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All the ideas for 'Thinking About Mathematics', 'Parts' and 'The Emotions'

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118 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analytic philosophers may prefer formal systems because natural language is such mess [Simons]
2. Reason / A. Nature of Reason / 5. Objectivity
The personal view can still be objective, so I call sciences 'impersonal', rather than objective [Goldie]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Classical mereology doesn't apply well to the objects around us [Simons]
Complement: the rest of the Universe apart from some individual, written x-bar [Simons]
Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional? [Simons]
A 'part' has different meanings for individuals, classes, and masses [Simons]
4. Formal Logic / G. Formal Mereology / 2. Terminology of Mereology
Proper or improper part: x < y, 'x is (a) part of y' [Simons]
Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons]
Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons]
Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons]
Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons]
Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons]
General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons]
General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons]
Universe: the mereological sum of all objects whatever, written 'U' [Simons]
Atom: an individual with no proper parts, written 'At x' [Simons]
Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons]
4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons]
The part-relation is transitive and asymmetric (and thus irreflexive) [Simons]
Each wheel is part of a car, but the four wheels are not a further part [Simons]
Classical mereology doesn't handle temporal or modal notions very well [Simons]
4. Formal Logic / G. Formal Mereology / 4. Groups
A 'group' is a collection with a condition which constitutes their being united [Simons]
The same members may form two groups [Simons]
'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions [Simons]
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]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
Philosophy is stuck on the Fregean view that an individual is anything with a proper name [Simons]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Some natural languages don't distinguish between singular and plural [Simons]
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 / B. Change in Existence / 1. Nature of Change
Four-dimensional ontology has no change, since that needs an object, and time to pass [Simons]
There are real relational changes, as well as bogus 'Cambridge changes' [Simons]
7. Existence / B. Change in Existence / 2. Processes
I don't believe in processes [Simons]
Fans of process ontology cheat, since river-stages refer to 'rivers' [Simons]
7. Existence / B. Change in Existence / 3. Moments
Moments are things like smiles or skids, which are founded on other things [Simons]
Moving disturbances are are moments which continuously change their basis [Simons]
A smiling is an event with causes, but the smile is a continuant without causes [Simons]
A wave is maintained by a process, but it isn't a process [Simons]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
I do not think there is a general identity condition for events [Simons]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
Relativity has an ontology of things and events, not on space-time diagrams [Simons]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
Independent objects can exist apart, and maybe even entirely alone [Simons]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'. [Simons]
Mass terms (unlike plurals) are used with indifference to whether they can exist in units [Simons]
Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons [Simons]
7. Existence / C. Structure of Existence / 8. Stuff / b. Mixtures
A mixture can have different qualities from its ingredients. [Simons]
Mixtures disappear if nearly all of the mixture is one ingredient [Simons]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
To individuate something we must pick it out, but also know its limits of variation [Simons]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Sortal nouns for continuants tell you their continuance- and cessation-conditions [Simons]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
A whole requires some unique relation which binds together all of the parts [Simons]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't [Simons]
Does Tibbles remain the same cat when it loses its tail? [Simons]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Without extensional mereology two objects can occupy the same position [Simons]
9. Objects / C. Structure of Objects / 5. Composition of an Object
Composition is asymmetric and transitive [Simons]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand [Simons]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'. [Simons]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons]
'Mereological extensionality' says objects with the same parts are identical [Simons]
If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons]
Sums are more plausible for pluralities and masses than they are for individuals [Simons]
Sums of things in different categories are found within philosophy. [Simons]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
The wholeness of a melody seems conventional, but of an explosion it seems natural [Simons]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Objects have their essential properties because of the kind of objects they are [Simons]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence [Simons]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
Original parts are the best candidates for being essential to artefacts [Simons]
9. Objects / D. Essence of Objects / 12. Essential Parts
An essential part of an essential part is an essential part of the whole [Simons]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four dimensional-objects are stranger than most people think [Simons]
9. Objects / E. Objects over Time / 7. Intermittent Objects
Intermittent objects would be respectable if they occurred in nature, as well as in artefacts [Simons]
Objects like chess games, with gaps in them, are thereby less unified [Simons]
9. Objects / E. Objects over Time / 9. Ship of Theseus
An entrepreneur and a museum curator would each be happy with their ship at the end [Simons]
The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?' [Simons]
9. Objects / E. Objects over Time / 12. Origin as Essential
The zygote is an essential initial part, for a sexually reproduced organism [Simons]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
The limits of change for an individual depend on the kind of individual [Simons]
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 / 4. Other Minds / c. Knowing other minds
We know other's emotions by explanation, contagion, empathy, imagination, or sympathy [Goldie]
Empathy and imagining don't ensure sympathy, and sympathy doesn't need them [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Unlike moods, emotions have specific objects, though the difference is a matter of degree [Goldie]
Emotional intentionality as belief and desire misses out the necessity of feelings [Goldie]
A long lasting and evolving emotion is still seen as a single emotion, such as love [Goldie]
'Having an emotion' differs from 'being emotional' [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / b. Types of emotion
Some Aborigines have fifteen different words for types of fear [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
Emotional responses can reveal to us our values, which might otherwise remain hidden [Goldie]
If we have a 'feeling towards' an object, that gives the recognition a different content [Goldie]
When actions are performed 'out of' emotion, they appear to be quite different [Goldie]
It is best to see emotions holistically, as embedded in a person's life narrative [Goldie]
If emotions are 'towards' things, they can't be bodily feelings, which lack aboutness [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / d. Emotional feeling
If reasons are seen impersonally (as just causal), then feelings are an irrelevant extra [Goldie]
We have feelings of which we are hardly aware towards things in the world [Goldie]
An emotion needs episodes of feeling, but not continuously [Goldie]
Moods can focus as emotions, and emotions can blur into moods [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / e. Basic emotions
Emotions are not avocado pears, with a rigid core and changeable surface [Goldie]
A basic emotion is the foundation of a hierarchy, such as anger for types of annoyance [Goldie]
Early Chinese basic emotions: joy, anger, sadness, fear, love, disliking, and liking [Goldie]
Cross-cultural studies of facial expressions suggests seven basic emotions [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
Some emotions are direct responses, and neither rational nor irrational [Goldie]
Emotional thought is not rational, but it can be intelligible [Goldie]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Learning an evaluative property like 'dangerous' is also learning an emotion [Goldie]
We call emotions 'passions' because they are not as controlled as we would like [Goldie]
Emotional control is hard, but we are responsible for our emotions over long time periods [Goldie]
Emotions are not easily changed, as new knowledge makes little difference, and akrasia is possible [Goldie]
Emotional control is less concerned with emotional incidents, and more with emotional tendencies [Goldie]
20. Action / A. Definition of Action / 2. Duration of an Action
With activities if you are doing it you've done it, with performances you must finish to have done it [Simons]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Akrasia can be either overruling our deliberation, or failing to deliberate [Goldie]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Justifying reasons say you were right; excusing reasons say your act was explicable [Goldie]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
One false note doesn't make it a performance of a different work [Simons]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Character traits are both possession of and lack of dispositions [Goldie]
We over-estimate the role of character traits when explaining behaviour [Goldie]
Psychologists suggest we are muddled about traits, and maybe they should be abandoned [Goldie]
27. Natural Reality / G. Biology / 3. Evolution
Our capabilities did not all evolve during the hunter gathering period [Goldie]