Combining Texts

All the ideas for 'Isagoge ('Introduction')', 'Authority and the Individual' and 'Plurals and Complexes'

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40 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice is a non-logical principle of set-theory [Hossack]
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Extensional mereology needs two definitions and two axioms [Hossack]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Plural reference will refer to complex facts without postulating complex things [Hossack]
Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
A plural comprehension principle says there are some things one of which meets some condition [Hossack]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
The theory of the transfinite needs the ordinal numbers [Hossack]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
I take the real numbers to be just lengths [Hossack]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
A plural language gives a single comprehensive induction axiom for arithmetic [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
In arithmetic singularists need sets as the instantiator of numeric properties [Hossack]
Set theory is the science of infinity [Hossack]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We are committed to a 'group' of children, if they are sitting in a circle [Hossack]
8. Modes of Existence / D. Universals / 1. Universals
Are genera and species real or conceptual? bodies or incorporeal? in sensibles or separate from them? [Porphyry]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Complex particulars are either masses, or composites, or sets [Hossack]
The relation of composition is indispensable to the part-whole relation for individuals [Hossack]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
Leibniz's Law argues against atomism - water is wet, unlike water molecules [Hossack]
The fusion of five rectangles can decompose into more than five parts that are rectangles [Hossack]
18. Thought / A. Modes of Thought / 1. Thought
A thought can refer to many things, but only predicate a universal and affirm a state of affairs [Hossack]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
We divide mankind into friend and foe, and cooperate with one and compete with the other [Russell]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Gradually loyalty to a creed increased, which could even outweigh nationality [Russell]
Increasingly war expands communities, and unifies them through fear [Russell]
In early societies the leaders needed cohesion, but the rest just had to obey [Russell]
24. Political Theory / A. Basis of a State / 2. Population / b. State population
The economic and political advantages of great size seem to have no upper limit [Russell]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
Government has a negative purpose, to prevent trouble, and a positive aim of realising our desires [Russell]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
A monarch is known to everyone in the group, and can thus unite large groups [Russell]
24. Political Theory / C. Ruling a State / 4. Changing the State / b. Devolution
Power should be with smaller bodies, as long as it doesn't restrict central powers [Russell]
24. Political Theory / D. Ideologies / 2. Anarchism
In an anarchy universities, research, books, and even seaside holidays, would be impossible [Russell]
A state is essential, to control greedy or predatory impulses [Russell]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
In democracy we are more aware of being governed than of our tiny share in government [Russell]
24. Political Theory / D. Ideologies / 8. Socialism
Managers are just as remote from workers under nationalisation as under capitalism [Russell]
Socialists say economic justice needs some state control of industries, and of foreign trade [Russell]
Being a slave of society is hardly better than being a slave of a despot [Russell]
25. Social Practice / A. Freedoms / 1. Slavery
Slavery began the divorce between the work and the purposes of the worker [Russell]
25. Social Practice / B. Equalities / 1. Grounds of equality
Slaves can be just as equal as free people [Russell]
25. Social Practice / B. Equalities / 4. Economic equality
Scarce goods may be denied entirely, to avoid their unequal distribution [Russell]
25. Social Practice / D. Justice / 1. Basis of justice
Modern justice is seen as equality, apart from modest extra rewards for exceptional desert [Russell]
27. Natural Reality / C. Space / 2. Space
We could ignore space, and just talk of the shape of matter [Hossack]