Re: Information = Comprehension × Extension • Comment 3

Many things still puzzle me about Peirce’s account at this point.  The question marks I added to the Figures of the previous post indicate the node labels I have remaining doubts about.  For example, in Figure 3, is really an icon of object   Again, in Figure 4, is really an index of object   There is nothing for it but returning to Peirce’s text and trying again to follow his reasoning.

Let’s go back to Peirce’s example of abductive inference and try to get a clearer picture of why he connects it with conjunctive terms and iconic signs.

Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.

Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.

The relationship between conjunctive terms and iconic signs may be understood along the following lines.  If there is anything with all the properties described by the conjunctive term “spherical bright fragrant juicy tropical fruit” then sign users may use that thing as an icon of an orange, precisely because it shares those properties with an orange.  But the only natural examples of things with all those properties are oranges themselves, so the only thing qualified to serve as a natural icon of an orange by virtue of those very properties is that orange itself or another orange.

Reference

• Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Resources

• This Blog • Survey of Pragmatic Semiotic Information
• OEIS Wiki • Information = Comprehension × Extension
• C.S. Peirce • Upon Logical Comprehension and Extension

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