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All the ideas for 'Thinking About Mathematics', 'The Enneads' and 'Principles of Philosophy of the Future'

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55 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]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
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 is the product of pure intellect [Plotinus]
The One does not exist, but is the source of all existence [Plotinus]
The One is a principle which transcends Being [Plotinus]
Being posits essence, and my essence is my being [Feuerbach]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
Number determines individual being [Plotinus]
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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
If soul was like body, its parts would be separate, without communication [Plotinus]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
A person is the whole of their soul [Plotinus]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus]
The soul is outside of all of space, and has no connection to the bodily order [Plotinus]
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 / b. Rational ethics
The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus]
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]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by 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 / 6. Early Matter Theories / e. The One
How can multiple existence arise from the unified One? [Plotinus]
Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus]
Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus]
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 / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus]
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]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus]