What is Tom's newfound philosophy based upon the book he reads in The Great Gatsby?
Tom's newfound philosophy is one based on racism. According to the text, Tom has been reading a book named "The Rise of the Colored Empires" by someone named Goddard.
Tom's book, of course, is fictional, but it alludes to a book that actually discusses everything Tom's book does. That book would be The Rising Tide of Color by Lothrop Stoddard, a man who advocated the principles of white supremacy through the use of eugenics. Eugenics is the science of heredity and breeding: white supremacists like Stoddard believed that if white birth rates did not increase, the "colored" races would inundate and destroy western civilization completely.
Like the fictional Goddard, Lothrop Stoddard advocated what Tom refers to as scientific racism (or the use of eugenics to ensure the dominance of the white races). This is why, when Tom tries to rationalize his racist beliefs, he keeps repeating that it's "all scientific stuff; it’s been proved." Basically, Stoddard believes the white race is divided into three groups: the Nordics, Alpines, and Mediterraneans. In the book, Tom maintains that all his guests are Nordics. He cautions that it's "up to us who are the dominant race to watch out or these other races will have control of things." Of course, Tom sees the Nordics as the preeminent race.
Tom concurs with Stoddard (or Goddard, in The Great Gatsby) that the white race has "produced all the things that go to make civilization—oh, science and art and all that."
Goods, tools, ideas, men: all were produced at an unprecedented rate. So, by action and reaction, white progress grew by leaps and bounds. . . For four hundred years the pace never slackened, and at the close of the nineteenth century the white man stood the indubitable master of the world (Chapter 6: The White Flood; The Rising Tide of Color).
Stoddard maintained that "Never before has a race acquired such combined preponderance of numbers and dominion," and he warned that white hegemony was fast coming to an end. In The Great Gatsby, Tom echoes Stoddard's fears. His wife and the rest of his guests choose to ignore him, however, and Tom must keep his ideas to himself.