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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Causality and Determinism' and 'Meditations'

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139 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Modern science comes from Descartes' view that knowledge doesn't need moral purity [Descartes, by Foucault]
2. Reason / A. Nature of Reason / 2. Logos
Descartes impoverished the classical idea of logos, and it no longer covered human experience [Roochnik on Descartes]
2. Reason / A. Nature of Reason / 4. Aims of Reason
Reason says don't assent to uncertain principles, just as much as totally false ones [Descartes]
2. Reason / A. Nature of Reason / 7. Status of Reason
Since Plato all philosophers have followed the herd, except Descartes, stuck in superficial reason [Nietzsche on Descartes]
2. Reason / F. Fallacies / 4. Circularity
It is circular to make truth depend on believing God's existence is true [Arnauld on Descartes]
Descartes is right that in the Christian view only God can guarantee the reliability of senses [Nietzsche on Descartes]
Once it is clear that there is a God who is no deceiver, I conclude that clear and distinct perceptions must be true [Descartes]
3. Truth / A. Truth Problems / 8. Subjective Truth
My general rule is that everything that I perceive clearly and distinctly is true [Descartes]
Someone may think a thing is 'clear and distinct', but be wrong [Leibniz on Descartes]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Arithmetic and geometry achieve some certainty without worrying about existence [Descartes]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Surely maths is true even if I am dreaming? [Descartes]
I can learn the concepts of duration and number just from observing my own thoughts [Descartes]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
If I can separate two things in my understanding, then God can separate them in reality [Descartes]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
Substance cannot be conceived or explained to others [Gassendi on Descartes]
9. Objects / C. Structure of Objects / 7. Substratum
If we remove surface qualities from wax, we have an extended, flexible, changeable thing [Descartes]
9. Objects / D. Essence of Objects / 4. Essence as Definition
Descartes gives an essence by an encapsulating formula [Descartes, by Almog]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
We know by thought that what is done cannot be undone [Descartes]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Belief is not an intellectual state or act, because propositions are affirmed or denied by the will [Descartes, by Zagzebski]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
Descartes tried to model reason on maths instead of 'logos' [Roochnik on Descartes]
Labelling slightly doubtful things as false is irrational [Roochnik on Descartes]
Maybe there is only one certain fact, which is that nothing is certain [Descartes]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
Descartes transformed 'God is thinkable, so he exists' into 'I think, so I exist' [Descartes, by Feuerbach]
In the Meditations version of the Cogito he says "I am; I exist", which avoids presenting it as an argument [Descartes, by Baggini /Fosl]
If I don't think, there is no reason to think that I exist [Descartes]
Modern philosophy set the self-conscious ego in place of God [Descartes, by Feuerbach]
"I think therefore I am" is the absolute truth of consciousness [Sartre on Descartes]
I must even exist if I am being deceived by something [Descartes]
"I am, I exist" is necessarily true every time I utter it or conceive it in my mind [Descartes]
The Cogito is a transcendental argument, not a piece of a priori knowledge [Rey on Descartes]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
The Cogito proves subjective experience is basic, but makes false claims about the Self [Russell on Descartes]
Maybe 'I' am not the thinker, but something produced by thought [Nietzsche on Descartes]
The Cogito only works if you already understand what thought and existence are [Mersenne on Descartes]
It is a precondition of the use of the word 'I' that I exist [Ayer on Descartes]
The thing which experiences may be momentary, and change with the next experience [Russell on Descartes]
'I think' assumes I exist, that thinking is known and caused, and that I am doing it [Nietzsche on Descartes]
A thought doesn't imply other thoughts, or enough thoughts to make up a self [Ayer on Descartes]
That I perform an activity (thinking) doesn't prove what type of thing I am [Hobbes on Descartes]
Autistic children seem to use the 'I' concept without seeing themselves as thinkers [Segal on Descartes]
The Cogito assumes a priori the existence of substance, when actually it is a grammatical custom [Nietzsche on Descartes]
How can we infer that all thinking involves self-consciousness, just from my own case? [Kant on Descartes]
My self is not an inference from 'I think', but a presupposition of it [Kant on Descartes]
We cannot give any information a priori about the nature of the 'thing that thinks' [Kant on Descartes]
The fact that I am a subject is not enough evidence to show that I am a substantial object [Kant on Descartes]
Descartes' claim to know his existence before his essence is misleading or absurd [Descartes, by Lowe]
Modern self-consciousness is a doubtful abstraction; only senses and feelings are certain [Feuerbach on Descartes]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
My perceiving of things may be false, but my seeming to perceive them cannot be false [Descartes]
11. Knowledge Aims / C. Knowing Reality / 4. Solipsism
I myself could be the author of all these self-delusions [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
For Descartes, objects have one primary quality, which is geometrical [Descartes, by Robinson,H]
12. Knowledge Sources / B. Perception / 5. Interpretation
Why does pain make us sad? [Descartes]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Dogs can make the same judgements as us about variable things [Gassendi on Descartes]
We perceive objects by intellect, not by senses or imagination [Descartes]
The wax is not perceived by the senses, but by the mind alone [Descartes]
We don't 'see' men in heavy clothes, we judge them to be men [Descartes]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
To achieve good science we must rebuild from the foundations [Descartes]
Only one certainty is needed for progress (like a lever's fulcrum) [Descartes]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Even if my body and objects are imaginary, there may be simpler things which are true [Descartes]
Descartes can't begin again, because sceptics doubt cognitive processes as well as beliefs [Pollock/Cruz on Descartes]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
If pain is felt in a lost limb, I cannot be certain that a felt pain exists in my real limbs [Descartes]
