Combining Texts

All the ideas for 'fragments/reports', 'Meditations' and 'Grundlagen der Arithmetik (Foundations)'

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349 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom for one instant is as good as wisdom for eternity [Chrysippus]
1. Philosophy / A. Wisdom / 2. Wise People
Wise men should try to participate in politics, since they are a good influence [Chrysippus, by Diog. Laertius]
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]
1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
Three branches of philosophy: first logic, second ethics, third physics (which ends with theology) [Chrysippus]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
The syntactic category is primary, and the ontological category is derivative [Frege, by Wright,C]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Never lose sight of the distinction between concept and object [Frege]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Frege was the first to give linguistic answers to non-linguistic questions [Frege, by Dummett]
Frege initiated linguistic philosophy, studying number through the sense of sentences [Frege, by Dummett]
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
Frege developed formal systems to avoid unnoticed assumptions [Frege, by Lavine]
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 / 3. Pure Reason
Thoughts have a natural order, to which human thinking is drawn [Frege, by Yablo]
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 / 5. Objectivity
Frege sees no 'intersubjective' category, between objective and subjective [Dummett on Frege]
Keep the psychological and subjective separate from the logical and objective [Frege]
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 / B. Laws of Thought / 2. Sufficient Reason
Chrysippus said the uncaused is non-existent [Chrysippus, by Plutarch]
2. Reason / D. Definition / 7. Contextual Definition
Originally Frege liked contextual definitions, but later preferred them fully explicit [Frege, by Dummett]
Nothing should be defined in terms of that to which it is conceptually prior [Frege, by Dummett]
2. Reason / E. Argument / 6. Conclusive Proof
Proof aims to remove doubts, but also to show the interdependence of truths [Frege]
2. Reason / F. Fallacies / 4. Circularity
Once it is clear that there is a God who is no deceiver, I conclude that clear and distinct perceptions must be true [Descartes]
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]
2. Reason / F. Fallacies / 8. Category Mistake / a. Category mistakes
You can't transfer external properties unchanged to apply to ideas [Frege]
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 / B. Truthmakers / 5. What Makes Truths / c. States of affairs make truths
We need to grasp not number-objects, but the states of affairs which make number statements true [Frege, by Wright,C]
3. Truth / B. Truthmakers / 10. Making Future Truths
The causes of future true events must exist now, so they will happen because of destiny [Chrysippus, by Cicero]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Graspable presentations are criteria of facts, and are molded according to their objects [Chrysippus, by Diog. Laertius]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
How could you ever know that the presentation is similar to the object? [Sext.Empiricus on Chrysippus]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius]
Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set is only defensible if it is the extension of an empty concept [Frege, by Burge]
It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett]
Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
A class is, for Frege, the extension of a concept [Frege, by Dummett]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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
Every proposition is either true or false [Chrysippus, by Cicero]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge]
The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
We can show that a concept is consistent by producing something which falls under it [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
To understand axioms you must grasp their logical power and priority [Frege, by Burge]
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 / e. Ordinal numbers
We cannot define numbers from the idea of a series, because numbers must precede that [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Nought is the number belonging to the concept 'not identical with itself' [Frege]
Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett]
For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined [Frege, by Chihara]
If objects exist because they fall under a concept, 0 is the object under which no objects fall [Frege, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege]
One is the Number which belongs to the concept "identical with 0" [Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Units can be equal without being identical [Tait on Frege]
Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki]
You can abstract concepts from the moon, but the number one is not among them [Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
Frege's 'isolation' could be absence of overlap, or drawing conceptual boundaries [Frege, by Koslicki]
Non-arbitrary division means that what falls under the concept cannot be divided into more of the same [Frege, by Koslicki]
Our concepts decide what is countable, as in seeing the leaves of the tree, or the foliage [Frege, by Koslicki]
A concept creating a unit must isolate and unify what falls under it [Frege]
Frege says counting is determining what number belongs to a given concept [Frege, by Koslicki]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Frege's one-to-one correspondence replaces well-ordering, because infinities can't be counted [Frege, by Lavine]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
