Combining Texts

All the ideas for 'fragments/reports', 'Sets, Aggregates and Numbers' and 'Ordinatio'

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15 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
You can ask all sorts of numerical questions about any one given set [Yourgrau]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio]
If things were singular they would only differ numerically, but horse and tulip differ more than that [Duns Scotus, by Panaccio]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
What prevents a stone from being divided into parts which are still the stone? [Duns Scotus]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Two things are different if something is true of one and not of the other [Duns Scotus]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]