Combining Philosophers

All the ideas for Lucretius, Gottlob Frege and PG

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611 ideas

1. Philosophy / B. History of Ideas / 3. Greek-English Lexicon
Agathon: good [PG]
Aisthesis: perception, sensation, consciousness [PG]
Aitia / aition: cause, explanation [PG]
Akrasia: lack of control, weakness of will [PG]
Aletheia: truth [PG]
Anamnesis: recollection, remembrance [PG]
Ananke: necessity [PG]
Antikeimenon: object [PG]
Apatheia: unemotional [PG]
Apeiron: the unlimited, indefinite [PG]
Aphairesis: taking away, abstraction [PG]
Apodeixis: demonstration [PG]
Aporia: puzzle, question, anomaly [PG]
Arche: first principle, the basic [PG]
Arete: virtue, excellence [PG]
Chronismos: separation [PG]
Diairesis: division [PG]
Dialectic: dialectic, discussion [PG]
Dianoia: intellection [cf. Noesis] [PG]
Diaphora: difference [PG]
Dikaiosune: moral goodness, justice [PG]
Doxa: opinion, belief [PG]
Dunamis: faculty, potentiality, capacity [PG]
Eidos: form, idea [PG]
Elenchos: elenchus, interrogation [PG]
Empeiron: experience [PG]
Energeia: employment, actuality, power? [PG]
Enkrateia: control [PG]
Entelecheia: entelechy, having an end [PG]
Epagoge: induction, explanation [PG]
Episteme: knowledge, understanding [PG]
Epithumia: appetite [PG]
Ergon: function [PG]
Eristic: polemic, disputation [PG]
Eros: love [PG]
Eudaimonia: flourishing, happiness, fulfilment [PG]
Genos: type, genus [PG]
Hexis: state, habit [PG]
Horismos: definition [PG]
Hule: matter [PG]
Hupokeimenon: subject, underlying thing [cf. Tode ti] [PG]
Kalos / kalon: beauty, fineness, nobility [PG]
Kath' hauto: in virtue of itself, essentially [PG]
Kinesis: movement, process [PG]
Kosmos: order, universe [PG]
Logos: reason, account, word [PG]
Meson: the mean [PG]
Metechein: partaking, sharing [PG]
Mimesis: imitation, fine art [PG]
Morphe: form [PG]
Noesis: intellection, rational thought [cf. Dianoia] [PG]
Nomos: convention, law, custom [PG]
Nous: intuition, intellect, understanding [PG]
Orexis: desire [PG]
Ousia: substance, (primary) being, [see 'Prote ousia'] [PG]
Pathos: emotion, affection, property [PG]
Phantasia: imagination [PG]
Philia: friendship [PG]
Philosophia: philosophy, love of wisdom [PG]
Phronesis: prudence, practical reason, common sense [PG]
Physis: nature [PG]
Praxis: action, activity [PG]
Prote ousia: primary being [PG]
Psuche: mind, soul, life [PG]
Sophia: wisdom [PG]
Sophrosune: moderation, self-control [PG]
Stoicheia: elements [PG]
Sullogismos: deduction, syllogism [PG]
Techne: skill, practical knowledge [PG]
Telos: purpose, end [PG]
Theoria: contemplation [PG]
Theos: god [PG]
Ti esti: what-something-is, essence [PG]
Timoria: vengeance, punishment [PG]
To ti en einai: essence, what-it-is-to-be [PG]
To ti estin: essence [PG]
Tode ti: this-such, subject of predication [cf. hupokeimenon] [PG]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / a. Ancient chronology
323 (roughly): Euclid wrote 'Elements', summarising all of geometry [PG]
1000 (roughly): Upanishads written (in Sanskrit); religious and philosophical texts [PG]
750 (roughly): the Book of Genesis written by Hebrew writers [PG]
586: eclipse of the sun on the coast of modern Turkey was predicted by Thales of Miletus [PG]
570: Anaximander flourished in Miletus [PG]
563: the Buddha born in northern India [PG]
540: Lao Tzu wrote 'Tao Te Ching', the basis of Taoism [PG]
529: Pythagoras created his secretive community at Croton in Sicily [PG]
500: Heraclitus flourishes at Ephesus, in modern Turkey [PG]
496: Confucius travels widely, persuading rulers to be more moral [PG]
472: Empedocles persuades his city (Acragas in Sicily) to become a democracy [PG]
450 (roughly): Parmenides and Zeno visit Athens from Italy [PG]
445: Protagoras helps write laws for the new colony of Thurii [PG]
436 (roughly): Anaxagoras is tried for impiety, and expelled from Athens [PG]
170 (roughly): Marcus Aurelius wrote his private stoic meditations [PG]
-200 (roughly): Sextus Empiricus wrote a series of books on scepticism [PG]
263: Porphyry began to study with Plotinus in Rome [PG]
310: Christianity became the official religion of the Roman empire [PG]
387: Ambrose converts Augustine to Christianity [PG]
523: Boethius imprisoned at Pavia, and begins to write [PG]
529: the emperor Justinian closes all the philosophy schools in Athens [PG]
427: Gorgias visited Athens as ambassador for Leontini [PG]
399: Socrates executed (with Plato absent through ill health) [PG]
387 (roughly): Plato returned to Athens, and founded the Academy [PG]
387 (roughly): Aristippus the Elder founder a hedonist school at Cyrene [PG]
367: the teenaged Aristotle came to study at the Academy [PG]
360 (roughly): Diogenes of Sinope lives in a barrel in central Athens [PG]
347: death of Plato [PG]
343: Aristotle becomes tutor to 13 year old Alexander (the Great) [PG]
335: Arisotle founded his school at the Lyceum in Athens [PG]
330 (roughly): Chuang Tzu wrote his Taoist book [PG]
322: Aristotle retired to Chalcis, and died there [PG]
