tmoody@sjuvax.UUCP (T. Moody) (10/24/85)
[]
Logicians recognize two kinds of consistency, at least: semantic
and syntactic. Here are some definitions.
--> A set of statements, S, is semantically consistent if and only if
the members of S could all be true in the same possible world.
--> A set of statements, S, is syntactically consistent if and only if
no statement of the form P & ~P is derivable, using formal logical
principles, from S.
What makes the first kind of consistency semantic is its use of
the concept "truth." The second definition uses only formal or, if
you prefer, typographical concepts -- as long as you understand
"statement" to refer to a subset of typographical strings.
I think that semantic consistency is what most of us mean when we
wonder whether the human mind is often, or ever, consistent. We want
to know whether all of the things we believe could be true in this,
the actual world, or in any possible world.
I offer the following pair of statements; I think that most of us
would assent to both of them.
S1. Take any particular belief of mine that you choose; I hold
that belief to be true, since that's what it means for something to
*be* a belief.
S2. I believe that some of my beliefs are false.
The first statement is a necessary truth. The second statement
is an inductively grounded conclusion, based on past experiences of
being wrong. The point is that individually I hold my beliefs to be
true; there is not a belief of mine that I hold to be false. But one
of my beliefs is the belief that at least one of my beliefs -- I can't
specify which one -- is false. Call this the Principle of Humility.
I think that virtually everyone accepts the Principle of
Humility. But the set { S1, S2 } is obviously inconsistent. For
those who have been wondering whether the mind is consistent, I think
that this example at least shows that the belief systems of most --
perhaps all -- of us are in fact inconsistent.
Todd Moody | {allegra|astrovax|bpa|burdvax}!sjuvax!tmoody
Philosophy Department |
St. Joseph's U. | "I couldn't fail to
Philadelphia, PA 19131 | disagree with you less."rsl@ihwpt.UUCP (11/05/85)
> I offer the following pair of statements; I think that most of us > would assent to both of them. > S1. Take any particular belief of mine that you choose; I hold > that belief to be true, since that's what it means for something to > *be* a belief. I would dis-sent on S1 on the basis of incompleteness. Saying that something is a "belief" ALSO acknowledges that you do not KNOW that it is true and that you suspect that it, in fact, may not be true; otherwise, I contend that you would say that you KNOW that it is true. (e.g. I KNOW that I am typing this message; I BELIEVE that you will comprehend its meaning). The interesting question is: WHY do people "hold that belief to be true", given that they do not know that it is actually true? > > S2. I believe that some of my beliefs are false. I "assent" to S2. > The first statement is a necessary truth. Ain't "necessarily" so :-) > But one > of my beliefs is the belief that at least one of my beliefs -- I can't > specify which one -- is false. Call this the Principle of Humility. Dintiguishing your beliefs, AS BELIEFS, and not as truths or knowledge may be called the Principle of Honesty. > I think that virtually everyone accepts the Principle of > Humility. But the set { S1, S2 } is obviously inconsistent. For > those who have been wondering whether the mind is consistent, I think > that this example at least shows that the belief systems of most -- > perhaps all -- of us are in fact inconsistent. I hope that I have given you a clue as to how to regain any lost consistency. The concepts to believe and to know, when used properly, do distinguish different relationships to the concept truth. Inconsistency is the evidence of a "lack of truth". The consistency that really counts is the consistency of statements or claims with reality, not with other statements (as in semantic and syntactical consistency). Facts are statements which are consistent with reality; any other statement is simply non-factual and false. [ If theologians would strive for consistency with reality (instead of consistency with the "true doctrine"), they would find themselves without a field of study.] -- Eudaemonia, Richard S. Latimer [(312)-979-4886, Wheaton, IL]
charli@cylixd.UUCP (Charli Phillips) (11/06/85)
