In order to show that something is false, stick a minus sign in front of it. This is not the only way to negate things in logic. Another way might be to use the nand sign, which is the negation of and; and yet another way is to use a completely different symbol, as in the way that we may speak spanish or english.
So a different mathematical language might use a plus sign for negation. Some textbooks use a minus sign with a bend at the end.
Using negation is cool!
For instance, somebody might say that the sky is orange. In order to write that this is false, we would use quotes around the statement in order to talk about that statement, and then quote the negation around it.
This is more simply shown than typed out like I just did.
Example:
'The Sky is orange'
'not 'the Sky is Orange' '
Basic statements of declaring that some thing is a thing are written in their most basic forms and are called atomic sentences. In order to refer to the sky, if we wrote it out without an atomic sentence, we would write, 'something x that is the sky', but in order to write it with an atomic sentence, we could write s.
Predicates, which you remember are basically verb-parts of sentences, are shown with capital letters.
So now we have a handy way of writing all of these really large sentences in shorthand, very fast.
sO for 'the sky is orange'.
-sO for 'not ' the sky is orange'.
The really rock and roll essay and accompanying book set that blew this stuff out of the water was On Denoting by Bertrand Russell; and accompanying book was called Principles of Mathematics, which he wrote with White.
If you are asking where everyone is going with this, you are not alone in the least. I noted just now that this is handy simplification, but the question remains why anyone would want to speak in such a funny way. One answer is that we do speak this way. When people talk and communicate, the objectivity that the words access (different from the subjectivity of the people themselves) is real and truthful, and just because we do not break down every sentence into specifics does not mean that it cannot be broken down.
The cool stuff that mathematical-analytic logic dips into is this objectivity. Analytic logic has been part of the revolution of computers. Every engineer and math based major at my university, for instance, has to learn what is called discreet math. Discreet math is the logic I'm talking about.
First guys to really mess around with this stuff were Frege and Russell.
This is big time philosophy people.
This is the stuff of both obvious and harder to grasp truths. We can get to really sophisticated truths from mathematical logic. This is Spinoza and Leibniz's dream come true.
Two problems:
A) I tend to think of all philosophy as unstoppably fascinating, and every philosophical problem as non-trivial for living. That is, I considered every truth in philosophy to be essential to the whole of philosophy. I'm going to discuss some truth problems in the next bullet, but let it be known that there is a lot more to talk about here. Not so fast and not so with this stuff. This sentence stuff, and On Denoting, are really fun. The other stuff, however, (sometimes) looks more and more like mathematics and then complex mathematics until it's a cross between over-complexity, boredom, tedium, over-challenging-ness, and I felt as if I had been locked out of philosophy. If you move too fast with this stuff, beware. But then if you move at a normal pace and your personality or your cognitive consonance or your idiocy hijack your brain you won't be able to handle it (Am I speaking from experience? Yes. There's a lot more to say about Science Majors versus Liberal Arts majors that I have got to get off of my chest. Stuff for later: building a house versus knowing how to live in it. The cognitive dissonance management when a college student drops out of a scientific major for a liberal arts major. But they never really drop from the other end. The ease of bullshitting in a liberal arts major that is impossible in the sciences.) There's some big deals going on here that do not belong in parentheses.
B)
I've got in parenthesis above the house problem. If you could plainly build a house scientifically, which I hope everyone objectively recognizes; could that tell you how to live in it? My immediate answer to this is undoubtedly. Here's why: when we perform science or engineering, we make this world better. The science of building a sewer system is inseparable from the ethics of dispensing water. The science of building a house is inseparable from the ethics of living a life that is better when you live in that house. But I think these examples both argue for and against my point that quantitative truth is ambiguous by nature.
That is, great, you could deduce all of these truths from basic premises, but where do you get those premises and lemmas from? It turns out that these are easy enough to get, and really helpful. Computer science, which is this exchange right now, uses analytic logic.
No comments:
Post a Comment