307 (roughly): Epicurus founded his school at the Garden in Athens [PG]
301 (roughly): Zeno of Citium founded Stoicism at the Stoa Poikile in Athens [PG]
261: Cleanthes replaced Zeno as head of the Stoa [PG]
229 (roughly): Chrysippus replaced Cleanthes has head of the Stoa [PG]
157 (roughly): Carneades became head of the Academy [PG]
85: most philosophical activity moves to Alexandria [PG]
78: Cicero visited the stoic school on Rhodes [PG]
60 (roughly): Lucretius wrote his Latin poem on epicureanism [PG]
65: Seneca forced to commit suicide by Nero [PG]
80: the discourses of the stoic Epictetus are written down [PG]
1. Philosophy / C. History of Philosophy / 3. Earlier European Philosophy / a. Earlier European chronology
1090: Anselm publishes his proof of the existence of God [PG]
622 (roughly): Mohammed writes the Koran [PG]
642: Arabs close the philosophy schools in Alexandria [PG]
910 (roughly): Al-Farabi wrote Arabic commentaries on Aristotle [PG]
1015 (roughly): Ibn Sina (Avicenna) writes a book on Aristotle [PG]
1115: Abelard is the chief logic teacher in Paris [PG]
1166: Ibn Rushd (Averroes) wrote extensive commentaries on Aristotle [PG]
1266: Aquinas began writing 'Summa Theologica' [PG]
1280: after his death, the teaching of Aquinas becomes official Dominican doctrine [PG]
1328: William of Ockham decides the Pope is a heretic, and moves to Munich [PG]
1347: the Church persecutes philosophical heresies [PG]
1470: Marsilio Ficino founds a Platonic Academy in Florence [PG]
1513: Machiavelli wrote 'The Prince' [PG]
1543: Copernicus publishes his heliocentric view of the solar system [PG]
1580: Montaigne publishes his essays [PG]
1600: Giordano Bruno was burned at the stake in Rome [PG]
1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / a. Later European chronology
1619: Descartes's famous day of meditation inside a stove [PG]
1620: Bacon publishes 'Novum Organum' [PG]
1633: Galileo convicted of heresy by the Inquisition [PG]
1641: Descartes publishes his 'Meditations' [PG]
1650: death of Descartes, in Stockholm [PG]
1651: Hobbes publishes 'Leviathan' [PG]
1662: the Port Royal Logic is published [PG]
1665: Spinoza writes his 'Ethics' [PG]
1676: Leibniz settled as librarian to the Duke of Brunswick [PG]
1687: Newton publishes his 'Principia Mathematica' [PG]
1690: Locke publishes his 'Essay' [PG]
1697: Bayle publishes his 'Dictionary' [PG]
1713: Berkeley publishes his 'Three Dialogues' [PG]
1734: Voltaire publishes his 'Philosophical Letters' [PG]
1739: Hume publishes his 'Treatise' [PG]
1762: Rousseau publishes his 'Social Contract' [PG]
1781: Kant publishes his 'Critique of Pure Reason' [PG]
1785: Reid publishes his essays defending common sense [PG]
1798: the French Revolution [PG]
1807: Hegel publishes his 'Phenomenology of Spirit' [PG]
1818: Schopenhauer publishes his 'World as Will and Idea' [PG]
1840: Kierkegaard is writing extensively in Copenhagen [PG]
1843: Mill publishes his 'System of Logic' [PG]
1848: Marx and Engels publis the Communist Manifesto [PG]
1859: Darwin publishes his 'Origin of the Species' [PG]
1861: Mill publishes 'Utilitarianism' [PG]
1867: Marx begins publishing 'Das Kapital' [PG]
1. Philosophy / C. History of Philosophy / 5. Modern Philosophy / a. Modern philosophy chronology
1879: Peirce taught for five years at Johns Hopkins University [PG]
1879: Frege invents predicate logic [PG]
1892: Frege's essay 'Sense and Reference' [PG]
1884: Frege publishes his 'Foundations of Arithmetic' [PG]
1885: Nietzsche completed 'Thus Spake Zarathustra' [PG]
1888: Dedekind publishes axioms for arithmetic [PG]
1890: James published 'Principles of Psychology' [PG]
1895 (roughly): Freud developed theories of the unconscious [PG]
1900: Husserl began developing Phenomenology [PG]
1953: Wittgenstein's 'Philosophical Investigations' [PG]
1956: Place proposed mind-brain identity [PG]
1962: Kuhn's 'Structure of Scientific Revolutions' [PG]
1967: Putnam proposed functionalism of the mind [PG]
1971: Rawls's 'A Theory of Justice' [PG]
1972: Kripke publishes 'Naming and Necessity' [PG]
1975: Singer publishes 'Animal Rights' [PG]
1975: Putnam published his Twin Earth example [PG]
1986: David Lewis publishes 'On the Plurality of Worlds' [PG]
1903: Moore published 'Principia Ethica' [PG]
1904: Dewey became professor at Columbia University [PG]
1908: Zermelo publishes axioms for set theory [PG]
1910: Russell and Whitehead begin publishing 'Principia Mathematica' [PG]
1912: Russell meets Wittgenstein in Cambridge [PG]
1921: Wittgenstein's 'Tractatus' published [PG]
1927: Heidegger's 'Being and Time' published [PG]
1930: Frank Ramsey dies at 27 [PG]
1931: Gödel's Incompleteness Theorems [PG]
1933: Tarski's theory of truth [PG]
1942: Camus published 'The Myth of Sisyphus' [PG]
1943: Sartre's 'Being and Nothingness' [PG]
1945: Merleau-Ponty's 'Phenomenology of Perception' [PG]
1947: Carnap published 'Meaning and Necessity' [PG]
1950: Quine's essay 'Two Dogmas of Empiricism' [PG]
