By Stephen Law & Julian Baggini
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Additional resources for 30-Second Philosophies: The 50 Most Thought-provoking Philosophies, Each Explained in Half a Minute
Until the 19th century, the subject of logic pretty much consisted of Aristotle’s syllogisms. But syllogisms are only a small portion of all valid inferences, and do not include many of the patterns of valid inference that are employed in science and mathematics. In 1879 Gottlob Frege devised a much more general characterization of valid inference that is sufficient for representing mathematical and scientific reasoning. A descendant of Frege’s system, called “First Order Logic with Identity,” is now generally thought to be capable of representing mathematical theories and proofs, and is taught to all philosophy students.
A contemporary version is based on “1. ” If sentence 1 is true then it is not true, and if it is not true then it is true. The paradox arises because it seems to be part of the meaning of “is true” that, where S can be any sentence, one can validly infer “S” is true from S and also validly infer S from “S” is true. From 1 we can infer both that S is true and that S is not true. A paradox! The most famous response to the liar paradox came from the logician Alfred Tarski, who distinguished a language (L) from a meta-language (ML), in which one can refer to sentences of L.
Does God exist or not? How should I behave? What is real? How do we know what we know? In this book, leading philosophical writers will engage your thought processes with a crash course in understanding the foundations of understanding. Platonic idealism The “big” questions began with the great Greek philosophers. According to Plato, everything in the world is a reflection of its true ideal form that exists outside the world. Plato likened this experience to the flickering shadows of objects reflected on a cave wall by firelight.
30-Second Philosophies: The 50 Most Thought-provoking Philosophies, Each Explained in Half a Minute by Stephen Law & Julian Baggini