The number of natural numbers is not a natural number [Frege, by George/Velleman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Arithmetical statements can't be axioms, because they are provable [Frege, by Burge]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Numbers need to be objects, to define the extension of the concept of each successor to n [Frege, by George/Velleman]
The number of F's is the extension of the second level concept 'is equipollent with F' [Frege, by Tait]
Frege showed that numbers attach to concepts, not to objects [Frege, by Wiggins]
Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts [Frege, by Tait]
Zero is defined using 'is not self-identical', and one by using the concept of zero [Frege, by Weiner]
Frege said logical predication implies classes, which are arithmetical objects [Frege, by Morris,M]
Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright on Frege]
Frege claims that numbers are objects, as opposed to them being Fregean concepts [Frege, by Wright,C]
Numbers are second-level, ascribing properties to concepts rather than to objects [Frege, by Wright,C]
For Frege, successor was a relation, not a function [Frege, by Dummett]
A cardinal number may be defined as a class of similar classes [Frege, by Russell]
Numbers are more than just 'second-level concepts', since existence is also one [Frege, by George/Velleman]
"Number of x's such that ..x.." is a functional expression, yielding a name when completed [Frege, by George/Velleman]
Frege gives an incoherent account of extensions resulting from abstraction [Fine,K on Frege]
For Frege the number of F's is a collection of first-level concepts [Frege, by George/Velleman]
Frege started with contextual definition, but then switched to explicit extensional definition [Frege, by Wright,C]
Each number, except 0, is the number of the concept of all of its predecessors [Frege, by Wright,C]
Frege's account of cardinals fails in modern set theory, so they are now defined differently [Dummett on Frege]
Frege's incorrect view is that a number is an equivalence class [Benacerraf on Frege]
The natural number n is the set of n-membered sets [Frege, by Yourgrau]
A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege]
A statement of number contains a predication about a concept [Frege]
If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege]
Frege's problem is explaining the particularity of numbers by general laws [Frege, by Burge]
Individual numbers are best derived from the number one, and increase by one [Frege]
'Exactly ten gallons' may not mean ten things instantiate 'gallon' [Rumfitt on Frege]
Numerical statements have first-order logical form, so must refer to objects [Frege, by Hodes]
The Number for F is the extension of 'equal to F' (or maybe just F itself) [Frege]
Numbers are objects because they partake in identity statements [Frege, by Bostock]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
'The number of Fs' is the extension (a collection of first-level concepts) of the concept 'equinumerous with F' [Frege, by George/Velleman]
Frege's cardinals (equivalences of one-one correspondences) is not permissible in ZFC [Frege, by Wolf,RS]
Hume's Principle fails to implicitly define numbers, because of the Julius Caesar [Frege, by Potter]
Frege thinks number is fundamentally bound up with one-one correspondence [Frege, by Heck]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on Frege]
'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor [Frege, by George/Velleman]
From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number? [Frege, by Friend]
Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension) [Frege, by Shapiro]
Fregean numbers are numbers, and not 'Caesar', because they correlate 1-1 [Frege, by Wright,C]
One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock]
Our definition will not tell us whether or not Julius Caesar is a number [Frege]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
If numbers can be derived from logic, then set theory is superfluous [Frege, by Burge]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If numbers are supposed to be patterns, each number can have many patterns [Frege]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Numbers seem to be objects because they exactly fit the inference patterns for identities [Frege]
Frege's platonism proposes that objects are what singular terms refer to [Frege, by Wright,C]
How can numbers be external (one pair of boots is two boots), or subjective (and so relative)? [Frege, by Weiner]
Identities refer to objects, so numbers must be objects [Frege, by Weiner]
Numbers are not physical, and not ideas - they are objective and non-sensible [Frege]
Numbers are objects, because they can take the definite article, and can't be plurals [Frege]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Frege's logicism aimed at removing the reliance of arithmetic on intuition [Frege, by Yourgrau]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
There is no physical difference between two boots and one pair of boots [Frege]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman]
Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman]
'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege]
The number 'one' can't be a property, if any object can be viewed as one or not one [Frege]
For science, we can translate adjectival numbers into noun form [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic is analytic [Frege, by Weiner]
Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman]
Frege offered a Platonist version of logicism, committed to cardinal and real numbers [Frege, by Hale/Wright]
Mathematics has no special axioms of its own, but follows from principles of logic (with definitions) [Frege, by Bostock]
Numbers are definable in terms of mapping items which fall under concepts [Frege, by Scruton]
Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion]
Arithmetic is analytic and a priori, and thus it is part of logic [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Frege only managed to prove that arithmetic was analytic with a logic that included set-theory [Quine on Frege]
Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects [Wright,C on Frege]
Why should the existence of pure logic entail the existence of objects? [George/Velleman on Frege]
Frege's belief in logicism and in numerical objects seem uncomfortable together [Hodes on Frege]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Frege was completing Bolzano's work, of expelling intuition from number theory and analysis [Frege, by Dummett]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Abstraction from things produces concepts, and numbers are in the concepts [Frege]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / e. Psychologism
Mental states are irrelevant to mathematics, because they are vague and fluctuating [Frege]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Affirmation of existence is just denial of zero [Frege]
7. Existence / A. Nature of Existence / 4. Abstract Existence
If abstracta are non-mental, quarks are abstracta, and yet chess and God's thoughts are mental [Rosen on Frege]
The equator is imaginary, but not fictitious; thought is needed to recognise it [Frege]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Chrysippus says action is the criterion for existence, which must be physical [Chrysippus, by Tieleman]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
Many of us find Frege's claim that truths depend on one another an obscure idea [Heck on Frege]
Parallelism is intuitive, so it is more fundamental than sameness of direction [Frege, by Heck]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Frege refers to 'concrete' objects, but they are no different in principle from abstract ones [Frege, by Dummett]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
There are simple and complex facts; the latter depend on further facts [Chrysippus, by Cicero]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Vagueness is incomplete definition [Frege, by Koslicki]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
For Frege, ontological questions are to be settled by reference to syntactic structures [Frege, by Wright,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / c. Commitment of predicates
Second-order quantifiers are committed to concepts, as first-order commits to objects [Frege, by Linnebo]
7. Existence / E. Categories / 3. Proposed Categories
Stoics categories are Substrate, Quality, Disposition, and Relation [Chrysippus, by Pasnau]
8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
'Ancestral' relations are derived by iterating back from a given relation [Frege, by George/Velleman]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Frege treats properties as a kind of function, and maybe a property is its characteristic function [Frege, by Smith,P]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Not all objects are spatial; 4 can still be an object, despite lacking spatial co-ordinates [Frege]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Frege says singular terms denote objects, numerals are singular terms, so numbers exist [Frege, by Hale]
Frege establishes abstract objects independently from concrete ones, by falling under a concept [Frege, by Dummett]
9. Objects / A. Existence of Objects / 3. Objects in Thought
For Frege, objects just are what singular terms refer to [Frege, by Hale/Wright]
Without concepts we would not have any objects [Frege, by Shapiro]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Frege's universe comes already divided into objects [Frege, by Koslicki]
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 / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Dion and Theon coexist, but Theon lacks a foot. If Dion loses a foot, he ousts Theon? [Chrysippus, by Philo of Alexandria]
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]
9. Objects / E. Objects over Time / 2. Objects that Change
Change of matter doesn't destroy identity - in Dion and Theon change is a condition of identity [Chrysippus, by Long/Sedley]
9. Objects / F. Identity among Objects / 1. Concept of Identity
The idea of a criterion of identity was introduced by Frege [Frege, by Noonan]
Frege's algorithm of identity is the law of putting equals for equals [Frege, by Quine]
9. Objects / F. Identity among Objects / 3. Relative Identity
Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett]
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 / 2. Understanding
To understand a thought you must understand its logical structure [Frege, by Burge]
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
Maybe there is only one certain fact, which is that nothing is certain [Descartes]
Descartes tried to model reason on maths instead of 'logos' [Roochnik on Descartes]
Labelling slightly doubtful things as false is irrational [Roochnik on Descartes]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
I must even exist if I am being deceived by something [Descartes]
The Cogito is a transcendental argument, not a piece of a priori knowledge [Rey on Descartes]
"I think therefore I am" is the absolute truth of consciousness [Sartre on Descartes]
"I am, I exist" is necessarily true every time I utter it or conceive it in my mind [Descartes]
Modern philosophy set the self-conscious ego in place of God [Descartes, by Feuerbach]
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]
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]
It is a precondition of the use of the word 'I' that I exist [Ayer on Descartes]
Maybe 'I' am not the thinker, but something produced by thought [Nietzsche on Descartes]
Autistic children seem to use the 'I' concept without seeing themselves as thinkers [Segal 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]
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]
The Cogito only works if you already understand what thought and existence are [Mersenne 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 / 1. Nature of the A Priori
For Frege a priori knowledge derives from general principles, so numbers can't be primitive [Frege]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Mathematicians just accept self-evidence, whether it is logical or intuitive [Frege]
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]
An a priori truth is one derived from general laws which do not require proof [Frege]
