Magnus Anderson wrote: ↑Mon Mar 03, 2025 3:46 am
Age wrote: ↑Sun Mar 02, 2025 8:03 pm
If, the Law of Excluded Middle ( LEM ) is captured by the statement "For every proposition P, P is either true or it is false", then what captures the propositions, which are just nonsensical, and thus neither True, nor False?
For example, is the proposition, 'This statement is false', True, False, or just not able to be determined to be False, nor True, and thus just a nonsensical proposition?
If 'it' is the latter, then is the proposition, 'For every proposition P, P is either true or it is false', actually not True, itself?
LEM really only applies to propositions. A proposition has a subject ( a reference to a portion of reality ) and a predicate ( a description of that portion of reality. ) The statement "This statement is false" has no subject, so it's not really a proposition. That's why it has no truth value.
So, what part of the words, 'This statement', is, supposedly, 'not a reference to a portion of reality', exactly?
To me, 'this statement', is, literally, 'a reference', TO 'a reference' TO 'a portion' OF 'reality', itself. How could 'this statement' NOT be 'a reference' TO 'a portion' OF 'reality', itself?
Also, to me, the words, 'is false', is 'a description' OF 'that portion' OF 'reality', itself.
So, to me, 'the proposition', '
This statement is false', has A 'subject', ['
this statement'], and, A 'predicate', ['is false'], which means 'it' is, REALLY, 'A proposition'.
Although, and admitting, a Truly silly and/or nonsensical proposition, but nevertheless it is, STILL, 'A proposition', any way.
And, as I was POINTING OUT, and SHOWING, 'it' is just another 'proposition', which is NEITHER true NOR false.
Which then MEANS that there are some propositions P, where P is neither true, nor false.
As I have just, once again, showed, and proved, further, here.