True, but not provable
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From: John Jones on 25 Apr 2010 08:27 Akira Bergman wrote: > "A false mathematical statement isn't a mathematical statement." > > False. This refers to its meaning, not to the construction of the > statement. People have already pointed this out you many times but you > keep insisting and creating more confusion. This is probably your > purpose. You may also be nuts. > > For a statement to function as a binary switch, it has to be > constructed according to a grammar. If the grammar fails then the > meaning can not be considered, since it has no meaning. > > Grammar of language is like the axioms of mathematics. If there is no > foundation, there is no building. If there is no assumption, there is > no conversation. > > You made another statement before in another post (copied below). It > was also false, while being grammatically correct. If you believed the > truth of this statement then you should seek help. If you are doing > these things to confuse people you should seek another kind of help, > since this is all you do. > > "Thus the mathematical statement 2<4 means that there are fewer 2's > than > there are 4's." > > This statement is so bad that it makes me cringe on your behalf. Arithmetic deals with number, not bulk. So "less" means "fewer". So 2<4 means that there are fewer 2's than there are 4's."
From: Jim Burns on 25 Apr 2010 11:51 John Jones wrote: > Jim Burns wrote: [...] There is too much to include merely to refer to when I say you do not address any of my points. However, I will give you another chance to address a question at the heart of your argument: what is wrong with the usual sort of mathematical statements? >> *In the usual way*, whether something is a mathematical >> statement is determined by very simple syntactic rules, >> such as "If A is a mathematical statement >> then ~(A) is,too." One can then argue that a >> particular statement is true or false, but, either way, >> (or any other way) it remains a statement. >> What is wrong with doing things this way? > We judge a mathematical statement to be true only > when it is not false. There are no other grounds > for saying a mathematical statement is true or false. In the usual scheme of things, we judge a mathematical statement "to be true only when it is not false" and to be false only when it is not true. (There are other schemes, less usual, which are more complicated.) However, these are not grounds for saying a mathematical statement is true or false. It is just a slight restatement using different words: "not false" for "true", "not true" for "false". And, even if you were right (which you aren't), I don't see how you make the next step: > So truth and falsehood aren't significant statements > in mathematics. Nor do I see how you take the step after that: > Either something is a mathematical statement or > it isn't. Nor do I see how we are supposed to conclude from that that mathematical statements are only true. (One more time: what is wrong with calling what we usually call mathematical statements mathematical statements?) Jim Burns
From: Akira Bergman on 25 Apr 2010 23:18
On Apr 25, 10:27 pm, John Jones <jonescard...(a)btinternet.com> wrote: > Akira Bergman wrote: > > "A false mathematical statement isn't a mathematical statement." > > > False. This refers to its meaning, not to the construction of the > > statement. People have already pointed this out you many times but you > > keep insisting and creating more confusion. This is probably your > > purpose. You may also be nuts. > > > For a statement to function as a binary switch, it has to be > > constructed according to a grammar. If the grammar fails then the > > meaning can not be considered, since it has no meaning. > > > Grammar of language is like the axioms of mathematics. If there is no > > foundation, there is no building. If there is no assumption, there is > > no conversation. > > > You made another statement before in another post (copied below). It > > was also false, while being grammatically correct. If you believed the > > truth of this statement then you should seek help. If you are doing > > these things to confuse people you should seek another kind of help, > > since this is all you do. > > > "Thus the mathematical statement 2<4 means that there are fewer 2's > > than > > there are 4's." > > > This statement is so bad that it makes me cringe on your behalf. > > Arithmetic deals with number, not bulk. So "less" means "fewer". So 2<4 > means that there are fewer 2's than there are 4's." .. This has been replied in the "Bulk and number" thread. |