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
Note that "is" can assert existence, or predication, or identity, or classification [PG]
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]
Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege]
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 / 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]
There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner]
2. Reason / B. Laws of Thought / 1. Laws of Thought
We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher]
2. Reason / D. Definition / 2. Aims of Definition
A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett]
Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C]
2. Reason / D. Definition / 3. Types of Definition
A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
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]
We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
2. Reason / D. Definition / 10. Stipulative Definition
Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
2. Reason / D. Definition / 11. Ostensive Definition
Only what is logically complex can be defined; what is simple must be pointed to [Frege]
2. Reason / E. Argument / 6. Conclusive Proof
Proof aims to remove doubts, but also to show the interdependence of truths [Frege]
We must be clear about every premise and every law used in a proof [Frege]
2. Reason / F. Fallacies / 1. Fallacy
Fallacies are errors in reasoning, 'formal' if a clear rule is breached, and 'informal' if more general [PG]
2. Reason / F. Fallacies / 3. Question Begging
Question-begging assumes the proposition which is being challenged [PG]
2. Reason / F. Fallacies / 6. Fallacy of Division
What is true of a set is also true of its members [PG]
2. Reason / F. Fallacies / 7. Ad Hominem
The Ad Hominem Fallacy criticises the speaker rather than the argument [PG]
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 / 1. Truth
The concept of truth was originated by the senses [Lucretius]
3. Truth / A. Truth Problems / 2. Defining Truth
The word 'true' seems to be unique and indefinable [Frege]
3. Truth / A. Truth Problems / 5. Truth Bearers
Frege was strongly in favour of taking truth to attach to propositions [Frege, by Dummett]
3. Truth / A. Truth Problems / 6. Verisimilitude
Truth does not admit of more and less [Frege]
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 / C. Correspondence Truth / 3. Correspondence Truth critique
There cannot be complete correspondence, because ideas and reality are quite different [Frege]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Minimal theories of truth avoid ontological commitment to such things as 'facts' or 'reality' [PG]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge]
Since every definition is an equation, one cannot define equality itself [Frege]
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Frege did not think of himself as working with sets [Frege, by Hart,WD]
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]
The null set is indefensible, because it collects nothing [Frege, by Burge]
It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett]
A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege]
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]
Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
The laws of logic are boundless, so we want the few whose power contains the others [Frege]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
In 1879 Frege developed second order logic [Frege, by Putnam]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Frege frequently expressed a contempt for language [Frege, by Dummett]
Logic not only proves things, but also reveals logical relations between them [Frege]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner]
Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA]
For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn]
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]
'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege]
We can treat designation by a few words as a proper name [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
A Fregean proper name has a sense determining an object, instead of a concept [Frege, by Sainsbury]
People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander' [Frege]
Any object can have many different names, each with a distinct sense [Frege]
Proper name in modal contexts refer obliquely, to their usual sense [Frege, by Gibbard]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
The meaning of a proper name is the designated object [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Frege ascribes reference to incomplete expressions, as well as to singular terms [Frege, by Hale]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
If sentences have a 'sense', empty name sentences can be understood that way [Frege, by Sawyer]
It is a weakness of natural languages to contain non-denoting names [Frege]
In a logically perfect language every well-formed proper name designates an object [Frege]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 1. Quantification
A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
For Frege the variable ranges over all objects [Frege, by Tait]
Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege]
Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
Frege introduced quantifiers for generality [Frege, by Weiner]
Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
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 / H. Proof Systems / 1. Proof Systems
Proof theory began with Frege's definition of derivability [Frege, by Prawitz]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge]
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Frege, by Jacquette]
Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Frege, by Sawyer]
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]
Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
A truth can be an axiom in one system and not in another [Frege]
The truth of an axiom must be independently recognisable [Frege]
5. Theory of Logic / L. Paradox / 1. Paradox
Monty Hall Dilemma: do you abandon your preference after Monty eliminates one of the rivals? [PG]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
To create order in mathematics we need a full system, guided by patterns of inference [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Quantity is inconceivable without the idea of addition [Frege]
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 / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
Real numbers are ratios of quantities [Frege, by Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
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]
Nought is the number belonging to the concept 'not identical with itself' [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
One is the Number which belongs to the concept "identical with 0" [Frege]
We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
You can abstract concepts from the moon, but the number one is not among them [Frege]
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]
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]
Counting rests on one-one correspondence, of numerals to objects [Frege]
Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege]
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 / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
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]
If principles are provable, they are theorems; if not, they are axioms [Frege]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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]
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]
A cardinal number may be defined as a class of similar classes [Frege, by Russell]
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]
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 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]
In a number-statement, something is predicated of a concept [Frege]
If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege]
There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman]
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]
A number is a class of classes of the same cardinality [Frege, by Dummett]
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]
Our concepts recognise existing relations, they don't change them [Frege]
Numbers are not real like the sea, but (crucially) they are still objective [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]
Geometry appeals to intuition as the source of its axioms [Frege]
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]
The naïve view of number is that it is like a heap of things, or maybe a property of a heap [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
Logicism shows that no empirical truths are needed to justify arithmetic [Frege, by George/Velleman]
Arithmetic is analytic [Frege, by Weiner]
Arithmetic must be based on logic, because of its total generality [Frege, by Jeshion]
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]
The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
Arithmetic is analytic and a priori, and thus it is part of logic [Frege]
Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge]
Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend]
My Basic Law V is a law of pure logic [Frege]
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
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]
Late in life Frege abandoned logicism, and saw the source of arithmetic as geometrical [Frege, by Chihara]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism fails to recognise types of symbols, and also meta-games [Frege, by Brown,JR]
Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]
Only applicability raises arithmetic from a game to a science [Frege]
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
Existence is not a first-order property, but the instantiation of a property [Frege, by Read]
Affirmation of existence is just denial of zero [Frege]
7. Existence / A. Nature of Existence / 2. Types of Existence
Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Frege's logic showed that there is no concept of being [Frege, by Scruton]
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
Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo]
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 / C. Structure of Existence / 7. Abstract/Concrete / b. Levels of abstraction
If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
A fact is a thought that is true [Frege]
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]
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]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale]
8. Modes of Existence / D. Universals / 1. Universals
We can't get a semantics from nouns and predicates referring to the same thing [Frege, by Dummett]
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]
Logical objects are extensions of concepts, or ranges of values of functions [Frege]
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]
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett]
Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett]
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 / 3. Unity Problems / e. Vague objects
The first demand of logic is of a sharp boundary [Frege]
Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]
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]
Frege was asking how identities could be informative [Frege, by Perry]
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 / 5. Self-Identity
Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA]
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 / B. Possibility / 6. Probability
Everything has a probability, something will happen, and probabilities add up [PG]
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge]
To understand a thought you must understand its logical structure [Frege, by Burge]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
If reality is just what we perceive, we would have no need for a sixth sense [PG]
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
Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge]
Mathematicians just accept self-evidence, whether it is logical or intuitive [Frege]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge]
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 / 5. A Priori Synthetic
If my team is losing 3-1, I have synthetic a priori knowledge that they need two goals for a draw [PG]
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 / D. Empiricism / 4. Pro-Empiricism
If the senses are deceptive, reason, which rests on them, is even worse [Lucretius]
The senses are much the best way to distinguish true from false [Lucretius]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuitions cannot be communicated [Frege, by Burge]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
The only possible standard for settling doubts is the foundation of the senses [Lucretius]
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 / C. External Justification / 2. Causal Justification
Psychological logic can't distinguish justification from causes of a belief [Frege]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
Most supposed delusions of the senses are really misinterpretations by the mind [Lucretius]
14. Science / B. Scientific Theories / 1. Scientific Theory
The building blocks contain the whole contents of a discipline [Frege]
14. Science / C. Induction / 1. Induction
Even simple facts are hard to believe at first hearing [Lucretius]
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 / 1. Mind / d. Location of mind
The mind is in the middle of the breast, because there we experience fear and joy [Lucretius]
The mind is a part of a man, just like a hand or an eye [Lucretius]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
The separate elements and capacities of a mind cannot be distinguished [Lucretius]
16. Persons / F. Free Will / 2. Sources of Free Will
The actions of the mind are not determinate and passive, because atoms can swerve [Lucretius]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Only bodies can touch one another [Lucretius]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
The earth is and always has been an insentient being [Lucretius]
Particles may have sensation, but eggs turning into chicks suggests otherwise [Lucretius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
The mind moves limbs, wakes the body up, changes facial expressions, which involve touch [Lucretius]
Lions, foxes and deer have distinct characters because their minds share in their bodies [Lucretius]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
You needn't be made of laughing particles to laugh, so why not sensation from senseless seeds? [Lucretius]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
Maybe a mollusc's brain events for pain ARE of the same type (broadly) as a human's [PG]