A truth is a priori if it can be proved entirely from general unproven laws [Frege]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
Frege tried to explain synthetic a priori truths by expanding the concept of analyticity [Frege, by Katz]
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
The wax is not perceived by the senses, but by the mind alone [Descartes]
Dogs can make the same judgements as us about variable things [Gassendi on Descartes]
We don't 'see' men in heavy clothes, we judge them to be men [Descartes]
We perceive objects by intellect, not by senses or imagination [Descartes]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuitions cannot be communicated [Frege, by Burge]
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 / B. Internal Justification / 4. Foundationalism / d. Rational foundations
Justifications show the ordering of truths, and the foundation is what is self-evident [Frege, by Jeshion]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Descartes can't begin again, because sceptics doubt cognitive processes as well as beliefs [Pollock/Cruz on Descartes]
Even if my body and objects are imaginary, there may be simpler things which are true [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]
It is prudent never to trust your senses if they have deceived you even once [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]
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 / C. Induction / 1. Induction
Induction is merely psychological, with a principle that it can actually establish laws [Frege]
In science one observation can create high probability, while a thousand might prove nothing [Frege]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Ideas are not spatial, and don't have distances between them [Frege]
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 / A. Nature of Mind / 7. Animal Minds
Dogs show reason in decisions made by elimination [Chrysippus, by Sext.Empiricus]
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 / 4. For Free Will
My capacity to make choices with my free will extends as far as any faculty ever could [Descartes]
Chrysippus allows evil to say it is fated, or even that it is rational and natural [Plutarch on Chrysippus]
16. Persons / F. Free Will / 5. Against Free Will
A swerve in the atoms would be unnatural, like scales settling differently for no reason [Chrysippus, by Plutarch]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Everything is fated, either by continuous causes or by a supreme rational principle [Chrysippus, by Diog. Laertius]
Chrysippus is wrong to believe in non-occurring future possibilities if he is a fatalist [Plutarch on Chrysippus]
16. Persons / F. Free Will / 6. Determinism / b. Fate
The Lazy Argument responds to fate with 'why bother?', but the bothering is also fated [Chrysippus, by Cicero]
When we say events are fated by antecedent causes, do we mean principal or auxiliary causes? [Chrysippus]
Fate is an eternal and fixed chain of causal events [Chrysippus]
16. Persons / F. Free Will / 7. Compatibilism
Destiny is only a predisposing cause, not a sufficient cause [Chrysippus, by Plutarch]
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 / 1. Thought
Thought is the same everywhere, and the laws of thought do not vary [Frege]
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 / 1. Concepts / a. Nature of concepts
Early Frege takes the extensions of concepts for granted [Frege, by Dummett]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
The ideas of God and of my self are innate in me [Descartes]
The idea of a supremely perfect being is within me, like the basic concepts of mathematics [Descartes]
I can think of innumerable shapes I have never experienced [Descartes]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are, precisely, the references of predicates [Frege, by Wright,C]
A concept is a non-psychological one-place function asserting something of an object [Frege, by Weiner]
Fregean concepts have precise boundaries and universal applicability [Frege, by Koslicki]
Psychological accounts of concepts are subjective, and ultimately destroy truth [Frege]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
A concept is a possible predicate of a singular judgement [Frege]
18. Thought / E. Abstraction / 1. Abstract Thought
Defining 'direction' by parallelism doesn't tell you whether direction is a line [Dummett on Frege]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Frege accepts abstraction to the concept of all sets equipollent to a given one [Tait on Frege]
18. Thought / E. Abstraction / 3. Abstracta by Ignoring
Frege himself abstracts away from tone and color [Yablo on Frege]
If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Frege's logical abstaction identifies a common feature as the maximal set of equivalent objects [Frege, by Dummett]
Frege's 'parallel' and 'direction' don't have the same content, as we grasp 'parallel' first [Yablo on Frege]
Frege put the idea of abstraction on a rigorous footing [Frege, by Fine,K]
Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K]
We create new abstract concepts by carving up the content in a different way [Frege]
You can't simultaneously fix the truth-conditions of a sentence and the domain of its variables [Dummett on Frege]
From basing 'parallel' on identity of direction, Frege got all abstractions from identity statements [Frege, by Dummett]
19. Language / A. Nature of Meaning / 7. Meaning Holism / a. Sentence meaning
Words in isolation seem to have ideas as meanings, but words have meaning in propositions [Frege]
Never ask for the meaning of a word in isolation, but only in the context of a proposition [Frege]
19. Language / D. Propositions / 1. Propositions
A proposition is what can be asserted or denied on its own [Chrysippus]
19. Language / E. Analyticity / 1. Analytic Propositions
A statement is analytic if substitution of synonyms can make it a logical truth [Frege, by Boghossian]
Frege considered analyticity to be an epistemic concept [Frege, by Shapiro]
19. Language / E. Analyticity / 2. Analytic Truths
