Innate Ideas: Plato and the Meno
Philosopher Ian Hacking notes that Plato was fascinated by mathematics, and explains that his theory of innate ideas is based on the simple mathematical proof in his famous Socratic dialogue called the Meno.
Philosophy Over Time
Philosopher Hilary Putnam talks about philosophy since the time of Socrates. He notes that one constant about philosophy since the days of the ancient Greeks has been its concern with thinking carefully about how to live.
Rationalism
Philosopher Stephen Toulmin talks about rationalism, concluding that there have always been two driving forces behind it. On one hand, Professor Toulmin says, it comes from the desire to make theories as elegant as possible, which leads people to ma...
Innate Ideas and Mathematical Proof
Philosopher Ian Hacking observes that rationalists were fascinated by the possibility of mathematical proof, while empiricists were not. He notes that there is an enormous difference to this day among philosophers about this same subject. For those ...
Dividing Decimal Fractions: Dividing Decimals: Four Different Outcomes
This clip presents four different outcomes that may occur when dividing decimals: The first possibility is that the division comes out even "just as it stands, with no remainder." The second possibility is that the division comes out even only after...
Rounding Numbers: Summary Example and an Exercise
This clip walks us through two examples of rounding with decimal numbers, then invites the student to, "Â…try one yourself...(and) handle it like the problem we just finished." The clip then talks about the importance of, "Â…returning to the origina...
Is Reason the Source of Knowledge?: Theory of Innate Ideas, The
Rationalists believe in innate ideas, ideas that are present in the mind from birth. The concept had a long history beginning with Plato in the 4th century B.C.E. The difficulties and discoveries characteristic of Athens during this period are simil...
Is Reason the Source of Knowledge?: Sentiment of Rationality
In the 17th century, experimental sciences are in their infancy. As they have grown, they have demonstrated that much of our knowledge of the world comes through sense observation. But the basic question remains about whether all knowledge depends o...
Descartes and the Greeks (Part Two)
Philosopher Stephen Toulmin talks about the origins of differing branches of philosophy. On the one hand, Professor Toulmin notes, there have been those like Plato and Descartes, who have wanted theoretical certainty above all else. On the other han...
Descartes and the Greeks (Part 3)
Philosopher Stephen Toulmin concludes his discussion of the contrasting origins of philosophy, focusing here on Aristotle. Professor Toulmin notes that Aristotle had grown up in a medical family and was more impressed by the pragmatic underpinnings ...