On 9/1/2017 6:37 PM, Tommi Vehkavaara wrote:
I do not see how those who take ontology as the first philosophy could
be convinced with this diagram, because in it, metaphysics
is presented rather as the last philosophy, instead.
I googled "prima philosophia" and found an interesting discussion
of the commentaries by Avicenna and Thomas Aquinas on Aristotle:
https://link.springer.com/content/pdf/10.1007%2Fs11406-013-9484-8.pdf
The question Avicenna raised and Aquinas analyzed is the seemingly
circular reasoning in calling metaphysics "prima philosophia et
ultima scientia".
From p. 2 of the article:
According to the beliefs of the Medieval philosopher, the system
of knowledge encompasses mathematics as well as ethics, natural
sciences as well as theology...
I hope to disclose what Thomas Aquinas meant by metaphysics as
the first and simultaneously the last philosophy (prima in
dignitate, ultima in addiscendo, first in dignity, last in the
order of learning), while also revealing the difficulties faced
by those who ask: “What is first” in this particular context.
Since Peirce had studied Scholastic logic and philosophy early
in his career, he must have been aware of these issues for many
decades before his 1903 classification. I believe that the dotted
lines in CSPsciences.jpg, for which Peirce cited Comte, represent
ideas he had been contemplating for many years.
Tommi
So because anything that can be found real can also be merely
"imagined" (independently on its reality), it is always possible
to draw a mathematical structure out of it, i.e. some mathematical
concepts and structures are present in any other science (and
therefore
"nature appears to US as written in the language of mathematics").
Yes. That is why Peirce said that philosophy and the special sciences
depend on mathematics for their methods of reasoning. As he said,
mathematics is based on "diagrammatical reasoning": draw or imagine
a diagram of any kind and make observations about the connections
and patterns in it. The diagram need not conform to any prior
knowledge or experience.
Tommi
philosophical concepts should be somehow included in every theory
in special science... But from such principle follows severe
restrictions to the content of philosophical sciences (most of all
to metaphysics) and their application to special sciences (e.g. in
which sense psychology is dependent on logic).
That would explain the phrase "ultima in addiscendo" by Aquinas.
But a restriction on the content of metaphysics would not affect
the principles it derives from mathematics, phenomenology, and
the normative sciences.
I would also cite Peirce's article on "Logical Machines" (1887),
which he published in vol. 1 of the American Journal of Psychology:
http://history-computer.com/Library/Peirce.pdf
From p. 4 of "Logical Machines":
When we perform reasoning in our unaided minds, we do substantially
the same thing, that is to say, we construct an image in our fancy
under certain general conditions, and observe the result. In this
point of view too, every machine is a reasoning machine, in so much
as there are certain relations between its parts, which involve other
relations that were not expressly intended... [But] every machine
has two inherent impotencies...
In this comment, Peirce admitted that machines could do mathematical
reasoning. The two impotencies of a machine: "it is destitute of all
originality, of all initiative"; and "it has been contrived to do a
certain thing, and it can do nothing else".
He added "the mind working with a pencil and plenty of paper has
no such limitations... And this great power it owes, above all, to
one kind of symbol, the importance of which is frequently entirely
overlooked -- I mean the parentheses."
With that comment, Peirce stated the importance of recursion.
He used recursive methods in various writings, but most logicians
and philosophers who read his writings missed that point because
the word 'recursion' was not used in mathematics until the 1930s.
And by the way, recursion looks circular, but useful recursions
always include a test for stopping when the result is achieved.
These issues about recursion came out of the debates of Gödel,
Church, and Turing when they were together in Princeton.
John
