The Two Fundamental Problems of the Theory of Knowledge by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9781135626839
Publisher: Taylor & Francis (Unlimited)
Published: 2023-04-15T00:00:00+00:00

Chapter IX

STRICTLY UNIVERSAL STATEMENTS AND SINGULAR STATEMENTS

DOI: 10.4324/9780203371107-10

31. Implication and general implication

Our critical discussion of the pseudo-statement positions was interrupted in order to enable us to analyse (in sections 24–30) the set of problems posed by conventionalism, above all in order to allow a closer characterisation of the first pseudo-statement position.

On that occasion, logical (logistical) questions were discussed in perhaps greater detail than was absolutely necessary. This was done in part because a polemical treatment was desirable, but also because the terminological machinery acquired in that process will be needed in a further discussion, which is also polemical. Only after concluding this discussion can we return to the critique of the pseudo-statement positions.

This second polemic concerns the relationship between general implications on the one hand and universal and singular statements on the other.

The problem at the centre of this debate will be examined in the next section; the present section has the task of providing a recapitulation of the concept of general implication.

For this purpose, we discuss first the logistical concept of “implication” and then the concept of “general implication”. For a more detailed discussion of the latter, the concept of “implication” is almost indispensable.

The concept of “implication” is, however, important for other reasons too. Its examination will shed considerable light on certain aspects of the problem of induction itself. This important additional result will be used in the subsequent analysis – though it should be clearly understood that the analysis has, at the present stage, different objectives.

While a “general implication” asserts that a particular relationship holds between propositional functions, an “implication” asserts that a similar relationship holds between genuine statements. (The “implicans” and the “implicate” of an “implication” are thus statements and not statement functions.) Both “general implications” and “implications” are assertions; they are themselves genuine statements. An “implication” might, therefore, also be called a “statement about statements”, and a “general implication” a “statement about propositional functions”.*1

*1 These formulations (in particular the word “about”) again demonstrate the absence of a distinction between object language and metalanguage. What is meant is that an implication is a statement containing (two) statements, while a general implication is a statement containing statement functions.

An “implication” connects statements (its implicans and its implicate), thus forming a conditional proposition (“hypothetical judgement”). The latter is usually expressed linguistically by means of the connective “if … then …” (“If” introduces the implicans, “then” the implicate.) For example, “If Napoleon carries a sword, then he also wears a hat.”

This example was intentionally chosen so that no “internal” dependence whatever exists between the two interconnected statements involved (“Napoleon carries a sword”, “Napoleon wears a hat”). An “implication” should not be regarded as an assertion about the internal relations, or about the content of the two statements; it asserts only a relationship between their truth values.

What it asserts is only that if the implicans is true, then the implicate is also true.

Therefore, it asserts nothing about the content of the statements, nor does it say that “something is the case”, that

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