All analytic truths can become logical truths, by substituting definitions or synonyms [Frege, by Rey]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Frege fails to give a concept of analyticity, so he fails to explain synthetic a priori truth that way [Katz on Frege]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
Passions are judgements; greed thinks money is honorable, and likewise drinking and lust [Chrysippus, by Diog. Laertius]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
The highest degree of morality performs all that is appropriate, omitting nothing [Chrysippus]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Stoics say that beauty and goodness are equivalent and linked [Chrysippus, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Fate initiates general causes, but individual wills and characters dictate what we do [Chrysippus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Human purpose is to contemplate and imitate the cosmos [Chrysippus]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Stoics say justice is a part of nature, not just an invented principle [Chrysippus, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Only nature is available to guide action and virtue [Chrysippus]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Live in agreement, according to experience of natural events [Chrysippus]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
Living happily is nothing but living virtuously [Chrysippus, by Plutarch]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
Pleasure is not the good, because there are disgraceful pleasures [Chrysippus, by Diog. Laertius]
Justice can be preserved if pleasure is a good, but not if it is the goal [Chrysippus, by Plutarch]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
There are shameful pleasures, and nothing shameful is good, so pleasure is not a good [Chrysippus, by Diog. Laertius]
23. Ethics / A. Egoism / 2. Hedonism
People need nothing except corn and water [Chrysippus, by Plutarch]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
All virtue is good, but not always praised (as in not lusting after someone ugly) [Chrysippus]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Chrysippus says virtue can be lost (though Cleanthes says it is too secure for that) [Chrysippus, by Diog. Laertius]
Chrysippus says nothing is blameworthy, as everything conforms with the best nature [Chrysippus, by Plutarch]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
Rational animals begin uncorrupted, but externals and companions are bad influences [Chrysippus, by Diog. Laertius]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Justice, the law, and right reason are natural and not conventional [Chrysippus, by Diog. Laertius]
25. Social Practice / E. Policies / 5. Education / b. Education principles
To learn something, you must know that you don't know [Frege]
25. Social Practice / F. Life Issues / 6. Animal Rights
We don't have obligations to animals as they aren't like us [Chrysippus, by Diog. Laertius]
Justice is irrelevant to animals, because they are too unlike us [Chrysippus, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
Covers are for shields, and sheaths for swords; likewise, all in the cosmos is for some other thing [Chrysippus]
Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
The later Stoics identified the logos with an air-fire compound, called 'pneuma' [Chrysippus, by Long]
Fire is a separate element, not formed with others (as was previously believed) [Chrysippus, by Stobaeus]
Stoics say earth, air, fire and water are the primary elements [Chrysippus, by Plutarch]
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]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
The laws of number are not laws of nature, but are laws of the laws of nature [Frege]
27. Natural Reality / D. Time / 1. Nature of Time / h. Presentism
The past and the future subsist, but only the present exists [Chrysippus, by Plutarch]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
The present does not exist, so our immediate experience is actually part past and part future [Chrysippus, by Plutarch]
Time is continous and infinitely divisible, so there cannot be a wholly present time [Chrysippus, by Stobaeus]
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
Stoics say that God the creator is the perfection of all animals [Chrysippus, by Diog. Laertius]
It is self-evident that deception is a natural defect, so God could not be a deceiver [Descartes]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
The origin of justice can only be in Zeus, and in nature [Chrysippus]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
Stoics teach that law is identical with right reason, which is the will of Zeus [Chrysippus, by Diog. Laertius]
The source of all justice is Zeus and the universal nature [Chrysippus]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
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]
Existence and God's essence are inseparable, like a valley and a mountain, or a triangle and its properties [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]
Descartes cannot assume that a most perfect being exists without contradictions [Leibniz on Descartes]
Existence is not a first-level concept (of God), but a second-level property of concepts [Frege, by Potter]
Because existence is a property of concepts the ontological argument for God fails [Frege]
We can never conceive of an infinite being [Gassendi on Descartes]
Existence is not a perfection; it is what makes perfection possible [Gassendi on Descartes]
29. Religion / B. Monotheistic Religion / 1. Monotheistic Religion
Stoics teach that God is a unity, variously known as Mind, or Fate, or Jupiter [Chrysippus, by Diog. Laertius]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
Death can't separate soul from body, because incorporeal soul can't unite with body [Chrysippus]
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
There is a rationale in terrible disasters; they are useful to the whole, and make good possible [Chrysippus]
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]