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Here I will publish the works I'm still writing: my main interests are Mathematics and Philosophy, but probably I will include other interesting things - at least for me.
In Mathematics, all the theorems seem to be linked each other in a never
ending chain: A is proved by B, B is proved by C... but what is the beginning
of the chain? What are the principles from which it's possible to demonstrate
all other theorems?
Whitehead and Russell in 1910-13 managed to reduce all ordinary Mathematics
to logic principles, establishing new foundations for mathematical knowledge,
and demonstrating that there's no distinction between Logic and Mathematics,
since the latter can be regarded as an extension of the former.
These pages contain a general overview of Principia Mathematica, showing
the actual principles of Mathematics. Personally, I've discovered that
I've always used some very complex logical structures without knowing what
they really are; for example I found the answers to these questions: "what's
a number?" , "what does finite/infinite mean?" , "is the part always less
than the whole?" , "what does 'addition' mean?". Note that all of these
have a proper definition in Principia Mathematica and that even if it may
seem hard to define basic concepts like "number" they turn out to be very
complex structures once they are deeply analysed.
Note: To write symbols in these pages the "Symbol" font has been used in couple with the <FONT FACE> tag. In order to display them properly, make sure that your browser accepts the tag and that the font is available in your system ( if --> À0 <-- seems similar to the Aleph in the background and in the entry image, your browser and your system are OK; if it seems something like --> À0 <-- you won't see symbols if you proceed.