autological
Rising Star
Hi, DMT-Nexus. I am J.
I was thinking the other day that true statements are as plentiful as false statements, because every true statement has a negation which is false and vice versa. Yet there are three classes of statements: (1) true statements, (2) false statements, and (3) nonsensical statements. Every true or false statement may be made nonsensical by putting in or taking out words in the true or false statement. Therefore, nonsensical statements are at least as numerous as true or false statements; therefore, the number of nonsensical statements equals at least the number of true statements added to the number of false statements.
Furthermore, every nonsensical statement may be conjoined with every other nonsensical statement, yielding a new nonsensical statement. This new nonsensical statement may be joined with another nonsensical statement which reads, "The nonsensical statement formed from the conjunction of every nonsensical statement is true," (this is a nonsensical statement since a nonsensical statement cannot have a truth-value of "true", otherwise it would not be nonsensical). This can be applied indefinitely, yielding a set of nonsensical statements with a cardinality of infinite. But it was already mentioned that the number of true statements added to the number of false statements equaled the number of nonsensical statements, and the number of nonsensical statements is infinite; therefore, the number of true statements is infinite, as is the number of false statements (this is implied by the notion of Dedekind infinite: if two numbers sum to aleph-zero (the number of natural numbers), then both numbers are aleph-zero).
Now, if the number of true statements is infinite, then we could not possibly know all of it, implying (I think) there are some things which will never be known.
What do you think of this?
I was thinking the other day that true statements are as plentiful as false statements, because every true statement has a negation which is false and vice versa. Yet there are three classes of statements: (1) true statements, (2) false statements, and (3) nonsensical statements. Every true or false statement may be made nonsensical by putting in or taking out words in the true or false statement. Therefore, nonsensical statements are at least as numerous as true or false statements; therefore, the number of nonsensical statements equals at least the number of true statements added to the number of false statements.
Furthermore, every nonsensical statement may be conjoined with every other nonsensical statement, yielding a new nonsensical statement. This new nonsensical statement may be joined with another nonsensical statement which reads, "The nonsensical statement formed from the conjunction of every nonsensical statement is true," (this is a nonsensical statement since a nonsensical statement cannot have a truth-value of "true", otherwise it would not be nonsensical). This can be applied indefinitely, yielding a set of nonsensical statements with a cardinality of infinite. But it was already mentioned that the number of true statements added to the number of false statements equaled the number of nonsensical statements, and the number of nonsensical statements is infinite; therefore, the number of true statements is infinite, as is the number of false statements (this is implied by the notion of Dedekind infinite: if two numbers sum to aleph-zero (the number of natural numbers), then both numbers are aleph-zero).
Now, if the number of true statements is infinite, then we could not possibly know all of it, implying (I think) there are some things which will never be known.
What do you think of this?
