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Logical form

DOI
10.4324/9780415249126-X021-1
DOI: 10.4324/9780415249126-X021-1
Version: v1,  Published online: 1998
Retrieved March 01, 2021, from https://www.rep.routledge.com/articles/thematic/logical-form/v-1

3. Comparing theories of logical form

The central principle for comparing theories of logical form is the following:

  • CP T′ is preferable (prima facie) to T if T′ explains a greater range of logical behaviour than T without appeal to extralogical principles (or, ‘meaning postulates’).

To illustrate, intuitively (10) follows directly from (5):

  • (10) Someone gave something to Andrea.

And yet, in Aristotle’s theory, as noted, (5) must be analysed along the lines of (6) and (10) along the lines of (11):

  • (11) Some person is a giver of something to Andrea.

However, then the analyses (6) and (11) exhibit only the obviously invalid argument pattern

  • (12) Some A is a B.

  • Some A is a C.

To capture the original entailment, (12) must be treated as enthymematic: that is, there is a suppressed premise with the logical form ‘Every B is a C‘, namely

  • (13) Every giver of The Brothers Karamazov to Andrea is a giver of something to Andrea.

Aristotle’s logic, therefore, explains the relation between (5) and (10) by introducing an extralogical principle linking the two predicate terms, in effect reducing it to an instance of the argument pattern (2).

By contrast, represented in predicate logic, the logical forms of (5) and (10) constitute the valid pattern

  • (14) ∃xHxyz

  • ∃y ∃xHxyz

Hence, that (10) is a consequence of (5) is explained on the basis of their logical forms alone, without appeal to any extralogical principles. So, prima facie, a theory based on predicate logic is preferable to Aristotle’s theory.

The ‘prima facie’ qualification in CP marks the influence of other factors besides extent of explanatory range that are relevant to an evaluation of competing theories of logical form. Two particularly influential principles can be observed in recent debates over the logical forms of one or another class of sentences: logical conservatism and ontological conservatism.

The shift from Aristotle to Russell exhibits a typical way in which one theory T′ of logical form can broaden the explanatory range of another T; namely, by extending or otherwise subsuming the canonical language and logic of T. In such cases, the language of T′ is able to provide logical forms for all sentences in the target class of T. In addition, the language of T′ includes logical constants and classes of complex expressions not present in the language of T that enable T′ to construct logical forms not available to T. Appropriate logical principles for its new forms then enable T′ to explain logical phenomena that are left unexplained (without extralogical principles) in T, for example, (10)’s being a logical consequence of (5). The principle of logical conservatism stipulates that supplementation to a given canonical language should be kept to a minimum. More exactly, let T and T′ be theories with roughly equal target classes and let L be a background logical theory (first-order logic, for example) that is common to both T and T′; then

  • LC T′ is preferable (prima facie) to T if T′ requires fewer extensions to L than T.

The increase in explanatory range of predicate logic, of course, is far too vast for LC to override CP in the choice between Aristotle and Russell. A better example is found in recent well-known work on the logical form of action sentences with adverbial modifiers. For example:

  • (15) April kissed Jonathan tenderly.

It is intuitively clear that (15) entails

  • (16) April kissed Jonathan.

Typical predicate logic analyses of these sentences represent ‘kissed’ and ‘kissed tenderly’ as distinct two-place predicates. The entailment is then explained by means of a meaning postulate to the effect that if A kisses B tenderly, then A kisses B. As with Aristotle’s explanation of the relation between (5) and (10), then, in this explanation the apparent entailment is actually enthymematic. However, the entailment can be explained directly by treating an adverb such as ‘tenderly’ as an adverbial operator t that, when prefixed to an n-place predicate F (such as ‘kissed’), yields a new n-place predicate [tF] (‘tenderly kissed’) (see Adverbs §1). The logic of these new constructions is then characterized generally by the principle that

  • (17) [αΠ]x1xnΠx1xn , for any adverbial operator α and n-place predicate Π.

The logical forms of (15) and (16), then, on this approach, are (18) and (19), respectively:

  • (18) [tF]xy

  • (19) Fxy

and so by the new logical principle (17), (16) follows from (15) directly in virtue of their logical forms.

Most philosophers would probably agree that this increase in explanatory range is significant enough to override LC and warrant the added apparatus. However, Davidson (1967) proposed a logically more conservative analysis which avoids the new apparatus. Specifically, for Davidson, the proper analysis of action sentences takes the structure of an action verb such as ‘kissed’ to involve an implicit parameter for an event. Thus, (15) is to be analysed as

  • (20) ∃x (kissing-of(April, Jonathan, x) & tender(x))

(read, roughly, as ‘There is an event x such that x is a kissing of Jonathan by April and x is tender’), and (16) as

  • (21) ∃x (kissing-of(April, Jonathan, x))

The entailment from (15) to (16) is then explained by standard logical principles governing conjunction and the existential quantifier, and the apparently hasty introduction of new constructions and unfamiliar logical principles is avoided. Since their explanatory ranges are the same, then, CP provides no support for the adverbial operator account over Davidson‘s, and so, by LC, Davidson’s account is to be preferred (see Adverbs).

As Davidson’s account illustrates, however, conservatism with regard to logic is often accompanied by liberalism with regard to ontology – in this case, the postulation of events. The ‘ontological commitments’ of a theory T of logical form consist of the kinds of things that must exist if the analyses that T assigns to the sentences of its target class are to be meaningful (see Ontological commitment). The second principle – ontological conservatism – is that such commitments are to be kept to a minimum; that is, more exactly, where again T and T′ have roughly equal target classes,

  • OC T′ is preferable (prima facie) to T if T′ has fewer ontological commitments than T.

Unlike LC, this principle favours the operator account of adverbial modification over Davidson’s more ontologically permissive account. The choice between the two thus turns on one’s preferred brand of conservatism.

LC tends to be overridden by CP when they conflict, as additional apparatus is usually viewed as a small price to pay for greater explanatory range. However, more is often at stake in conflicts between CP and OC, as theories of logical form that have great explanatory range often exact a high price in ontological commitment: possibilia (that is, possible but non-actual objects) are introduced to explain sentences involving modality (see Modal logic, philosophical issues in §§1–2), intensional entities to explain the logic of attitude verbs (see Propositional attitude statements §§1–2) and so on. One must either choose between the two or offer a competing account with the same explanatory range but fewer ontological commitments. Since Russell first formulated his theory of descriptions (see Descriptions) to counter what he saw as Meinong’s ontological excesses, the development of competing theories of logical form has been, and largely remains, the primary tool for metaphysical discovery and the central approach to metaphysical debate in the twentieth century (see Analytical philosophy).

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Citing this article:
Menzel, Christopher. Comparing theories of logical form. Logical form, 1998, doi:10.4324/9780415249126-X021-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/logical-form/v-1/sections/comparing-theories-of-logical-form.
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