Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and '23: Book of Isaiah'

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8 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Let us reason together, saith the Lord [Isaiah]
     Full Idea: Come now, and let us reason together, saith the Lord.
     From: Isaiah (23: Book of Isaiah [c.680 BCE], 01.18)
     A reaction: A verse which not only offers Biblical support for philosophy, but would also seem to be a challenge to Christian fideists.
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?
27. Natural Reality / E. Cosmology / 1. Cosmology
The world is established, and cannot be moved [Isaiah]
     Full Idea: The world is also established, that it cannot be moved.
     From: Isaiah (23: Book of Isaiah [c.680 BCE], 93.1)
     A reaction: This verse caused big trouble for Galileo. The only reason I can think of for Isaiah to write this is that occasionally people were prone to panic, and worry that the Earth might suddenly and abruptly be moved.
28. God / A. Divine Nature / 1. God
Beside me there is no God [Isaiah]
     Full Idea: I am the first, and I am the last; and beside me there is no God.
     From: Isaiah (23: Book of Isaiah [c.680 BCE], 44.06)
     A reaction: This seems to be the first clear statement (c. 680 BCE) of monotheism, certainly preceding any Greek views on the subject (cf. Idea 2629,Idea 7347). It is not just an arrogant assertion by the jews, but a humble sacrifice, donating their god to humanity.