Combining Texts

All the ideas for 'Infinity: Quest to Think the Unthinkable', 'Things and Their Parts' and 'Principles of Philosophy of the Future'

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52 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
6928 Only that which can be an object of religion is an object of philosophy [Feuerbach]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
6918 Philosophy should not focus on names, but on the determined nature of things [Feuerbach]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
6904 Modern philosophy begins with Descartes' abstraction from sensation and matter [Feuerbach]
6931 Empiricism is right about ideas, but forgets man himself as one of our objects [Feuerbach]
2. Reason / B. Laws of Thought / 1. Laws of Thought
6933 The laws of reality are also the laws of thought [Feuerbach]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
4. Formal Logic / G. Formal Mereology / 1. Mereology
13331 Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
6919 Absolute thought remains in another world from being [Feuerbach]
19457 Being is what is undetermined, and hence indistinguishable [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
6920 Being posits essence, and my essence is my being [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
6921 Particularity belongs to being, whereas generality belongs to thought [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
6926 The only true being is of the senses, perception, feeling and love [Feuerbach]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
13332 Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
9. Objects / C. Structure of Objects / 3. Matter of an Object
13333 The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
13326 A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K]
13327 A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13329 An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
13330 An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
13328 Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
6908 Consciousness is absolute reality, and everything exists through consciousness [Feuerbach]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
6932 Ideas arise through communication, and reason is reached through community [Feuerbach]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
6935 In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach]
18. Thought / E. Abstraction / 1. Abstract Thought
6925 The new philosophy thinks of the concrete in a concrete (not a abstract) manner [Feuerbach]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
6924 Plotinus was ashamed to have a body [Feuerbach]
22. Metaethics / B. Value / 2. Values / g. Love
6927 If you love nothing, it doesn't matter whether something exists or not [Feuerbach]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
6934 Man is not a particular being, like animals, but a universal being [Feuerbach]
6936 The essence of man is in community, but with distinct individuals [Feuerbach]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
6913 God's existence cannot be separated from essence and concept, which can only be thought as existing [Feuerbach]
28. God / C. Attitudes to God / 4. God Reflects Humanity
6903 If God is only an object for man, then only the essence of man is revealed in God [Feuerbach]
6923 God is what man would like to be [Feuerbach]
6911 God is for us a mere empty idea, which we fill with our own ego and essence [Feuerbach]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
6902 Catholicism concerns God in himself, Protestantism what God is for man [Feuerbach]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
6905 Absolute idealism is the realized divine mind of Leibnizian theism [Feuerbach]