules, i.e., Rules 3 and 4, respectively. Furthermore, we now have,



ON THE LoGIc OF PRESUPPOSITION 525

(1) pre2 (k p) - pre, (1, yp),

serving again to justify our reference to "strong" and "weak" property presupposition.

If we adopt Definitions 1 and 2, these new definitions entail the conse- quences,

(2) pre, (: p) *-+ (x)(ox -* Vx), and

(3) pre2 (O: Vp) +-+ (x)(OOx -- px).

Here again, we observe by the relationship (2) that weak property presupposition is not a new and distinctive conception but represents a familiar idea: we have that prel (O: V) is equivalent to the circumstance that the property 0 contains the property Up in its intension. Thus weak property presuppositions amounts simply to intentional subsumption.

IV. Inferential Presupposition. A third fundamental sense of the term relates to the "presuppositions"

of inference. The validity of an inference can require the satisfaction of some appropriate precondition or prerequisite. An illustration is:

Example 10. To infer "X is an A" from "X is a B" presupposes that "All B's are A's."

This is an instance of the paradigm: "To infer q from p presupposes r." We will represent this relationship by the symbolic abbreviation: PRE (p F q : r).

It is clear that in any such instance of inferential presupposition it is the case that when (but only when) the presupposed condition (i.e., r) is satisfied, then if the premise or protasis of the presupposing inference (i.e., p) is given, then we can infer its conclusion or apodasis (i.e., q). In other words, we have that inferential presupposition is subject to the rule:

Rule 5. PRE (p F q : r) -+ [([p & r] -> q) & (p -> q)].

But now the question once more arises: What is the logical situation when the presupposition is not satisfied, that is, when Or? Here once again, we have two possibilities. In the case of the "weak" sense of inferential presupposition PRE1, we are simply unable to say what happens when r; this sense is governed by Rule 5 exclusively. Thus we can give:

Definition 5. PRE1 (p F q : r) =Df [([P & r] -+ q) & (p -> q)].

Here, if we have r, then we are simply unable to say whether q is or is not the case when p is given (though we do know that p does not entail q).




However, in the case of what I shall term the "strong" sense of inferential presupposition, PRE2, we have that r is absolutely essential to the inference from p to q in the sense that if we have r, then we can count on the fact that q will be false if p is given. Thus "strong" inferential presupposition is governed by the additional rule:

Rule 6. PRE2(p FIq : r) ->[(p& r)-> q].

Since "PRE2" is characterized by Rules 5 and 6 together, we obtain,

(1) PRE2(p Fq:r) -[([p&r]-+q)&([p&'- r] -I-rq)&-. (p -+q)].

This suggests,

Definition 6. PRE2 (p F q: r) Df [([P & r] q) & ([p & --..r] ? q) & --(p -> q)].

Here again we have,

(2) PRE2 (p F q : r) -> PRE1 (p F q : r),

to justify speaking of "weak" and "strong" inferential presupposition. Some illustrations are in order. An instance of weak inferential pre-

supposition is:

Example 11. To infer "X will refuse an even-money bet on event E" from "X knows that the probability of the event E is less than one-half" presupposes that "X is a rational person."

Clearly, when we know that a person is not rational, we can make no inference whatever regarding his conduct in a betting situation. By contrast, an instance of strong inferential presupposition is afforded by:

Example 12. To infer "Some S is P" from "All S is P" presupposes that "There are S's." 2

Here when the presupposed condition fails, we can actually infer the falsity of the consequent from the truth of the antecedent.

Definitions 5 and 6, it should be noted, show that inferential presupposition also is definable in terms of propositional presupposition, through the use of Definition 1.

V. Conclusion Let us examine briefly some of the results and implications of the

foregoing analysis of presuppositional concepts. It has appeared that

2 This example assumes an interpretation of categorical propositions in which universal propositions do not have existential import, but particular propositions do.



ON THE LOGIC OF PRESUPPOSITION 527

"presupposition" is by no means a univocal term, but embraces a diversity of ideas. Propositions, properties, and inferences can all involve presuppositions. However, each of these is definable in terms of the concept of propositional presupposition, whose archetype is "to assert that p presupposes q." However, this concept itself, i.e., propositional presupposition, has been shown to be equivocal, and to cover three distinct concepts. Of these, the prima face construction of "p presupposes q" as "q is a necessary condition for p" is only one. The other, and perhaps more fundamental, constructions are "q is a necessary condition for the possibility of p, i.e., for K p," and "q is a necessary condition for the meaningfulness of p." The second of these three senses, in particular, illustrates the fact that a correct understanding of the nature of presupposition requires the use of modal concepts. Here, modalities prove to be an indispensable instrument for the explication of philosophically important ideas.

Finally, I should like to revert briefly to the thesis that it is one task of philosophy to enquire into the presuppositions of our discourse about the phenomena of this world (be it in commonsense or in scientific contexts). I have tried here to show that a critical sense of the fundamental paradigm "p presupposes q" is its interpretation as "q is a necessary condition for the very possibility (or even the meaningfulness) of p." With this central sense of "presupposition" in mind, we see that the aforementioned task becomes that of enquiring into the "presuppositions" of our knowledge in the precise sense of the question: under what conditions and circumstances would our familiar modes discourse about the phenomena of the world about us come to be - not merely false, but - impossible or even meaningless? In this formulation, as derived from our analysis of the logic of presupposition, the question is clearly seen to rest upon that intimate combination of logical, linguistic, and factual considerations that constitute the very hallmark of the problems of philosophy. This question of course rests upon presuppositions of its own - as questions so frequently do. But to probe into these leads beyond the logical scope of the present investigation.

NICHOLAS RESCIHER. LEHIGH UNIVERSITY.



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