Re: Logic playing at undermining itself



Jan Burse wrote:
John Jones schrieb:
herbzet wrote:
John Jones wrote:

There CANNOT be a distinction between 'and' and 'or' in logic.
Why? Because, as it stands, logic has not given the element that arises
from a conjunction or disjunction of 2 elements.

Usually, if we use the terms "conjunction" and "disjunction", we
are interpreting the elements as propositions (or statements, or
sentences). In that case the element that arises from a conjunction
or disjunction is a proposition. A compound proposition.

--
hz


I haven't placed much weight on the distinction between an object and a
proposition. I don't think that distinction is important here.

Regarding a 'compound' proposition, that looks like a rephrasing of 'A
and B'. At least, the term 'compound' is another way of indicating that
unspecified, or unintelligible logical movement that takes us from 'A'
and 'B' to 'A and B'.

Actually you are right. Only when considering valuations
the view is such that there is an operator that takes
us from val(A) and val(B) to val(A and B). This model
theoretic thinking.

But in proof theoretic thinking, there is not necessarely
such an operator present. Although it can be constructed
via lindenbaum algebras etc.. Clearly one must adapt an
other viewpoint.

The reason for the other viewpoint is as follows. We might
have presupposed 'A and B' already without any saying about
'A' and 'B'. Thus 'A and B' might follow from 'A and B'
itself directly.

Um, is your final sentence supposed to read

Thus 'A' and 'B' might follow from 'A and B' itself directly

or is it correct as written?

--
hz
.

Relevant Pages

  • Re: Logic playing at undermining itself
    ... from a conjunction or disjunction of 2 elements. ... In that case the element that arises from a conjunction ... Regarding a 'compound' proposition, that looks like a rephrasing of 'A and B'. ... The reason for the other viewpoint is as follows. ...
    (sci.logic)
  • Re: Logic playing at undermining itself
    ... from a conjunction or disjunction of 2 elements. ... In that case the element that arises from a conjunction ... A compound proposition. ... I don't think that distinction is important here. ...
    (sci.logic)
  • Re: Logic playing at undermining itself
    ... from a conjunction or disjunction of 2 elements. ... In that case the element that arises from a conjunction ... I haven't placed much weight on the distinction between an object and a proposition. ... Regarding a 'compound' proposition, that looks like a rephrasing of 'A and B'. ...
    (sci.logic)
  • Re: Logic playing at undermining itself
    ... from a conjunction or disjunction of 2 elements. ... In that case the element that arises from a conjunction ... Regarding a 'compound' proposition, that looks like a rephrasing of 'A and B'. ... But in proof theoretic thinking, ...
    (sci.logic)
  • Re: Existential, Universal Quantifiers, Generalize Booleans
    ... The similarity between conjunction and universal ... "infinite" conjunction or existential quantification as ... similarly a type of disjunction is central to the proof ... don't you mean to say 'the framework Dr. Ullrich _opposes_ '? ...
    (sci.math)
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