Francisco asked:

What is logic? What are paradigms?

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I'm not going to answer your first question; that's just too big a topic. However, in answer to your
second, you might say that a paradigm is a viewpoint, a reasonably coherent viewpoint based on,
hopefully, fact. In other words, there are multiple ways of interpreting a given set of facts. Think of the
story of the blind men and the elephant. What the elephant is depends on your interpretation of the
facts you're presented with, roughly speaking. That interpretation, that viewpoint, is your paradigm.
Now, if another blind person, or deaf person, comes along and says, "you're wrong, thisis what an
elephant reallyis", what do you do? First, you disagree. Then as they become more persuasive, you
either keep arguing, or you say, "ok, I was wrong; you're right", or the other person says that; or,even
better, the two of you say, "wow, we bothhave something to say about what an elephant is, let's
come up with some really good idea between us".

Now, conceivably, we could take the same story, and let allthe blind people feel their way around the
wholeelephant, ask them what an elephant was, and stillget three (or more) different versions... one
with a trunk, say, interpreted as a weapon as well as a nose, one interpreting the feet as good for
stomping enemies while another sees them as just good for standing on... and so forth. Which of
those are held to be true, and what further data would be needed to confirm one viewpoint over
another is the kind of thing that supports or changes paradigms.

Take a look at:

Kuhn, T. S. (1996) The structure of scientific revolutionsChicago, IL, The University of Chicago Press

and,

Kitcher, P. (1993) The advancement of science; science without legend, objectivity without illusions
New York, NY, Oxford University Press

Steven Ravett Brown

If you look up "logic" in for example the Cambridge Dictionary of Philosophyyou will among many
other entries be referred to combinatory logic, deontic logic, epistemic logic, intensional logic and
modal logic, but the dictionary refuses any concise answer to the question "What is logic?" Though it
is indeed impossible to give a brief explanation of what logic is, a few general remarks may help to
give an idea of what (elementary) logic is about.

Logic as discipline dates back to the ancient Greeks and was part of philosophy in these days. Today
it's a science on it's own and is a link between mathematics and philosophy. As an everyday definition
logic can be said to be the art of correct reasoning (not all thinking is reasoning). More academically
logic can be defined as the study of consistent sets of beliefs. Some people prefer to define logic as
the study of validity of arguments.

We express our beliefs in sentences. Only sentences, which can be said to be true or false are
objects of logical investigation. Such sentences are called statements or propositions. Logic then has
to do with analysis of statements. More statements form arguments, when one of the statements,
called the conclusion, is claimed to follow (indicated by words like "so" or "therefore") from the others
(called the premisses). Logic has to do with the analysis of the structure of arguments. Another
important branch of logic is that of definitions. One of the aims here is to weed out ambiguity.

There seem to be elementary laws of reasoning. For example no-one would doubt that a sentence
like "I'm awake and I'm asleep" is illogical, as it is contradictory. Logic itself builds on these
elementary laws of reasoning.

As arguments in natural language often are vague, one of the aims of logic from the beginning was to
formalize arguments in a way that the structure of the argument is a guarantee for the soundness of
the argument, or in other words that conclusions follow necessarily as true, as long as the premisses
are true. The oldest version of formal logic goes back to Aristotle and is called syllogism. The modern
embodiment is called formal or symbolic logic. Formal languages are only fragments of natural
language. The bigger one wants this fragment to have, the more complicated a formal language will
be. The result is a vast field of branches of logic (see above).

"The best way to find out what logic is, is to do some", E. J. Lemmon states in the introduction to the
Propositional Calculus in his book Beginning Logic.So if you are interested in doing some logic, there
are two introductory books I can recommend:

Wilfrid Hodges Logic — An introduction to elementary logicPenguin books

5. J. Lemmon: Beginning LogicHackett Publ. Comp.

Now to your second question: The term paradigm was made popular by Thomas Kuhn (first used by
G. C. Lichtenberg) and is connected with scientific progress. While in the previous centuries science
was believed to be an ongoing smooth and cumulative process and to be the custodian of rationality,
it becomes more and more apparent that these assumptions are perhaps no more than superstitions.

As an overall judgement Kuhn says "A paradigm is common to the members of an academic
community and reverse an academic community consists of members sharing that paradigm". What
is meant here, is that academic theories are not only a result of academic research, but also a result
of the cultural environment with it's framework of ideas and presuppositions, in that researchers live.

According to Kuhn, once a theory is established, it becomes a paradigm (greek: paradeigma
example). As much as possible is tried to be integrated in this paradigm (the linear and cumulative
stage). Further, if still successful, this paradigm becomes part of academic teaching and serves as
model. Kuhn sees this as the stage of "normal science", a more or less conservative and ideological
activity. And once a theory has reached this level, it is as difficult to challenge as any other prejudice,
even if much of the theory is already empirically falsified. Therefore a new theory, also empirically
tested but not compatible to the old one, cannot simply supply the "old paradigm", but has to replace
it: the fight of the experts begins. Normal science has reached a crisis, suffers a breakdown and the
community undergoes a shift of vision, or change of paradigm. This paradigm change involves not
only scientific arguments, but also propaganda, persuasion and opinions of authorities, which are all
irrational elements.

Simone Klein