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All the ideas for 'Thinking About Mathematics', 'The Conscious Mind' and 'Meditations'

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182 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]
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 / 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 / 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 / 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 / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
Properties supervene if you can't have one without the other [Chalmers]
7. Existence / C. Structure of Existence / 5. Supervenience / b. Types of supervenience
Logical supervenience is when one set of properties must be accompanied by another set [Chalmers]
Natural supervenience is when one set of properties is always accompanied by another set [Chalmers]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
Reduction requires logical supervenience [Chalmers]
7. Existence / D. Theories of Reality / 6. Physicalism
Physicalism says in any two physically indiscernible worlds the positive facts are the same [Chalmers, by Bennett,K]
7. Existence / E. Categories / 3. Proposed Categories
All facts are either physical, experiential, laws of nature, second-order final facts, or indexical facts about me [Chalmers]
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 / A. Necessity / 5. Metaphysical Necessity
Strong metaphysical necessity allows fewer possible worlds than logical necessity [Chalmers]
Metaphysical necessity is a bizarre, brute and inexplicable constraint on possibilities [Chalmers]
10. Modality / A. Necessity / 10. Impossibility
How can we know the metaphysical impossibilities; the a posteriori only concerns this world [Chalmers]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
We know by thought that what is done cannot be undone [Descartes]
Kripke is often taken to be challenging a priori insights into necessity [Chalmers]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Maybe logical possibility does imply conceivability - by an ideal mind [Chalmers]
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]
One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
We attribute beliefs to people in order to explain their behaviour [Chalmers]
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 / 1. Perception
'Perception' means either an action or a mental state [Chalmers]
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 / 4. Sense Data / a. Sense-data theory
The structure of the retina has already simplified the colour information which hits it [Chalmers]
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]
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
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]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Reductive explanation is not the be-all and the end-all of explanation [Chalmers]
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]
Why are minds homogeneous and brains fine-grained? [Chalmers]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Can we be aware but not conscious? [Chalmers]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / d. Purpose of consciousness
Can we explain behaviour without consciousness? [Chalmers]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
Hard Problem: why brains experience things [Chalmers]
What turns awareness into consciousness? [Chalmers]
Going down the scale, where would consciousness vanish? [Chalmers]
15. Nature of Minds / B. Features of Minds / 3. Privacy
Nothing in physics even suggests consciousness [Chalmers]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Is intentionality just causal connections? [Chalmers]
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]
Sometimes we don't notice our pains [Chalmers]
Why should qualia fade during silicon replacement? [Chalmers]
15. Nature of Minds / B. Features of Minds / 6. Inverted Qualia
It seems possible to invert qualia [Chalmers]
15. Nature of Minds / B. Features of Minds / 7. Blindsight
In blindsight both qualia and intentionality are missing [Chalmers]
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 / C. Self-Awareness / 4. Errors in Introspection
When distracted we can totally misjudge our own experiences [Chalmers]
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 / 4. For Free Will
My capacity to make choices with my free will extends as far as any faculty ever could [Descartes]
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]
Maybe dualist interaction is possible at the quantum level? [Chalmers]
Supervenience makes interaction laws possible [Chalmers]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
It is odd if experience is a very recent development [Chalmers]
17. Mind and Body / A. Mind-Body Dualism / 7. Zombies
If I can have a zombie twin, my own behaviour doesn't need consciousness [Chalmers]
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]
17. Mind and Body / C. Functionalism / 3. Psycho-Functionalism
Does consciousness arise from fine-grained non-reductive functional organisation? [Chalmers]
17. Mind and Body / C. Functionalism / 7. Chinese Room
Maybe the whole Chinese Room understands Chinese, though the person doesn't [Chalmers]
17. Mind and Body / C. Functionalism / 8. Functionalism critique
The Chinese Mind doesn't seem conscious, but then nor do brains from outside [Chalmers]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
H2O causes liquidity, but no one is a dualist about that [Chalmers]
17. Mind and Body / D. Property Dualism / 4. Emergentism
Perhaps consciousness is physically based, but not logically required by that base [Chalmers]
17. Mind and Body / D. Property Dualism / 5. Supervenience of mind
Zombies imply natural but not logical supervenience [Chalmers]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
Phenomenal consciousness is fundamental, with no possible nonphenomenal explanation [Chalmers, by Kriegel/Williford]
Nothing external shows whether a mouse is conscious [Chalmers]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Temperature (etc.) is agreed to be reducible, but it is multiply realisable [Chalmers]
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 / A. Modes of Thought / 9. Indexical Thought
Indexicals may not be objective, but they are a fact about the world as I see it [Chalmers]
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]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
Rationalist 2D semantics posits necessary relations between meaning, apriority, and possibility [Chalmers, by Schroeter]
The 'primary intension' is non-empirical, and fixes extensions based on the actual-world reference [Chalmers]
Meaning has split into primary ("watery stuff"), and secondary counterfactual meaning ("H2O") [Chalmers]
The 'secondary intension' is determined by rigidifying (as H2O) the 'water' picked out in the actual world [Chalmers]
Primary and secondary intensions are the a priori (actual) and a posteriori (counterfactual) aspects of meaning [Chalmers]
We have 'primary' truth-conditions for the actual world, and derived 'secondary' ones for counterfactual worlds [Chalmers]
19. Language / D. Propositions / 1. Propositions
Two-dimensional semantics gives a 'primary' and 'secondary' proposition for each statement [Chalmers]
19. Language / E. Analyticity / 2. Analytic Truths
In two-dimensional semantics we have two aspects to truth in virtue of meaning [Chalmers]
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 / 8. Particular Causation / c. Conditions of causation
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
God the creator is an intelligent, infinite, powerful substance [Descartes]
Nothing apart from God could have essential existence, and such a being must be unique and eternal [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 / A. Divine Nature / 4. Divine Contradictions
Presumably God can do anything which is logically possible [Chalmers]
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]
One idea leads to another, but there must be an initial idea that contains the reality of all the others [Descartes]
I cannot think of a supremely perfect being without the supreme perfection of existence [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
Since God does not wish to deceive me, my judgement won't make errors if I use it properly [Descartes]
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]
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]