Combining Texts

All the ideas for 'teaching', 'Substance' and 'Grundgesetze der Arithmetik 2 (Basic Laws)'

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25 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
5896 Speak the truth, for this alone deifies man [Pythagoras, by Porphyry]
1. Philosophy / B. History of Ideas / 2. Ancient Thought
3051 Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius]
2. Reason / D. Definition / 2. Aims of Definition
13886 Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 7. Contextual Definition
9845 We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 11. Ostensive Definition
10019 Only what is logically complex can be defined; what is simple must be pointed to [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9886 Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
9889 Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
7485 For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
10553 A number is a class of classes of the same cardinality [Frege, by Dummett]
10020 Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
9887 Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
8751 Only applicability raises arithmetic from a game to a science [Frege]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
15391 A substance is, roughly, a basic being or subject at the foundation of reality [Robb]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9891 The first demand of logic is of a sharp boundary [Frege]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
15392 If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
9890 The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
18. Thought / E. Abstraction / 8. Abstractionism Critique
11846 If we abstract the difference between two houses, they don't become the same house [Frege]
22. Metaethics / B. Value / 2. Values / d. Health
3053 Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
5244 For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
644 For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle]
638 Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle]
553 Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle]
554 Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle]
375 When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
7467 The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson]