Combining Texts

All the ideas for 'Mathematics without Foundations', 'Letters to Antoine Arnauld' and 'Enquiry Conc Human Understanding'

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133 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom is the science of happiness [Leibniz]
1. Philosophy / A. Wisdom / 2. Wise People
Wise people have fewer acts of will, because such acts are linked together [Leibniz]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
The observation of human blindness and weakness is the result of all philosophy [Hume]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Metaphysics is geometrical, resting on non-contradiction and sufficient reason [Leibniz]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
If we suspect that a philosophical term is meaningless, we should ask what impression it derives from [Hume]
1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
All experimental conclusions assume that the future will be like the past [Hume]
2. Reason / D. Definition / 4. Real Definition
Definitions can only be real if the item is possible [Leibniz]
2. Reason / E. Argument / 3. Analogy
All reasoning concerning matters of fact is based on analogy (with similar results of similar causes) [Hume]
3. Truth / A. Truth Problems / 1. Truth
The predicate is in the subject of a true proposition [Leibniz]
A truth is just a proposition in which the predicate is contained within the subject [Leibniz]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
There is no multiplicity without true units [Leibniz]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Reason assists experience in discovering laws, and in measuring their application [Hume]
Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
What is not truly one being is not truly a being either [Leibniz]
7. Existence / A. Nature of Existence / 4. Abstract Existence
We can't think about the abstract idea of triangles, but only of particular triangles [Hume]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
A thing 'expresses' another if they have a constant and fixed relationship [Leibniz]
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
A substance contains the laws of its operations, and its actions come from its own depth [Leibniz]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
We cannot form an idea of a 'power', and the word is without meaning [Hume]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Philosophy needs the precision of the unity given by substances [Leibniz]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Accidental unity has degrees, from a mob to a society to a machine or organism [Leibniz]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
We find unity in reason, and unity in perception, but these are not true unity [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
A body is a unified aggregate, unless it has an indivisible substance [Leibniz]
Unity needs an indestructible substance, to contain everything which will happen to it [Leibniz]
Every bodily substance must have a soul, or something analogous to a soul [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance [Leibniz]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Basic predicates give the complete concept, which then predicts all of the actions [Leibniz]
Essences exist in the divine understanding [Leibniz]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Bodies need a soul (or something like it) to avoid being mere phenomena [Leibniz]
9. Objects / D. Essence of Objects / 10. Essence as Species
Truths about species are eternal or necessary, but individual truths concern what exists [Leibniz]
10. Modality / B. Possibility / 6. Probability
We transfer the frequency of past observations to our future predictions [Hume]
10. Modality / B. Possibility / 7. Chance
There is no such thing as chance [Hume]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
If varieties of myself can be conceived of as distinct from me, then they are not me [Leibniz]
If someone's life went differently, then that would be another individual [Leibniz]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Belief is stronger, clearer and steadier than imagination [Hume]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
Belief can't be a concept plus an idea, or we could add the idea to fictions [Hume]
Belief is just a particular feeling attached to ideas of objects [Hume]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
'Natural beliefs' are unavoidable, whatever our judgements [Hume, by Strawson,G]
Beliefs are built up by resemblance, contiguity and causation [Hume]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
I cannot think my non-existence, nor exist without being myself [Leibniz]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
I can't just know myself to be a substance; I must distinguish myself from others, which is hard [Leibniz]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Relations of ideas are known by thought, independently from the world [Hume]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
If secondary qualities (e.g. hardness) are in the mind, so are primary qualities like extension [Hume]
12. Knowledge Sources / B. Perception / 3. Representation
It never occurs to people that they only experience representations, not the real objects [Hume]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
All reasoning about facts is causal; nothing else goes beyond memory and senses [Hume]
All ideas are copies of impressions [Hume]
Hume is loose when he says perceptions of different strength are different species [Reid on Hume]
Impressions are our livelier perceptions, Ideas the less lively ones [Hume]
All objects of enquiry are Relations of Ideas, or Matters of Fact [Hume]
If books don't relate ideas or explain facts, commit them to the flames [Hume]
12. Knowledge Sources / D. Empiricism / 2. Associationism
All ideas are connected by Resemblance, Contiguity in time or place, and Cause and Effect [Hume]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
We cannot form the idea of something we haven't experienced [Hume]
Only madmen dispute the authority of experience [Hume]
When definitions are pushed to the limit, only experience can make them precise [Hume]
How could Adam predict he would drown in water or burn in fire? [Hume]
We can only invent a golden mountain by combining experiences [Hume]
You couldn't reason at all if you lacked experience [Hume]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Hume mistakenly lumps sensations and perceptions together as 'impressions' [Scruton on Hume]
If a person had a gap in their experience of blue shades, they could imaginatively fill it in [Hume]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Nothing should be taken as certain without foundations [Leibniz]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
Reasons for belief must eventually terminate in experience, or they are without foundation [Hume]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
There is no certain supreme principle, or infallible rule of inference [Hume]
13. Knowledge Criteria / C. External Justification / 7. Testimony
We think testimony matches reality because of experience, not some a priori connection [Hume]
Good testimony needs education, integrity, motive and agreement [Hume, by PG]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Reason can never show that experiences are connected to external objects [Hume]
