My recent interest in Leibniz has been influenced by a question concerning Wittgenstein’s Tractatus Logico-Philosophicus. This might sound odd. I promise it isn’t. You see, Leibniz had this crazy idea about language. He noted around 1677 that there was a relationship between things and the signs (words) we use to name them which is very peculiar. When words are used in the language with each other they admit of a connection between each other that is formally like the connections between the things they describe. He calls this connection the ‘foundation of truth.’
Since one sentence is certainly not going to do this relationship justice, I will attempt to give an example: You notice that every Monday morning the trash is picked up on your street unless you have been otherwise notified of a change to this routine. You tell your friend during conversation that “When Monday morning rolls around the trash gets picked up on our street.” Later on, you have a similar conversation and you say “On the second day of the week the rubbish is taken up on our road.”
Note that both sentences say the same thing, they use different common words. In fact, the words which align themselves with objects in the statements can be arbitrary. Any number of contexts could allow for any number of signs (words), but in all cases the sentences have the same form: If Monday morning, then trash pickup. If (x), then (y).
The easiest place to see the phenomenon is in algebra. The value of the variable in 2x = 4 is always going to be 2 regardless of what variable sign we put in the formula. y = 2 in 2y = 4. (In fact, we can substitute other signs for any of the parts of the statement as long as they indicate the same things. x = II in IIx = IV.)
Leibniz puts it all this way:
“Although truths necessarily presuppose some characters and even sometimes have characters as objects –as when we demonstrate the rule for casting out nines– truth is not based on what is arbitrary in characters but on what is permanent in them: namely, the relationship which marks among themselves have to things.”
What is so interesting about Leibniz’s discovery is that the very next move he makes after this is the one beginning in the last post on this blog. If we could find clear and fully expressive (exact) signs to use for every single thing there is, then we could do with the world and its truths what we do with mathematics. Thus, Leibniz started on a path towards an ‘ideal’ language. In his terms, he was attempting a Characteristica Universalis.
Now, there are two parts to any good Characteristica Universalis. There are all the fancy ideal signs, and there is a Calculus Ratiocinator which sets the logical rules for their use. Think of the Calculus as a form of symbolic logic, more specifically, think of it as an Algebraic system of logic. So, the language is logical, and its signs are as ‘metaphysically fundamental’ and as infinite as number. Let that suffice for now as a reading of Gottfried.
In 1882 Gottlob Frege mentioned that the logic in his Begriffsschrift was something he called a Lingua Characterica, not a Calculus Ratiocinator. Part of the interest in Leibniz is, then, what he can say to us about the nature of Frege’s logic, and by way of Frege what he can tell us about Wittgenstein.
I’ll attack all this from another route soon. I might even mention what that question about the Tractatus is…