Predicate

The notion of predicate is a tricky one that needs consideration in the history
of philosophy, certainly is one is trying to find one's way through the
development of the various logic disciplines:

Beginning with Frege, predicate logic uses the following quantifiers:

Existential, there is an A.

Universal, for all B.

One can then construct propositions, which have truth values ie true or false.

Bertrand Russell is impressed with Frege's work, and certainly taken with the idea that one must do away with universals. Thus begins his own work.

 

Predicate logic gave rise to a number of paradoxes.

 

Today, we use second order logic to quantify over relations. An example would be:

 

For every P for every x(x is a member of P or x is not a member of P).

 

                                                       * * *

 

 

During the 1870s, mathematicians - for example Dedekind - had success in using set theory to clarify some mathematics, essentially laying the groundwork for what became Logicism, ie the notion that mathematics is an extension of logic. The latter is quite a program because it involves  translating mathematical notions purely with set theory, and without larger than, smaller than, succession and so forth. Frege's Begriffsschritt, whose first book appears in 1879, proposes logical tools for the task.

 

By the time the second book appears, young Russell in England is acquainted with the paradox from

set theory, and launches his own take on these issues. He will later produce Principia Mathematica

with Whitehead. Interestingly, dealing with the incompleteness  opens the door to

expanding the claims of logic even more, to linguistic utterances.

 

By 1929, the Vienna Circle (philosophers and physicists) is making strong claims about the primacy of scientific utterances: metaphysical statements are about language, but carry no meaning. We

have reached logical positivism.

 

 

 

                                                         * **

 

There are many works and issues to be considered in these developments. and if the positions seem extreme,one need consider that this is also the period of the appearance of many sciences we take today for granted.

 

I was reading this morning that the defense in the trial of the Boston bomber had called

a social scientist form Princeton University to explain the patriarchal culture that

reigns in the Caucasus. These ideas are meaningful descriptions in a legal context - quite

an advance for the scientific -  and the whole a fait de culture.