Maybe a frog's brain events for fear are functionally like ours, but not phenomenally [PG]
18. Thought / A. Modes of Thought / 1. Thought
Thought is the same everywhere, and the laws of thought do not vary [Frege]
Many people have the same thought, which is the component, not the private presentation [Frege]
We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege]
Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett]
A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
We don't judge by combining subject and concept; we get a concept by splitting up a judgement [Frege]
18. Thought / A. Modes of Thought / 9. Indexical Thought
Thoughts about myself are understood one way to me, and another when communicated [Frege]
18. Thought / B. Mechanics of Thought / 5. Mental Files
We need definitions to cram retrievable sense into a signed receptacle [Frege]
We use signs to mark receptacles for complex senses [Frege]
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 / 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]
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
A concept is a function whose value is always a truth-value [Frege]
'The concept "horse"' denotes a concept, yet seems also to denote an object [Frege, by McGee]
Frege equated the concepts under which an object falls with its properties [Frege, by Dummett]
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
A concept is a possible predicate of a singular judgement [Frege]
As I understand it, a concept is the meaning of a grammatical predicate [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
If we abstract 'from' two cats, the units are not black or white, or cats [Tait on Frege]
Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege]
How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege]
The modern account of real numbers detaches a ratio from its geometrical origins [Frege]
Frege himself abstracts away from tone and color [Yablo 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]
Fregean abstraction creates concepts which are equivalences between initial items [Frege, by Fine,K]
Frege put the idea of abstraction on a rigorous footing [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]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Frege said concepts were abstract entities, not mental entities [Frege, by Putnam]
Number-abstraction somehow makes things identical without changing them! [Frege]
If we abstract the difference between two houses, they don't become the same house [Frege]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam]
Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege]
Identity baffles psychologists, since A and B must be presented differently to identify them [Frege]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Frege failed to show when two sets of truth-conditions are equivalent [Frege, by Potter]
A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A]
The meaning (reference) of a sentence is its truth value - the circumstance of it being true or false [Frege]
19. Language / A. Nature of Meaning / 6. Meaning as Use
A sign won't gain sense just from being used in sentences with familiar components [Frege]
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]
We understand new propositions by constructing their sense from the words [Frege]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
Holism says all language use is also a change in the rules of language [Frege, by Dummett]
19. Language / B. Reference / 1. Reference theories
The reference of a word should be understood as part of the reference of the sentence [Frege]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
Frege's Puzzle: from different semantics we infer different reference for two names with the same reference [Frege, by Fine,K]
Frege's 'sense' is ambiguous, between the meaning of a designator, and how it fixes reference [Kripke on Frege]
Every descriptive name has a sense, but may not have a reference [Frege]
Frege started as anti-realist, but the sense/reference distinction led him to realism [Frege, by Benardete,JA]
The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense [Frege]
In maths, there are phrases with a clear sense, but no actual reference [Frege]
We are driven from sense to reference by our desire for truth [Frege]
Senses can't be subjective, because propositions would be private, and disagreement impossible [Frege]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
Expressions always give ways of thinking of referents, rather than the referents themselves [Frege, by Soames]
19. Language / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
19. Language / C. Assigning Meanings / 4. Compositionality
Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A]
'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A]
'Sense' gives meaning to non-referring names, and to two expressions for one referent [Frege, by Margolis/Laurence]
Frege was the first to construct a plausible theory of meaning [Frege, by Dummett]
