Logic, symbols and icons

What is symbolic logic? The very use of the adjective implies that there are other kinds of logic. This (purported) distinction is largely based on the languages used: artificial notations vs. ‘ordinary’ language. Now, is there a principled, clear-cut division between symbolic and non-symbolic logic? Obviously, it all depends on one’s definition of symbol. I propose to examine the consequences of Peirce’s concept of symbol to the status of symbolic logic. According to Peirce [1], sig ns are of three kinds: symbols, icons and indexes. Symbols are signs established by pure convention, by the acceptance of rules governing the relation between signs and their objects; icons as signs whose relations with the corresponding objects are found ed on similarity icons depict their objects. Now, following this trichotomy, artificially created symbols as well as ordinary words both belong to the same category, i.e. symbols, and thus systems of logic expressed with ‘plain’ words are just as symbolic. What then (if anything) gives a special status to what we usually refer to as ‘symbolic logic’? I argue that what is special about the symbols we use in logic is that they are actually less symbolic and more iconic than ordinary words. But th e signs used in so-called ‘symbolic’ logic are iconic not in the same way that a painting depicts a person. More than individual objects, logical systems of signs depict structures the mutual configuration of objects by means of the concatena tion of its signs (their syntax). Thus, I conclude that the grounds for the expressivity of so-called ‘symbolic’ logical languages is, ironically, their iconic nature.