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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Philosophical Essay on Probability' and 'The Principles of Human Knowledge'

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53 ideas

3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
An idea can only be like another idea [Berkeley]
     Full Idea: An idea can be like nothing but an idea.
     From: George Berkeley (The Principles of Human Knowledge [1710], §08), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 43 'Mean'
     A reaction: I take this to be relevant to the correspondence theory, but also to be one of Berkeley's best observations. We understand ideas, but we can't map them onto the world (because they are not maps!). ...But then how is one idea like another? Hm.
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
     Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
     Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do?
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
     Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
     Full Idea: 'Analysis' is the theory of the real numbers.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
     Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
     Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'!
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
     Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
     Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2)
     A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
     Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight?
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
     Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6)
     A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start.
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
     Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7)
     A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds..
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
     Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9)
     A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind?
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
     Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3)
     A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations.
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
     Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
     Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator.
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
     Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5)
     A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
     Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity.
7. Existence / A. Nature of Existence / 4. Abstract Existence
Abstract ideas are impossible [Berkeley]
     Full Idea: We have, I think, shown the impossibility of Abstract Ideas.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §21)
     A reaction: He achieves this by an attack on universals, offering the nominalist view that there are only particulars. There seems to be a middle ground, where universals don't actually exist, but there are settled conventional abstraction, beyond particulars.
7. Existence / D. Theories of Reality / 4. Anti-realism
Berkeley does believe in trees, but is confused about what trees are [Berkeley, by Cameron]
     Full Idea: I think that we should consider Berkeley as believing in trees; we should simply claim that he has false beliefs about what trees are.
     From: report of George Berkeley (The Principles of Human Knowledge [1710]) by Ross P. Cameron - Truthmakers, Realism and Ontology 'Realism'
     A reaction: I can be realist about spots before my eyes, or a ringing in my ears, but be (quite sensibly) unsure about what they are, so Cameron's suggestion sounds plausible.
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Universals do not have single meaning, but attach to many different particulars [Berkeley]
     Full Idea: There is no such thing as one precise and definite signification annexed to any general name, they all signifying indifferently a great number of particular ideas.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §18)
     A reaction: The term 'red' may be assigned to a range of colours, but we also recognise the precision of 'that red'. For 'electron', or 'three', or 'straight', the particulars are indistinguishable.
No one will think of abstractions if they only have particular ideas [Berkeley]
     Full Idea: He that knows he has no other than particular ideas, will not puzzle himself in vain to find out and conceive the abstract idea annexed to any name.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §24)
     A reaction: A nice point against universals. Maybe gods only think in particulars. One particular on its own could never suggest a universal. How are you going to spot patterns if you don't think in universals? Maths needs patterns.
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Universals do not have any intrinsic properties, but only relations to particulars [Berkeley]
     Full Idea: Universality, so far as I can comprehend it, does not consist in the absolute, positive nature or conception of anything, but in the relation it bears to the particulars signified or represented by it.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §15)
     A reaction: I always think it is a basic principle in philosophy that some sort of essence must precede relations (and functions). What is it about universals that enables them to have a relation to particulars?
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
     Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity.
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Material substance is just general existence which can have properties [Berkeley]
     Full Idea: The most accurate philosophers have no other meaning annexed to 'material substance' but the idea of being in general, together with the relative notion of its supporting accidents.
     From: George Berkeley (The Principles of Human Knowledge [1710], §17)
     A reaction: This is part of the attack on Aristotle's concept of 'substance', and is a nice way of dissolving the concept. 'Substance' will never reappear in physics, but modern philosopher have returned to it, as possibly inescapable in metaphysics.
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
A die has no distinct subject, but is merely a name for its modes or accidents [Berkeley]
     Full Idea: To me a die seems to be nothing distinct from those things which are termed its modes or accidents. And to say a die is hard, extended and square is not to attribute those qualities to a distinct subject, but only an explication of the word 'die'.
