By Roger Teichmann (auth.)
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Extra info for Abstract Entities
An extension of the language to include, in addition to that of pronoun, the grammatical categories of proverb, prosentence, and so on, would be a step in the direction of logical perspicuity. There are, it is true, several expressions which may be dubbed 'pro-adverbs', for example, 'somehow', 'thereby', and 'thus'. The noun-biased form 'There is a way of talking which annoys Cedric' can be paraphrased as 'One can talk somehow such that talking thus annoys Cedric'. We also have the more specific (locative) pro-adverbs 'somewhere', 'where' and 'there'.
For a simple argument shows that'-a' is of a different logical type from 'a', since it and 'a' are not properly intersubstitutable in all contexts: that is, there is (on occasion) more than one way of substituting' --a' for 'a', and this indicates difference of level. Consider the sentence (3x)(Socrates died before x). There are two equally good ways of substituting '--Socrates' for 'Socrates' in this sentence, namely, - 3x(Socrates died before x) 3x( - Socrates died before x). We may choose either of these to be the result of substituting '--Socrates' for 'Socrates', but we cannot have both.
Thus, the predicables '- loves Bill' and '- loves Ben' are as close logical relatives as one could hope to find - but one cannot substitute the latter for the former in the argument 'Bill loves Bill; so someone loves himself, without losing validity. Here, one must also substitute 'Ben' for 'Bill'. Nevertheless, it is clearly through such processes as the substituting of expressions throughout valid arguments that one does determine when two expressions are of the same logical category. How then is it that we give 'the logical form' of a sentence, very often, by means of a rendition, or schema of a rendition, which we say shows the logical form of the sentence?
Abstract Entities by Roger Teichmann (auth.)