Karl Malbrain wrote: > cbr...@cbrownsystems.com wrote: > > Karl Malbrain wrote: > > > Patricia Shanahan wrote: > > > > Karl Malbrain wrote: > > > > > Patricia Shanahan wrote: > > > > >> Ultimately, I don't think the subject of this thread even asks the right > > > > >> question. It should be "Set theory: Should you use?". I don't even know > > > > >> what it means to believe set theory. > > > > >> > > > > > > > > > > Believing means to agree with the axioms of set theory. > > > > > > > > > > intransitive verb > > > > > 1 a : to have a firm religious faith b : to accept as true, genuine, or > > > > > real <ideals we believe in> <believes in ghosts> > > > > > > > > > > karl m > > > > > > > > > > > > > That pushes it back to the question of what does it mean to "agree with > > > > the axioms". > > > > > > agree: > > > 1. To harmonize in opinion, statement, or action; to be in > > > unison or concord; to be or become united or consistent; > > > to concur; as, all parties agree in the expediency of the > > > law. > > > > > > You agree with the given system of axioms that negate the > > > inconsistencies of the previous system. > > > > > > > It could either mean "agree that they appear to be good, workable, > > > > axioms", or "agree that they are true, in some absolute sense that would > > > > make contradictory sets of axioms false". > > > > > > Yes, sets of axioms that are contradictory within themselves make an > > > inconsistent system. So both are true. > > > > > > > I agree with them in the first sense, but not the second. > > > > > > I don't see how. > > > > > > > Let theory A be geometry using Euclid's rules, including the parallel > > postulate; i.e., loosely speaking, that parallel lines don't intersect. > > > > > > Let theory B be Euclid's postulates, excluding the parallel postulate, > > and instead including the postulate that every pair of distinct > > parallel lines intersect at two points. > > > > Theory A is useful in certain cases; theory B is useful in other cases. > > Why must one be "true" and the other "false", simply because the two > > theories contradict each other? > > Yes, the two systems within themselves must hold their counterparts > false. >
So according to you, on one day, I believe that planar geometry is true (if I am working that day in the plane), and the next day, I cease to believe in the truth of planar geometry, and instead believe in the truth of spherical geometry?
I don't find that to be the case for me; at least for the usual meanings of the terms "believe" and "truth" /in this context/.
If I ask you: "suppose my mother and father are both dead; does that make me an orphan?", do you need to actually believe that my parents are truly dead before you can respond? Can't you simply "suppose" it, hypothetically?
Likewise, if I ask, "assume Euclid's postulates with the parallel postulate; is it then the case that all trinagles have angles summing to 180 degrees?", do you need to actually believe that planar geometry is the only true geometry in order to respond?
I find that, for me, the answer to both these questions is "no" (i.e., I don't need to actually believe in the truth of these suppositions; in the sense that I /do/ believe that my parents are truly /not/ dead, or that the sun will truly rise tommorow).
On the other hand, I do believe in the truth of the statement "if we assume Euclidean geometry with the parallel postulate, then all triangles have angles summing to 180 degrees"; but that is a belief in the truth of the fact that it logically follows from the given axioms - not a belief in the truth of the axioms themselves.
> > > > > > I do not believe in them as a matter of religious or similar belief. For > > > > example, I would not be particularly disturbed if I heard tomorrow that > > > > someone competent to evaluate proofs had found a proof of inconsistency > > > > of ZF. > > > > > > religion: > > > 4. Strictness of fidelity in conforming to any practice, as > > > if it were an enjoined rule of conduct. > > > > > > > Licensed plumbers conform to a strict practice with great fidelity, "as > > if" it were an enjoined rule of conduct. Do you claim that "Plumbing" > > is a religion? > > enjoin: > To lay upon, as an order or command; to give an injunction > to; to direct with authority; to order; to charge > > Yes, more so than not. Plumbers don't accept outsiders to enjoin the > trade. You describe the problem you're having to a plumber and he > fixes it (or not). >
You have a rather odd approach to the dictionary; it seems intended to blur meanings, rather than to clarify them.
If "Plumbing" is a religion, then what /isn't/ a religion? Is "taking out the garbage" a religion, requiring a weekly observance where a proscribed device for conveying garbage (the garbage can) is deposited at a specific location (the curb) on a particular day of the week ("garbage day")? Is "going to the bathroom" a religion, as there is an extremely strict set of practices associated with this activity, which each culture strongly enjoins upon its members?
If you believe all these activities are examples of religions, then what word is left over that distinguishes these activities from the activities that we normally associate with people when they go to church / temple / mosque, engage in prayer, etc.?