>Saying that >something is a "belief" ALSO acknowledges that you do not KNOW that >it is true and that you suspect that it, in fact, may not be true; >otherwise, I contend that you would say that you KNOW that it is >true. (e.g. I KNOW that I am typing this message; I BELIEVE that >you will comprehend its meaning). >The interesting question is: WHY do people "hold that belief to be >true", given that they do not know that it is actually true? >. . . . >Facts are statements which are >consistent with reality; any other statement is simply non-factual >and false. [Richard S. Latimer] Fact: I love my husband. Belief: My husband loves me. I hold this belief to be true. I do not (indeed, I *cannot*) KNOW that it is true, I simply BELIEVE that it is. I have no proof that he does, in fact, love me; he may be dissembling. My statement about my husband's love for me is obviously a statement of belief, and therefore non-factual. This does not make it false. Now, Mr. Latimer, do you now "WHY...people 'hold that belief to be true', given that they do not know that it is actually true?" charli
torek@umich.UUCP (Paul V. Torek ) (11/06/85)
In article <546@ihwpt.UUCP> rsl@ihwpt.UUCP writes: >> S1. Take any particular belief of mine that you choose; I hold >> that belief to be true, since that's what it means for something to >> *be* a belief. >I would dis-sent on S1 on the basis of incompleteness. Saying that >something is a "belief" ALSO acknowledges that you do not KNOW that >it is true and that you suspect that it, in fact, may not be true; >otherwise, I contend that you would say that you KNOW that it is >true. (e.g. I KNOW that I am typing this message; I BELIEVE that >you will comprehend its meaning). It does seem that when a person says "I believe so-and-so" he is admitting to some uncertainty, but this is only a connotation of the word "belief" and not strictly part of its meaning. At least, that's the way it is over here; I don't know about Illinois, where they may have accepted Ayn Rand's redefinitions of many words including "belief". :-> Anyway, take the set of things that a person *claims* to know. We could make up an S1' by substituting the words "thing that I claim to know" in place of the occurrences of "belief" in S1. Isn't it usually the case, indeed isn't it likely in your own case, that S2'. Something the person claims to know, is false. (I got this by modifying something said by the person rsl was responding to, namely this:) >> S2. I believe that some of my beliefs are false. So, that person's basic point: >> I think that virtually everyone accepts the Principle of >> Humility. But the set { S1, S2 } is obviously inconsistent. For >> those who have been wondering whether the mind is consistent, I think >> that this example at least shows that the belief systems of most -- >> perhaps all -- of us are in fact inconsistent. is probably right, even when S2 is replaced by S2' and S1 is replaced by S1'. >Eudaemonia, Richard S. Latimer [(312)-979-4886, Wheaton, IL] --Hedone, Paul V Torek torek@umich
js2j@mhuxt.UUCP (sonntag) (11/07/85)
> >> S1. Take any particular belief of mine that you choose; I hold > >> that belief to be true, since that's what it means for something to > >> *be* a belief. > >I would dis-sent on S1 on the basis of incompleteness. Saying that > >something is a "belief" ALSO acknowledges that you do not KNOW that > >it is true and that you suspect that it, in fact, may not be true; > >otherwise, I contend that you would say that you KNOW that it is > >true. (e.g. I KNOW that I am typing this message; I BELIEVE that > >you will comprehend its meaning). > > It does seem that when a person says "I believe so-and-so" he is admitting > to some uncertainty, but this is only a connotation of the word > "belief" and not strictly part of its meaning. Well, even using this definition of 'belief', the paradox can be resolved. I have certain beliefs. I believe that under the assumptions of ordinary arithmatic, 1+1=2. I believe that under the assumptions of plane geometry, the pythagorean theorem is true. I do not hold the belief that any of these beliefs are in fact false. I *assume* many things about the phenomena called the 'real world'. Though I have never seen it, I *assume* that the Golden Gate bridge exists. Though I haven't seen it since a couple of hours ago, I assume that my apartment still exists. I assume that some of my assumptions may be wrong. There is no paradox, as long as you don't go around believing just anything. In particular, I have no proof that the 'real world' is anything more than a subjective phenomena, thus it would be impossible to hold any beliefs concerning it. (That the real world exists is an assumption I have found very useful, but it is an assumption, nonetheless.) -- Jeff Sonntag ihnp4!mhuxt!js2j "What would Captain Kirk say?"