Objective Frameworks • Properties and Instances : 1

Dealing with sign relations that contain many types of signs — icons, indices, symbols, and more complex types — is a task that calls for a flexible and powerful organizational framework, one with the ability to grow and develop over time.  This is one of those applications where I found it useful to consider a “relative membership” relation, adding a parameter for the interpreter to the ordinary set-theoretic membership.

I laid out the details of a formalization in the following paragraphs:

It begins as follows:

In accounting for the special characters of icons and indices that arose in previous discussions, it was necessary to open the domain of objects coming under formal consideration to include unspecified numbers of properties and instances of whatever objects were initially set down.  This is a general phenomenon, affecting every motion toward explanation whether pursued by analytic or synthetic means.  What it calls for in practice is a way of organizing growing domains of objects, without having to specify in advance all the objects there are.

This entry was posted in Icon Index Symbol, Interpretive Frameworks, Logic, Logic of Relatives, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Semiotics, Set Theory, Sign Relations and tagged , , , , , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s