We correct sense errors with other senses, not intellect [Mersenne on Descartes]
The senses can only report, so perception errors are in the judgment [Gassendi on Descartes]
It is prudent never to trust your senses if they have deceived you even once [Descartes]
13. Knowledge Criteria / D. Scepticism / 4. Demon Scepticism
God may have created nothing, but made his creation appear to me as it does now [Descartes]
To achieve full scepticism, I imagine a devil who deceives me about the external world and my own body and senses [Descartes]
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
Waking actions are joined by memory to all our other actions, unlike actions of which we dream [Descartes]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
I can only sense an object if it is present, and can't fail to sense it when it is [Descartes]
15. Nature of Minds / A. Nature of Mind / 3. Mental Causation
Can the pineal gland be moved more slowly or quickly by the mind than by animal spirits? [Spinoza on Descartes]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
We discovers others as well as ourselves in the Cogito [Sartre on Descartes]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
Faculties of the mind aren't parts, as one mind uses them [Descartes]
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
Descartes put thought at the centre of the mind problem, but we put sensation [Rey on Descartes]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Descartes mentions many cognitive faculties, but reduces them to will and intellect [Descartes, by Schmid]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
Imagination and sensation are non-essential to mind [Descartes]
16. Persons / A. Concept of a Person / 1. Existence of Persons
Some cause must unite the separate temporal sections of a person [Descartes]
16. Persons / D. Continuity of the Self / 7. Self and Thinking
Since I only observe myself to be thinking, I conclude that that is my essence [Descartes]
I can exist without imagination and sensing, but they can't exist without me [Descartes]
For Descartes a person's essence is the mind because objects are perceived by mind, not senses [Descartes, by Feuerbach]
16. Persons / F. Free Will / 1. Nature of Free Will
Our 'will' just consists of the feeling that when we are motivated to do something, there are no external pressures [Descartes]
16. Persons / F. Free Will / 3. Constraints on the will
Freedom involves acting according to an idea [Anscombe]
16. Persons / F. Free Will / 4. For Free Will
My capacity to make choices with my free will extends as far as any faculty ever could [Descartes]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
To believe in determinism, one must believe in a system which determines events [Anscombe]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
The mind is a non-extended thing which thinks [Descartes]
Mind is not extended, unlike the body [Descartes]
Descartes is a substance AND property dualist [Descartes, by Kim]
The mind is utterly indivisible [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Interaction between mental and physical seems to violate the principle of conservation of energy [Rowlands on Descartes]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
The 'thinking thing' may be the physical basis of the mind [Hobbes on Descartes]
Knowing different aspects of brain/mind doesn't make them different [Rorty on Descartes]
Descartes gives no clear criterion for individuating mental substances [Cottingham on Descartes]
Does Descartes have a clear conception of how mind unites with body? [Spinoza on Descartes]
Even Descartes may concede that mental supervenes on neuroanatomical [Lycan on Descartes]
Superman's strength is indubitable, Clark Kent's is doubtful, so they are not the same? [Maslin on Descartes]
18. Thought / A. Modes of Thought / 2. Propositional Attitudes
In some thoughts I grasp a subject, but also I will or fear or affirm or deny it [Descartes]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
Descartes created the modern view of rationality, as an internal feature instead of an external vision [Descartes, by Taylor,C]
18. Thought / A. Modes of Thought / 6. Judgement / b. Error
I make errors because my will extends beyond my understanding [Descartes]
18. Thought / C. Content / 2. Ideas
True ideas are images, such as of a man, a chimera, or God [Descartes]
18. Thought / C. Content / 10. Causal Semantics
All ideas are adventitious, and come from the senses [Gassendi on Descartes]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
The ideas of God and of my self are innate in me [Descartes]
I can think of innumerable shapes I have never experienced [Descartes]
The idea of a supremely perfect being is within me, like the basic concepts of mathematics [Descartes]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes]
26. Natural Theory / C. Causation / 5. Direction of causation
With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe]
26. Natural Theory / C. Causation / 6. Causation as primitive
The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J]
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe]
There must be at least as much in the cause as there is in the effect [Descartes]
28. God / A. Divine Nature / 2. Divine Nature
Nothing apart from God could have essential existence, and such a being must be unique and eternal [Descartes]
God the creator is an intelligent, infinite, powerful substance [Descartes]
28. God / A. Divine Nature / 3. Divine Perfections
It is self-evident that deception is a natural defect, so God could not be a deceiver [Descartes]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Existence and God's essence are inseparable, like a valley and a mountain, or a triangle and its properties [Descartes]
The idea of God in my mind is like the mark a craftsman puts on his work [Descartes]
I cannot think of a supremely perfect being without the supreme perfection of existence [Descartes]
One idea leads to another, but there must be an initial idea that contains the reality of all the others [Descartes]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
We mustn't worship God as an image because we have no idea of him [Hobbes on Descartes]
We can never conceive of an infinite being [Gassendi on Descartes]
Descartes cannot assume that a most perfect being exists without contradictions [Leibniz on Descartes]
Existence is not a perfection; it is what makes perfection possible [Gassendi on Descartes]
29. Religion / D. Religious Issues / 3. Problem of Evil / c. Human Error
Error arises because my faculty for judging truth is not infinite [Descartes]
God didn't give us good judgement even about our own lives [Gassendi on Descartes]
Since God does not wish to deceive me, my judgement won't make errors if I use it properly [Descartes]
29. Religion / D. Religious Issues / 3. Problem of Evil / d. Natural Evil
If we ask whether God's works are perfect, we must not take a narrow viewpoint, but look at the universe as a whole [Descartes]