Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Art and Its Objects' and 'Rules for the Direction of the Mind'

expand these ideas     |    start again     |     specify just one area for these texts


39 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Clever scholars can obscure things which are obvious even to peasants [Descartes]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes]
2. Reason / A. Nature of Reason / 4. Aims of Reason
The secret of the method is to recognise which thing in a series is the simplest [Descartes]
2. Reason / A. Nature of Reason / 5. Objectivity
One truth leads us to another [Descartes]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Unity is something shared by many things, so in that respect they are equals [Descartes]
I can only see the proportion of two to three if there is a common measure - their unity [Descartes]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
Among the simples are the graspable negations, such as rest and instants [Descartes]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
Classes rarely share properties with their members - unlike universals and types [Wollheim]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
If we accept mere probabilities as true we undermine our existing knowledge [Descartes]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes]
When Socrates doubts, he know he doubts, and that truth is possible [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Clear and distinct truths must be known all at once (unlike deductions) [Descartes]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
The method starts with clear intuitions, followed by a process of deduction [Descartes]
15. Nature of Minds / A. Nature of Mind / 8. Brain
Nerves and movement originate in the brain, where imagination moves them [Descartes]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
We often treat a type as if it were a sort of token [Wollheim]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
The force by which we know things is spiritual, and quite distinct from the body [Descartes]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Interpretation is performance for some arts, and critical for all arts [Wollheim]
A love of nature must precede a love of art [Wollheim]
21. Aesthetics / B. Nature of Art / 1. Defining Art
A criterion of identity for works of art would be easier than a definition [Wollheim]
21. Aesthetics / B. Nature of Art / 2. Art as Form
If beauty needs organisation, then totally simple things can't be beautiful [Wollheim]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
Some say art must have verbalisable expression, and others say the opposite! [Wollheim]
It is claimed that the expressive properties of artworks are non-physical [Wollheim]
21. Aesthetics / B. Nature of Art / 6. Art as Institution
Style can't be seen directly within a work, but appreciation needs a grasp of style [Wollheim]
The traditional view is that knowledge of its genre to essential to appreciating literature [Wollheim]
21. Aesthetics / B. Nature of Art / 7. Ontology of Art
If artworks are not physical objects, they are either ideal entities, or collections of phenomena [Wollheim]
The ideal theory says art is an intuition, shaped by a particular process, and presented in public [Wollheim]
The ideal theory of art neglects both the audience and the medium employed [Wollheim]
A musical performance has virtually the same features as the piece of music [Wollheim]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
An interpretation adds further properties to the generic piece of music [Wollheim]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
A drawing only represents Napoleon if the artist intended it to [Wollheim]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
All the sciences searching for order and measure are related to mathematics [Descartes]