In 2006 I published this book for the first time, and I’m proud to say that this is the fourth edition of The Relation between Formal Science and Natural Science. In this book, I use Edmund Husserl’s philosophy of logic and mathematics, as well as his semantic doctrine, in order to understand the nature of formal sciences. It posits the existence of ideal meanings and mathematical objects, which are themselves a condition of possibility for any truth and any science whatsoever. It advocates for the search for a criterion to determine the distinction between analytic and synthetic judgments, while rejecting Quine’s arguments against it. At the same time it rejects several antiplatonist options such as Mario Bunge’s fictionalism, and Karl Popper’s semiplatonism, while proposing Husserlian epistemology of mathematics as an alternative, which is essentially a sort of "rationalist epistemology" as Jerrold Katz suggested. Finally, the book criticizes the Quine-Putnam theses, especially the one which states that logic and mathematics can be revised in light of recalcitrant experience. Usually three cases for such revision are constantly presented in this debate: quantum logic, non-euclidean geometry and the general theory of relativity, and chaos theory. I show that none of these a posteriori matters-of-fact have revised any a priori formal fields such as mathematics and logic.
The book’s website has also undergone major surgery, changing it from plain HTML to a Drupal platform. This is how it used to look like:
(Click for Larger Version)
This is how it looks like:
(Click for Larger Version)
You can look at the new website by going to http://uos.pmrb.net. I hope you like it. Any comments or questions about it, please, let me know.
The book is completely available online under different formats. You can download it for free and copy it as many times as you wish just under two conditions: the original work will be preserved verbatim, and no commercial use of it is allowed unless you have reached an agreement with me. Additional to this, because the cover is a derived copylefted version of a GPLed wallpaper in KDE-Look.org, I released the cover and all of its new graphic elements under the GNU GPL as well, and allow people to download it and use it as they wish commercially or non-commercially as long as they comply with that license.
The book is also available for sale for now in Lulu.com.
I hope that this book will help contribute to a clearer understanding about the nature and role of formal sciences such as logic and mathematics, and natural sciences such as physics and biology.
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