Mitigated scepticism draws attention to the limitations of human reason, and encourages modesty [Hume]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Mitigated scepticism sensibly confines our enquiries to the narrow capacity of human understanding [Hume]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
Examples of illusion only show that sense experience needs correction by reason [Hume]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
The main objection to scepticism is that no good can come of it [Hume]
It is a very extravagant aim of the sceptics to destroy reason and argument by means of reason and argument [Hume]
14. Science / C. Induction / 2. Aims of Induction
We assume similar secret powers behind similar experiences, such as the nourishment of bread [Hume]
14. Science / C. Induction / 3. Limits of Induction
Induction can't prove that the future will be like the past, since induction assumes this [Hume]
If we infer causes from repetition, this explains why we infer from a thousand objects what we couldn't infer from one [Hume]
All inferences from experience are effects of custom, not reasoning [Hume]
Reason cannot show why reliable past experience should extend to future times and remote places [Hume]
Fools, children and animals all learn from experience [Hume]
14. Science / C. Induction / 4. Reason in Induction
Premises can support an argument without entailing it [Pollock/Cruz on Hume]
Hume just shows induction isn't deduction [Williams,M on Hume]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Nature is explained by mathematics and mechanism, but the laws rest on metaphysics [Leibniz]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
To fully conceive the subject is to explain the resulting predicates and events [Leibniz]
15. Nature of Minds / A. Nature of Mind / 1. Mind / b. Purpose of mind
Mind is a thinking substance which can know God and eternal truths [Leibniz]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
It seems probable that animals have souls, but not consciousness [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
A picture of a friend strengthens our idea of him, by resemblance [Hume]
General ideas are the connection by resemblance to some particular [Hume]
Hume does not distinguish real resemblances among degrees of resemblance [Shoemaker on Hume]
15. Nature of Minds / C. Capacities of Minds / 8. Remembering Contiguity
When I am close to (contiguous with) home, I feel its presence more nearly [Hume]
15. Nature of Minds / C. Capacities of Minds / 9. Perceiving Causation
An object made by a saint is the best way to produce thoughts of him [Hume]
Our awareness of patterns of causation is too important to be left to slow and uncertain reasoning [Hume]
16. Persons / F. Free Will / 5. Against Free Will
The doctrine of free will arises from a false sensation we have of freedom in many actions [Hume]
16. Persons / F. Free Will / 7. Compatibilism
Liberty is merely acting according to the will, which anyone can do if they are not in chains [Hume]
Hume makes determinism less rigid by removing the necessity from causation [Trusted on Hume]
Everything which happens is not necessary, but is certain after God chooses this universe [Leibniz]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
Concepts are what unite a proposition [Leibniz]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Only experience teaches us about our wills [Hume]
20. Action / C. Motives for Action / 4. Responsibility for Actions
Praise and blame can only be given if an action proceeds from a person's character and disposition [Hume]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty increases with familiarity [Leibniz]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
If you deny all necessity and causation, then our character is not responsible for our crime [Hume]
Repentance gets rid of guilt, which shows that responsibility arose from the criminal principles in the mind [Hume]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Happiness is advancement towards perfection [Leibniz]
25. Social Practice / A. Freedoms / 3. Free speech
No government has ever suffered by being too tolerant of philosophy [Hume]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
We can discover some laws of nature, but never its ultimate principles and causes [Hume]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena [Leibniz]
26. Natural Theory / C. Causation / 1. Causation
A priori it looks as if a cause could have absolutely any effect [Hume]
If a singular effect is studied, its cause can only be inferred from the types of events involved [Hume]
26. Natural Theory / C. Causation / 7. Eliminating causation
Hume never even suggests that there is no such thing as causation [Hume, by Strawson,G]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
At first Hume said qualities are the causal entities, but later he said events [Hume, by Davidson]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Hume says we can only know constant conjunctions, not that that's what causation IS [Hume, by Strawson,G]
In both of Hume's definitions, causation is extrinsic to the sequence of events [Psillos on Hume]
Hume's definition of cause as constantly joined thoughts can't cover undiscovered laws [Ayer on Hume]
A cause is either similar events following one another, or an experience always suggesting a second experience [Hume]
It is only when two species of thing are constantly conjoined that we can infer one from the other [Hume]
No causes can be known a priori, but only from experience of constant conjunctions [Hume]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
Cause is where if the first object had not been, the second had not existed [Hume]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
In observing causes we can never observe any necessary connections or binding qualities [Hume]
Hume never shows how a strong habit could generate the concept of necessity [Harré/Madden on Hume]
Hume's regularity theory of causation is epistemological; he believed in some sort of natural necessity [Hume, by Strawson,G]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Each possible world contains its own laws, reflected in the possible individuals of that world [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
Motion alone is relative, but force is real, and establishes its subject [Leibniz]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
It can never be a logical contradiction to assert the non-existence of something thought to exist [Hume]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
You can't infer the cause to be any greater than its effect [Hume]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
Everything, even miracles, belongs to order [Leibniz]
Miracles are extraordinary operations by God, but are nevertheless part of his design [Leibniz]
All experience must be against a supposed miracle, or it wouldn't be called 'a miracle' [Hume]
To establish a miracle the falseness of the evidence must be a greater miracle than the claimed miraculous event [Hume]
A miracle violates laws which have been established by continuous unchanging experience, so should be ignored [Hume]
28. God / C. Attitudes to God / 4. God Reflects Humanity
The idea of an infinite, intelligent, wise and good God arises from augmenting the best qualities of our own minds [Hume]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Immortality without memory is useless [Leibniz]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The soul is indestructible and always self-aware [Leibniz]
29. Religion / D. Religious Issues / 2. Immortality / c. Animal Souls
Animals have souls, but lack consciousness [Leibniz]