Wyman wrote:Right, I see the brain in the vat metaphor as essentially Cartesian doubt, which is what I thought you(Arising) were alluding to when you began with 'I am' which I took to mean 'I think therefore I am,' 'I think in language' and language requires more than one person.
Language could be created by an evil genius as easily as the rest of the corporeal world - i.e. the 'vat' could make it seem to you that your language must have been created elsewhere. That was my point; it may be that I am misunderstanding your argument, as you put it somewhat cryptically.
The 'brain in a vat' is Putnam's version of Descarte's thought and it makes no difference to my point as your evil genius must be able to speak or understand English to do what you say and as such I can infer from my being able to speak or understand it as confirmation that there is at least one other out there, evil genius or whatnot.
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A proposition can be either true or false, but not both. A proposition is a well formed formula in the language we choose to use as an interpretation for the axiom system we are employing.
Not quite, in Logic a proposition is on the whole a declarative sentence expressing a fact or a relation about things in the world, wffs are how we can analyse the process.
'not(p and not p)' is an axiom of logic and deals with such propositions. So when you say 'something cannot both be and not be at the same time,' you are interpreting the axioms of logic in a particular way and I think it requires justification.
Show me a thing or fact that can refute this axiom?
I think you are trying make this law of non-contradiction something it is not - i.e. a statement about the world. It is just a tautology. ...
I disagree and agree with Boole, Logic can be understood as the study of relations and there are two kinds, between things and facts, facts are expressed as propositions and so can be understood as relations between propositions but in reality they are about facts. As such it is about the World or more specifically about how we reason about the world.
A 'proposition' is what is (sometimes, as in physics, but not mathematics) interpreted as a statement about the world. The proposition, when so interpreted, is defined as an assertion about the world (a fact) that is either true or false - i.e. it is syntactically correct and makes sense semantically and must make an assertion that is true or false, but not both or neither. See the circularity? ...
Show me a thing than can be and cannot be at the same time?
On this standard interpretation of propositions in logic, the rule of non-contradiction is assumed in the very definition of a proposition. It is a tautology and tautologies are always circular in this sense and so say nothing new about the subject matter of the interpreted axiom system.
Or they say what is always true or always false about things and their relations, i.e they say what is necessary or impossible in this world, so in a sense say nothing about the World other than set its boundaries. I like Wittgenstein with respect to Language, Logic and the World, to wit,
"3.1432 We must not say, “The complex sign ‘aRb’ says ‘a stands in relation R to b’”; but we must say, “That ‘a’ stands in a certain relation to ‘b’ says that aRb”. - TLP.
I probably could have said all this more clearly - for instance, it may help if you think of a mathematical interpretation of a proposition. 1+1=2 is a true proposition in math. To say 'not((1+1=2) and not(1+1=2)) must be true as well', while also a true proposition, adds nothing to your mathematical knowledge, as it is a mere tautology.
That's because Maths is not Logic, in Logic to say (P and Not P) is to say something that is false under all possible conditions, hence it is an impossibity and on the whole this discovery can be used to point to a false deduction. To say Not(P and Not P) is to say this is always true under all conditions and, I'll agree, whilst necessary is not of much use other than pointing out how reason works. I also think it points to how things work but accept that it's not much use to the Physicist as they work within the contingent propositions.