Earlier Frege focuses on content itself; later he became interested in understanding content [Frege, by Dummett]
Frege divided the meaning of a sentence into sense, force and tone [Frege, by Dummett]
Frege uses 'sense' to mean both a designator's meaning, and the way its reference is determined [Kripke on Frege]
Frege explained meaning as sense, semantic value, reference, force and tone [Frege, by Miller,A]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
For all the multiplicity of languages, mankind has a common stock of thoughts [Frege]
Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege]
A thought is the sense expressed by a sentence, and is what we prove [Frege]
A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
A sentence is only a thought if it is complete, and has a time-specification [Frege]
The parts of a thought map onto the parts of a sentence [Frege]
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]
'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner]
19. Language / E. Analyticity / 2. Analytic Truths
All analytic truths can become logical truths, by substituting definitions or synonyms [Frege, by Rey]
Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A]
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]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
One man's meat is another man's poison [Lucretius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Our bodies weren't created to be used; on the contrary, their creation makes a use possible [Lucretius]
22. Metaethics / B. Value / 2. Values / e. Death
The dead are no different from those who were never born [Lucretius]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Nature only wants two things: freedom from pain, and pleasure [Lucretius]
23. Ethics / E. Utilitarianism / 4. Unfairness
Utilitarianism seems to justify the discreet murder of unhappy people [PG]
25. Social Practice / E. Policies / 5. Education / b. Education principles
To learn something, you must know that you don't know [Frege]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Nature runs the universe by herself without the aid of gods [Lucretius]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There can be no centre in infinity [Lucretius]
The universe must be limitless, since there could be nothing outside to limit it [Lucretius]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
Everything is created and fed by nature from atoms, and they return to atoms in death [Lucretius]
If an object is infinitely subdivisible, it will be the same as the whole universe [Lucretius]
In downward motion, atoms occasionally swerve slightly for no reason [Lucretius]
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]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
Nothing can break the binding laws of eternity [Lucretius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Atoms move themselves [Lucretius]
If there were no space there could be no movement, or even creation [Lucretius]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / d. Entropy
It is quicker to break things up than to assemble them [Lucretius]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
We can only sense time by means of movement, or its absence [Lucretius]
27. Natural Reality / E. Cosmology / 1. Cosmology
This earth is very unlikely to be the only one created [Lucretius]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
Nothing can be created by divine power out of nothing [Lucretius]
27. Natural Reality / G. Biology / 2. Life
Life is Movement, Respiration, Sensation, Nutrition, Excretion, Reproduction, Growth (MRS NERG) [PG]
28. God / A. Divine Nature / 4. Divine Contradictions
How could God know there wasn't an unknown force controlling his 'free' will? [PG]
An omniscient being couldn't know it was omniscient, as that requires information from beyond its scope of knowledge [PG]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner]
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]
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
If matter wasn't everlasting, everything would have disappeared by now [Lucretius]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
The universe can't have been created by gods, because it is too imperfect [Lucretius]
28. God / C. Attitudes to God / 3. Deism
Gods are tranquil and aloof, and have no need of or interest in us [Lucretius]
28. God / C. Attitudes to God / 5. Atheism
Why does Jupiter never hurl lightning from a blue sky? [Lucretius]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Spirit is mortal [Lucretius]
For a separated spirit to remain sentient it would need sense organs attached to it [Lucretius]
An immortal mind couldn't work harmoniously with a mortal body [Lucretius]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The mind is very small smooth particles, which evaporate at death [Lucretius]
If spirit is immortal and enters us at birth, why don't we remember a previous existence? [Lucretius]