- Sep 21, 2007
> Is "completeness" a matter of "degree"?
Right. I recognize that mathematicians and logicians probably never talk about the “degree” of completeness. But as a practical matter in everyday speech we make all kinds of compromises w.r.t. consistency in order to increase the descriptive power of our utterances. Think of the classic paradoxes that so exercised Bertrand Russell, et al, such as:
“This sentence is false.”
The sentence can’t be true, because if it is, then it must be false. But neither can it be false, because if it is, then it must be true. But you simply cannot avoid this kind of paradox the minute you allow the sentence to refer to itself, and I don’t *want* to be restricted in that way.
For instance, these are perfectly good & meaningful sentences:
“This sentence has a subject and a predicate.”
“This sentence parses easily and has an intransitive verb.”
We cannot even purify philosophical language, much less everyday language of self-reference.
From: Aquinas_Catholic_Doctor@yahoogroups.com [mailto:Aquinas_Catholic_Doctor@yahoogroups.com] On Behalf Of PaedoSocrates@...
Sent: Friday, September 21, 2007 5:03 AM
To: Aquinas_Catholic_Doctor@yahoogroups.com
Subject: [Aquinas_Catholic_Doctor] RE: [aquinas] Re: Is Akrasia best explain by re...In a message dated 15/09/07 12:25:44 PM Mountain Daylight Time, pluviosilla@ gmail.com writes:
Yes, I agree with this statement (as applied to Judy’s prior comment). You cannot make reference to free will within a definition of free will. By doing so, for instance, you can dodge the question as to whether notions of free-will imply indeterminism or not. That should be out-of-bounds within this discussion, because one of my objectives in starting this thread was to get people to confront the issue of indeterminism.
:-)
Of course, do not forget that as a practical matter, in most philosophical dialog, we have to make a difficult choice w.r.t. self-reference. We know from Goedel that formal systems cannot be both complete and consistent, so unfortunately (I hope I do not misstate this) completeness often requires a certain amount of self-reference. It is just a question of determining how much consistency we are willing to sacrifice in order to obtain the degree of completeness we seek.
In this discussion, I would say that consistency should prevail
QUESTIONS:
What is the relationship between "self reference" consistency and completeness? Why must you "sacrifice consistency" to obtain a "degree" of "completeness" ? Is "completeness" a matter of "degree"?
Kevin - << Previous post in topic
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