LOGIC the notions of argument and function offers a more flexible method of analysing the sentence This is how it works Suppose that we take our sentence ‘Wellington defeated Napoleon’ and put into it, in place of the name ‘Napoleon’, the name ‘Nelson’ Clearly this alters the content of the sentence, and indeed it turns it from a true sentence into a false sentence We can think of the sentence as in this way consisting of a constant component, ‘Wellington defeated ’, and a replaceable element, ‘Napoleon’ Frege calls the first, fixed component a function, and the second component the argument of the function The sentence ‘Wellington defeated Napoleon’ is, as Frege would put it, the value of the function ‘Wellington defeated ’ for the argument ‘Napoleon’ and the sentence ‘Wellington defeated Nelson’ is the value of the same function for the argument ‘Nelson’ We could also analyse the sentence in a different way ‘Wellington defeated Napoleon’ is also the value of the function ‘ defeated Napoleon’ for the argument ‘Wellington’ We can go further, and say that the sentence is the value of the function ‘ defeated ’ for the arguments ‘Wellington’ and ‘Napoleon’ (taken in that order) In Frege’s terminology, ‘Wellington defeated ’ and ‘ defeated Napoleon’ are functions of a single argument; ‘ defeated ’ is a function of two arguments.3 It will be seen that in comparison with the subject–predicate distinction the function–argument dichotomy provides a much more flexible method of bringing out logically relevant similarities between sentences Subject– predicate analysis is sufficient to mark the similarity between ‘Caesar conquered Gaul’ and ‘Caesar defeated Pompey’, but it is blind to the similarity between ‘Caesar conquered Gaul’ and ‘Pompey avoided Gaul’ This becomes a matter of logical importance when we deal with sentences such as those occurring in syllogisms that contain not proper names like ‘Caesar’ and ‘Gaul’, but quantified expressions such as ‘all Romans’ or ‘some province’ Having introduced these notions of function and argument, Frege’s next step is to introduce a new notation to express the kind of generality expressed by a word like ‘all’ no matter where it occurs in a sentence If ‘Socrates is As I have explained them above, following Begriffsschrift, functions and arguments and their values are all bits of language: names and sentences, with or without gaps In his later writings Frege applied the notions more often not to linguistic items, but to the items that language is used to express and talk about I will discuss this in the chapter on metaphysics (Ch 7) 103