Logic and Language

The Hobbesian account presents the idea of the Two-name theory of the proposition, this is evident also in Nominalism. This theory states that a proposition is only true if both predicate and subject are names of the same thing.

John Stuart Mills however believed this theory to be wrong and that it only makes sense when both predicate 

and subject are proper names. He presented this idea with his book ‘System of logic’ which included his theory on language with his theory of naming.

Mills considers a name to be either a description, for example, ‘that book is red’…  an actual name, for example, ‘Helen’…  as well as general terms such as ‘man’ or ‘wise’. All names he considers to denote things. Proper names denote the things they name and general terms denote the things they are true of. General terms also have a connotation, they connote the attributes they signify. Every proposition is therefore a conjunction of a name.

Mills believed that there are two types of inference in any proposition, both verbal inference and real inference. Verbal inference implies that the knowledge of language alone is enough to understand the premiss. In other words that language has the ability to ascertain validity and truthfulness, for example, the two statements ‘no great general is a rash man’ and ‘no rash man is a great general’ maintain the same conclusion and are therefore verifiable.

The other type of inference Mills refers to is that of a ‘real inference’. A real inference therefore infers to a truth in the conclusion which is not contained in the premiss.

Outside of his book, Mills explained that new truths could be discovered by general reasoning by accepting that all reasoning was syllogistic. This meant that any conclusion from an inference is actually implied or contained in the premiss.

Frege believed however that there was an evident fallacy in the use of subject and predicate in order to explain language. He presented this idea in his ‘refoundation of logic’. He believed that logic was a priori and analytic and can be considered to be the second founder of logic.

Frege argued that in order to resolve the problem surrounding the two terms subject and predicate it was necessary to replace them with the two terms argument and function. This, he suggested provided more flexibility when analysing the logic behind language.

He proposed that the argument is the constant or ‘fixed’ element in a sentence or proposition, for example, the first part of the sentence; ‘wellington defeated Napolean’, can be changed to ‘Wellington defeated Nelson’. Napolean can be changed whether it makes the statement verifiable or not but the first part of the sentence is the argument and therefore the changeable word or (name) can be considered in this case to be the function, e.g. ‘William defeated…’ is the argument and ‘Nelson’ is the function. This method provides flexibility because you can name or choose different parts of the sentence according to the circumstance. The word ‘defeated’ could also be considered the argument with the functions both ‘Wellington’ and ‘Nopolean’ (or Nelson) as the elements of the propositions which can be changed.

Frege wrote more specifically on theories in language with his work ‘sense and reference’ in 1892

He addressed the topic of meaning and aimed to uncover some of the fundamental flaws within meaning in language. Some of the questions which he aimed to explore where; what do words and sentences signify? How do they signify and do they all signify in the same way? What is the relationship between meaning and truth?

He aimed to achieve this by attempting an explanation of what identity could be considered as. He went about this by using the two terms sense and reference.

What he meant by a reference can be explained as relational to that of an object to which a name, sentence or word refers to. An example of this is that the planet Venus can be the reference of ‘the morning star’.

The sense of an expression however is the particular mode in which a sign presents what it designates, for example ‘The evening star’ differs in sense from ‘the morning star’ even though it has been discovered that both expressions refer to venus.

Therefore, an identity statement will be true if the sign of the identity is flanked by two names with the same reference but different senses… generally.

He explains that there are items at 3 levels… signs, sense and reference. ‘By using signs we express a sense and denote a reference.’