Aw: Re: [PEIRCE-L] Re: Laws of Nature as Signs

[Helmut Raulien]

 

John, Jon, List,

I have not fully understood the example wit Mary and the camera (in Hamburg it is very late now), but I think, that it would be good to replace the concept of "linguistic turn", which is nominalistic, with a kind of "social turn", see the other thread by Jon, about inquiry being dependent on social communication. This was just a guess, I have not understood the difference between obligatory and optional, sorry, I will try, but not now, I go to sleep.

Best,

Helmut


 08. Mai 2017 um 21:56 Uhr
Von: "John F Sowa" 
 

On 5/8/2017 10:40 AM, Jon Awbrey wrote:
> The question then is whether we keep or lose information in passing
> from a triadic relation to the collection of its dyadic projections.

Linguists use the term 'obligatory'. For example:

Obligatory: "Mary gave Bill a camera."
Optional: "Mary saw Bill with a camera at the party."

In the first sentence 'gave' has three obligatory participants.
If you omit one, its absence can be noticed or inferred:
"Everyone gave Bill a present for his birthday. Mary gave a camera."

In the second sentence, 'saw' has an obligatory object,
but "with a camera" and "at the party" are optional adjuncts.

John



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Aw: Re: [PEIRCE-L] Re: Laws of Nature as Signs

[Helmut Raulien]

Jon, John, List,

Is it reasonable to say that a relation has an intension and an extension, the intension is firstness, and the extension secondness (of the relation, which is secondness)?

Best,

Helmut

 

20. April 2017 um 15:14 Uhr
Von: "John F Sowa" 
 

Jon,

That is an extensional definition of a relation:

> Following the pattern of the functional case, let the notation
> “L ⊆ X × Y” bring to mind a mathematical object specified by
> three pieces of data, the set X, the set Y, and a particular
> subset of their cartesian product X × Y}. As before we have
> two choices, either let L = (X, Y, graph(L)) or let “L” denote
> graph(L) and choose another name for the triple.

Nominalists prefer extensional definitions. But Peirce would
usually state intensional definitions (rules) for the functions
or relations he was considering.

Alonzo Church (1941) stated the intensional definition:
> A function is a rule of correspondence by which when anything is
> given (as argument) another thing (the value of the function for
> that argument) may be obtained. That is, a function is an operation
> which may be applied on one thing (the argument) to yield another
> thing (the value of the function).

For further discussion of the distinction between intensions
extensions, see pp. 1 to 3 of Church's book:
http://www.jfsowa.com/logic/alonzo.htm

By the way, Church was not a nominalist. See the transcript of his
talk "On the ontological status of women and abstract entities":
http://www.jfsowa.com/ontology/church.htm

John

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