Combining Texts

All the ideas for 'fragments/reports', 'Introduction to the Philosophy of Mathematics' and 'Principles of Philosophy of the Future'

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47 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Only that which can be an object of religion is an object of philosophy [Feuerbach]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Philosophy should not focus on names, but on the determined nature of things [Feuerbach]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Modern philosophy begins with Descartes' abstraction from sensation and matter [Feuerbach]
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
The laws of reality are also the laws of thought [Feuerbach]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
Rejecting double negation elimination undermines reductio proofs [Colyvan]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinal numbers represent order relations [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Intuitionists only accept a few safe infinities [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Most mathematical proofs are using set theory, but without saying so [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Absolute thought remains in another world from being [Feuerbach]
Being is what is undetermined, and hence indistinguishable [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
Being posits essence, and my essence is my being [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
Particularity belongs to being, whereas generality belongs to thought [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
The only true being is of the senses, perception, feeling and love [Feuerbach]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Consciousness is absolute reality, and everything exists through consciousness [Feuerbach]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
Ideas arise through communication, and reason is reached through community [Feuerbach]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
In man the lowest senses of smell and taste elevate themselves to intellectual acts [Feuerbach]
14. Science / C. Induction / 6. Bayes's Theorem
Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Mathematics can reveal structural similarities in diverse systems [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
Mathematics can show why some surprising events have to occur [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
Reductio proofs do not seem to be very explanatory [Colyvan]
If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
18. Thought / E. Abstraction / 1. Abstract Thought
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
Plotinus was ashamed to have a body [Feuerbach]
22. Metaethics / B. Value / 2. Values / g. Love
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
Man is not a particular being, like animals, but a universal being [Feuerbach]
The essence of man is in community, but with distinct individuals [Feuerbach]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
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
If God is only an object for man, then only the essence of man is revealed in God [Feuerbach]
God is what man would like to be [Feuerbach]
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
Catholicism concerns God in himself, Protestantism what God is for man [Feuerbach]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Absolute idealism is the realized divine mind of Leibnizian theism [Feuerbach]