     From: George Berkeley (The Principles of Human Knowledge [1710], n 49)
     A reaction: This is apparently a reaction to Locke, and a final rejection of the medieval idea of a 'substance'. Unfortunately it leaves Berkeley with a 'bundle' view of objects (a typical empiricist account), which is even worse.
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
Perception is existence for my table, but also possible perception, by me or a spirit [Berkeley]
     Full Idea: The table I write on I say exists, that is, I see and feel it; and if I were out of my study I should say it existed - meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it.
     From: George Berkeley (The Principles of Human Knowledge [1710], §3)
     A reaction: Berkeley is always (understandably) labelled as an 'idealist', but this seems to be what we call 'phenomenalism', because it allows possible experiences as well as actual ones. See Ideas 5170 and 6522.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
The only substance is spirit, or that which perceives [Berkeley]
     Full Idea: It is evident that there is not any other Substance than spirit, or that which perceives.
     From: George Berkeley (The Principles of Human Knowledge [1710], §7)
     A reaction: Weird. To say that this is 'evident' seems to be begging the question. Why should he assume that there is nothing more to reality than his perception of it? He seems strangely unimaginative.
The 'esse' of objects is 'percipi', and they can only exist in minds [Berkeley]
     Full Idea: The absolute existence of unthinking things with no relation to their being perceived is unintelligible to me; their 'esse' is 'percipi', nor is it possible they should have any existence out of the minds or thinking things which perceive them.
     From: George Berkeley (The Principles of Human Knowledge [1710], §3)
     A reaction: "Esse est percipi" (to be is to be perceived) is the well-known slogan associated with Berkeley. I cannot see how Berkeley can assert that the separate existence of things is impossible. He is the classic confuser of epistemology and ontology.
When I shut my eyes, the things I saw may still exist, but in another mind [Berkeley]
     Full Idea: When I shut my eyes, the things I saw may still exist, but it must be in another mind.
     From: George Berkeley (The Principles of Human Knowledge [1710], §90)
     A reaction: This strikes me as ridiculous. What kind of theory says that a table goes out of existence when someone forgets to look at it for a moment, but is then recreated in identical form? Epistemology is not ontology.
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
No one can, by abstraction, conceive extension and motion of bodies without sensible qualities [Berkeley]
     Full Idea: I desire any one to reflect and try whether he can, by any abstraction of thought, conceive the extension and motion of a body without any sensible qualities.
     From: George Berkeley (The Principles of Human Knowledge [1710], §10)
     A reaction: The rather geometrical view of objects found in Descartes and Russell is an attempt to do this. I don't think the fact that we can't really achieve it matters much. We divide primary from secondary qualities in our understanding, not in experience.
Motion is in the mind, since swifter ideas produce an appearance of slower motion [Berkeley]
     Full Idea: Is it not reasonable to say that motion is not without the mind, since if the succession of ideas in the mind become swifter the motion, it is acknowledged, shall appear slower without any alteration in any external object.
     From: George Berkeley (The Principles of Human Knowledge [1710], §14)
     A reaction: An intriguing argument, based on what is now the principle of slow-motion photography. Fast minds slow down movement, like great tennis players. By what right does Berkeley say that the external subject is unaltered?
Figure and extension seem just as dependent on the observer as heat and cold [Berkeley]
     Full Idea: If heat and cold are only affections of the mind (since the same body seems cold to one hand and warm to the other), why may we not argue that figure and extension also appear different to the same eye at different stations?
     From: George Berkeley (The Principles of Human Knowledge [1710], §14)
     A reaction: If the assessment of the qualities of an object is entirely a matter of our experiences of it, there is no denying Berkeley on this. However, judgement goes beyond experience, into speculations, inferences, and explanations.
12. Knowledge Sources / B. Perception / 3. Representation
Berkeley's idealism resulted from fear of scepticism in representative realism [Robinson,H on Berkeley]
     Full Idea: It was fear of scepticism based upon representative realism that motivated Berkeley's idealism.
