Stanford Metaphysics Research Lab: "The Theory of Abstract Objects"

I try to read something new in the Wide World of Metaphysics at least weekly. Often I have to re-Google and/or hyper-clickalate in order to find stuff I haven’t already read (and which I can sort of understand). Any-hoo, this week’s Read was a great Find on the principles and language of abstract objects. The gist is that a research group at Stanford came up with metaphysical formulas supporting two Principles of the Abstract: “existence conditions” and “identity conditions.” (For those who aren’t clear on the difference between Physics and Metaphysics, all theories of the abstract or conceptual fall under the heading of Metaphysical theory whereas Physics deals with concrete objects.)

Before they present, the Stanford guys explain that their theories of Abstract “existence” and “identity” are supported by Ernst Mally's distinction between exemplifying (typifying) and encoding (instructing) a given property. This distinction can be seen in the difference between the atomic formulas ‘Fx’ (where ‘x exemplifies F’) and ‘xF ’ (where ‘x encodes F’). The formula ‘Fx’ could be used to logically analyze simple sentences like ‘Anne is happy’, ‘Bush is president’, and ‘Leo is a cat.’ Mally's idea was that we should not represent sentences about fictional objects, such as ‘Sherlock Holmes is a detective’, ‘Pegasus has wings’, or ‘Zeus lived on Mt. Olympus’, in terms of the notation ‘Fx’...because only real, concrete objects can exemplify the properties of being a detective, having wings, or living on Mt. Olympus. Nevertheless, Mally reasoned that there must be some mode of predication, i.e. some sense of the words ‘is’ and ‘has’ for which it is true to say ‘Sherlock Holmes is a detective’ and ‘Pegasus has wings’ (for we wouldn't understand the story/myth properly if we didn't imagine objects that were instances of the properties in question). So, Mally informally introduced the notion ‘x encodes F’ as a new mode of predication that is more appropriate for the logical analysis of sentences about fictions and other Abstract objects.

What is so beautiful about Mally’s thinking is the exactness of the language in relation to the thing it describes. He skillfully analyzes and explains what the real meaning of the word “is” is, both in the Real and Fictional: something we all thought only Bill Clinton could do.

Stay tuned for Part II which will answer the burning question: Are theories postulating Abstract objects incompatible with the theories of natural science?