Combining Texts

All the ideas for 'Sets, Aggregates and Numbers', 'Plato on Parts and Wholes' and 'On 'Physics''

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15 ideas

2. Reason / F. Fallacies / 7. Ad Hominem
An ad hominem refutation is reasonable, if it uses the opponent's assumptions [Harte,V]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology began as a nominalist revolt against the commitments of set theory [Harte,V]
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]
7. Existence / A. Nature of Existence / 2. Types of Existence
Everything that exists is either a substance or an accident [Albert of Saxony]
7. Existence / B. Change in Existence / 1. Nature of Change
Traditionally, the four elements are just what persists through change [Harte,V]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Mereology treats constitution as a criterion of identity, as shown in the axiom of extensionality [Harte,V]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
What exactly is a 'sum', and what exactly is 'composition'? [Harte,V]
If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V]
The problem with the term 'sum' is that it is singular [Harte,V]
9. Objects / E. Objects over Time / 6. Successive Things
God could make a successive thing so that previous parts cease to exist [Albert of Saxony]
Successive entities just need parts to succeed one another, without their existence [Albert of Saxony]