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The object, on the other hand, is best thought of as whatever is signified, for example, the object to which the written or uttered word attaches, or the fire signified by the smoke.The interpretant, the most innovative and distinctive feature of Peirce's account, is best thought of as the understanding that we have of the sign/object relation.
Peirce uses numerous terms for the signifying element including “sign”, “representamen”, “representation”, and “ground”.
Here we shall refer to that element of the sign responsible for signification as the “sign-vehicle”.
Consequently, it is useful to begin with an account of the basic structure of signs according to Peirce.
I define a sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its interpretant, that the later is thereby mediately determined by the former.
As he himself said, “[…] it has never been in my power to study anything,—mathematics, ethics, metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economics, the history of science, whist, men and women, wine, metrology, except as a study of semiotic” (SS 1977, 85–6).
Peirce also treated sign theory as central to his work on logic, as the medium for inquiry and the process of scientific discovery, and even as one possible means for 'proving' his pragmatism.
Similarly, the sizes of molehills vary according to the size of the mole that makes them, so again, this feature is not primary in the molehill's ability to signify.
What is central here is the causal connection that exists between the type of mound in my lawn and moles: since moles make molehills, molehills signify moles.
Not every characteristic of the molehill plays a part in signifying the presence of moles.
The color of the molehill plays a secondary role since it will vary according to the soil from which it is composed.