Often, chi dedica la life ad una branca del know, believes that quella disciplina sia la base di tutta la knowledge Human. I witnessed more than once in dialectical clashes (sometimes to the edge of the dialectical, tending to physical!), between mathematical, Philosophy, scientists,...
But there is a category of scholars who, in my opinion, holds the record in the ability to estimate their discipline as a unique and central to all other: the category of Logical.
that time, a lesson in logic, the professor, young and very smart, era impegnato a spiegare un theorem.
«Questa è la base della knowledge" – said – "Thanks to this report, noi siamo in grado di conoscere il world. Tutte le altre scienze sarebbero anything, without the logic."
I must admit that I too have felt the charm of this demonstration (and I also feel for logica come science).
Then I had a doubt: "But we are in the context of discovery or justification?"- I asked the professor.
I'll explain. In case of deductive method, It start with principles, real and already proven, to obtain other through logic (from the particular to the universal). The problem is that the deductive method (su cui Plato voleva fondare la knowledge) can be applicato in pochi casi ed è difficile da applicare alle scienze della natura, which as everyone knows was founded on the opposite method, that inductive (I start with special cases, to derive the general law [Ref. inductive method]).
What I meant is that, in many circumstances, la legge logica serve a giustificare una knowledge già acquisita, the congetturata, but it can not serve to "make a finding". even in math, dove il metodo deduttivo può be applicato in misura molto maggiore rispetto alle altre scienze, often, mathematicians start from conjectures and then get to logically prove their assertions.
But how does the guess? Mystery,Brainstorm, or poetic intuition, as many have said.
Actually, the professor – che diceva di non comprendere la mia question – avrebbe potuto sottolineare che la potenza della math non risiede nelle intuizioni poetiche, As in the provability logic of all its assertions. An avalanche of propositions linked together, all rigorously proven logically (although remembering Godel, It will always be some unprovable proposition logically). If you drop a single proposition, cade tutta la math che contiene quella proposizione. A devastating domino effect. In case contrario, if I can prove a proposition from which this entails many other, ho creato molta math.
Then, about logic It is certainly important, but for the discoveries it is not sufficient.
Un’area dell’intelligenza artificiale search i modi di poter programmare una macchina in modo tale che possa creare autonomamente nuova knowledge, but still the results are poor. The machine is logic, but no insights, o mele che possa sentir fall sulla sua testa.
There is an anecdote about David Hilbert (one of the greatest mathematicians of all time), I can better understand what I mean.
One day they were told that one of his students had dropped out of college to become a poet. And Hilbert replied “I'm not surprised. He did not have enough imagination to become a mathematician.”
Foto di David Hilbert
The sum of the first N positive integers worth:
Sum = (N+1)* N/2
Se N= 100
Sum = 101 * 100/2 = 5050
How to get there intuitively?
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
49 + 52 = 101
50 + 51 = 101
As we can see, there is a basic structure that is repeated. The sum of some pairs of numbers gives the number N (100) added to 1. This happens for 50 times, that is, N / 2.
The discovery does not take place through the logic. And 'observation and intuition that allow the sharp transitions between the' 'ignore something "and his knowledge.