Peguntras sobre Lógica Universal a Jean-Yves Béziau

De a poco ire subiendo las preguntas que le hizo Linda Easthood a Béziau y sus respuestas.
La lógica universal no es principio lo que uno pensaría.... muy interesante!!!

1- . Although your proposal to develop a universal logic is

very appealing, isn’t it a utopian one? Isn’t it an absurd, or even

dangerous thing to believe that it would be possible to develop a

unique logic accounting for everything?

Let us immediately reject some misunderstanding; universal logic, as

I understand it, is not one universal logic. In fact, from the viewpoint of

universal logic the existence of one universal logic is not even possible, and

this is a result that can easily be shown. One might thus say somehow

ironically the following: according to universal logic there is no universal

logic.

Some people in some countries have always tried to elaborate a universal

system that would account for any sort of reasoning, or reasoning

as a whole. Aristotelian logic was depicted itself as a universal one. More

recently, first-order classical logic appeared to some as a universal system

accounting for mathematical reasoning as well as current one, that is, the

one used to buy your bread at the bakery.

But first-order classical logic was also criticized at length, whether

concerning its claim to describe mathematical reasoning or physical, computational,

current, philosophical ones, and the like. Many new logics were

further developed, namely: intuitionistic logic, combinatory logic, linear

logic, quantum logic, erotetic logic, modal logic, paraconsistent logic, polar

logic, relevant logic and so many others, all the more that each of these is

often to be divided into a disparate multiplicity, as in the case of modal

logics.

Among advocates of these logics, some forcefully believe that their

own logic is the best one, that it explains everything, solves everything,

so that their logic is universal, as was formerly the case with Stanis law

Le´sniewski or, more recently, with Jean-Yves Girard and its linear logic,

Jaakko Hintikka and its IF logic, and, even more explicitly, Ross Brady

with its relevant logic he squarely dubbed a “universal logic”.

Such a view is not shared by people working in quantum logic, for

example; indeed, these only want to account for one particular reasoning

related to one particular area, without ever claiming that such is the reasoning

we are using or should use whenever we go at the bakery. Now is

such a view consistent? Are we entitled to say the following: to each area,

to each situation, its own logic, or even to each group of persons, to each

individual, its own logic. So there would be a logic of chemistry, logic of

clouds, logic of sex, logic of women, logic of dogs, the logic of Bouvard and

the logic of P´ecuchet.

Actually, such a relativization of logic is equally absurd as the opposite

stance according to which only one logic could explain everything.

Obviously, there is also one intermediary situation according to which there

are neither only one nor thousand and one logics, but three or four: so is

the middle, not to say mediocre position of people who cut the cake into

three parts saying that there is the reasoning for formal sciences, on the one

hand, the reasoning for empirical sciences, on the other hand, and finally

the natural reasoning for daily life. Behind such a stance we see again the

old contradistinction between inductive logic and deductive logic.

The view of universal logic is that one plausibly can unify the large

kaleidoscopic variety of logics, while preserving their diversity. In the case of

universal logic, as opposed to those who support the view of one universal

logic, unity is entailed by diversity. Universal logic is not a logic but a

general theory of different logics. This general theory is no more a logic

itself than is meteorology a cloud.