逻辑学-思辨的科学
LOGIC - THE SCIENCE OF CORRECT ARGUMENT
By Linh ??ng - Nov 13th, 2008
Tag: introduction, article, logic
Logic is the study of the principles of valid demonstration and inference. Logic is a branch of philosophy, a part of the classical trivium of grammar, logic, and rhetoric. Logic concerns the structure of statements and arguments, in formal systems of inference and natural language. Topics include validity, fallacies and paradoxes, reasoning using probability and arguments involving causality. Logic is also commonly ud today in argumentation theory - Wikipedia
A Correct Argument
A correct argument is one in which anyone who accepts the premis ought to accept the c
onclusion. A correct argument is not the same as a persuasive argument. An argument can be persuasive without being correct (an appeal to the racial prejudices of the jury, for instance) or it can be correct without being persuasive (maybe the jurors were dozing off). A correct argument is an argument that ought to persuade, whether or not it actually succeeds in persuading.
To e whether an argument is correct, you look at the connection between the premis and the conclusion. In judging whether an argument is correct, you don't look to e whether there are good reasons for accepting the premis. You look at whether, once a person has accepted the premis, for whatever reasons, good or bad, some guy ought also to accept the conclusion. If the argument is the only reason to accept the conclusion, and if the person does not have good reason to accept the premis, that guy will not have good reason to accept the conclusion. But that's not the argument's fault; it's the premis' fault.
Purpos
There are two purpos for which we u arguments: to persuade others and to persuade ourlves. An example of the former is a procutor trying to persuade a jury. An example of the latter is a proof in geometry, in which you u an argument to prove a theorem, bad on things you already know. If you are sure the argument is correct, then you can be at least as confident of the conclusion as you are of the premis. Logic doesn't give you the premis, but, once you have the premis, it enables you to expand your knowledge by drawing new conclusions. The techniques of proof that logic gives you are the same, whether the person you want to convince is your neighbor or yourlf.
History
Logic, like the rest of western sciences, began in ancient Egypt, with the annual flooding of the Nile River. Every spring the Nile, richly loaded with silt from the melting snows of central Africa, flooded its banks. When the waters subsided, the land beneath was extremely fertile, and hence extremely valuable. But the floods washed away all conventi
onal boundary markers, such as fences and posts. So how could the owners of the valuable land on the flood plain keep track of their property lines? To solve this problem, the Egyptians invented geometry. Using geometry, they could determine the property lines by triangulation, using objects that weren't disturbed by the floods ─ pyramids and whatnot ─ as reference points.
Egyptian geometry was a haphazard affair. Formulas were discovered experimentally and written down. Most, but not all, the formulas were accurate. A few of them gave more-or-less accurate answers for the particular examples on which they had been tried out, but weren't generally valid. The Greeks took over the Egyptian geometry and reorganized it, and the Greek geometry was a marvel of careful and systematic organization.
Ancient Greek geometry, who classic exposition in Euclid's Elements, started out from certain basic principles, called axioms or postulates, which were regarded as obvious, lf-evident, and in no need of demonstration. From the axioms, one derived theorems.
The theorems were then ud, together with the original axioms, in deriving still further theorems. In this way, starting with the axioms and building up, very sophisticated geometric laws that weren't at all obvious were obtained from basic axioms that were entirely obvious. The axioms expresd a great deal of information in a compact form, so that, for virtually any geometrical problem you started with, you could solve it, eventually, by deriving the answer from the axioms.
Aristotle-Father of Logic
Aristotle made two important obrvations. First of all, sciences other than geometry could be organized in geometric fashion, starting out from basic axioms and building up. Second, the basic argumentative principles that you u in deriving the theorems from the axioms are the same in all the sciences. Aristotle hit upon the idea of singling out the principles of argument common to all the sciences for study in their own right. Thus the science of logic was born.
The patterns of argument Aristotle singled out for study were particularly simple patterns
called syllogisms. Examples are:
All APCS students are people.
All people can play game.
Therefore, all APCS students can play game.
All students are lazy.
No woodcutters are lazy.
Therefore, no students are woodcutters.
Aristotle's logic was quite crude by today's standards. Certainly the reasoning one encounters in Greek geometry is much more sophisticated than the mere chaining together of syllogisms. Still, we must not undervalue Aristotle's contribution. He created a science of logic where before there was nothing.
For the ancient Greeks, geometry was the paradigm of the sciences; Euclid's Elements was what a scientific theory ought to look like. Over the centuries, the geometric model has pretty much been abandoned. The problem has been that axioms that have emed lf-evident have often turned out to be fal. Thus it emed obvious to Aristotle that a moving body will come to rest unless something is pushing it. In fact, as Galileo discovered, moving bodies only come to rest becau something stops them; without interference, a moving body will keep moving with a constant velocity.