     From: comment on George Berkeley (The Principles of Human Knowledge [1710]) by Howard Robinson - Perception II.1
     A reaction: Personally I side with Russell, who accepts representative realism, and also accepts that some degree of scepticism is unavoidable, but without getting excited about it. The key to everything is to be a 'fallibilist' about knowledge.
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Knowledge is of ideas from senses, or ideas of the mind, or operations on sensations [Berkeley]
     Full Idea: The objects of knowledge are either ideas imprinted on the senses, or passions and operations of the mind, or ideas (formed by memory and imagination) compounding, dividing or barely representing the original perceptions.
     From: George Berkeley (The Principles of Human Knowledge [1710], §1)
     A reaction: This is the germ of Hume's 'associations' (Idea 2189). There is not much room here for synthetic a priori knowledge, as the a priori part seems to merely know the mind. Most of Russell's epistemology is contained in the last part of the sentence.
13. Knowledge Criteria / C. External Justification / 7. Testimony
The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
     Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite.
     From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8
     A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony.
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
Berkeley's idealism gives no grounds for believing in other minds [Reid on Berkeley]
     Full Idea: I can find no principle in Berkeley's system, which affords me even probable ground to conclude that there are other intelligent beings, like myself.
     From: comment on George Berkeley (The Principles of Human Knowledge [1710]) by Thomas Reid - Essays on Intellectual Powers 2: Senses 10
     A reaction: I agree, which means that Berkeley's position seems to entail solipsism, unless God is the Cartesian deus ex machina who rescues him from this wall of ignorance.
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
I know other minds by ideas which are referred by me to other agents, as their effects [Berkeley]
     Full Idea: The knowledge I have of other spirits is not immediate, as is the knowledge of my ideas; but depending on the intervention of ideas, by me referred to agents or spirits distinct from myself, as effects or concomitant signs.
     From: George Berkeley (The Principles of Human Knowledge [1710], §145)
     A reaction: This strikes me as gross intellectual dishonesty, since the argument Berkeley uses to assert other minds could equally be used to assert the existence of tables ('by me referred to agents distinct from myself, as effects'). Be a solipsist or a realist.
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
If animals have ideas, and are not machines, they must have some reason [Berkeley]
     Full Idea: If the brutes have any ideas at all, and are not bare machines (as some would have them), we cannot deny them to have some reason.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §11)
     A reaction: It seems possible to imagine a low level of mind, where a few ideas (or concepts) float around, but hardly anything worth the name of reason. However, a Darwinian view suggests that concepts must bestow an advantage, so the two go together.
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Berkeley replaced intentionality with an anti-abstractionist imagist theory of thought [Berkeley, by Robinson,H]
     Full Idea: By Berkeley - with his anti-abstractionism and imagist theory of thought - the classical sense-datum conception was firmly established, and intentionality had disappeared as an intrinsic property, not only of perceptual states, but of all mental contents.
     From: report of George Berkeley (The Principles of Human Knowledge [1710]) by Howard Robinson - Perception 1.6
     A reaction: Intentionality was originally a medieval concept, and was revived by Brentano in the late nineteenth century. Nowadays intentionality is taken for granted, but I still suspect that we could drop it, and talk of nothing but brain states caused by reality.
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
The mind creates abstract ideas by considering qualities separated from their objects [Berkeley]
     Full Idea: We are told that the mind being able to consider each quality of things singly, or abstracted from those other qualities with which it is united, does by that means frame to itself abstract ideas.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §7)
     A reaction: A helpful explanation of 'abstract' ideas. Berkeley gives colour and movement as examples. Fodor suggests that abstraction is the key strategy in empiricist epistemology. The difficulty is to decide whether the qualities are natural or conventional.
I can only combine particulars in imagination; I can't create 'abstract' ideas [Berkeley]
     Full Idea: Whether others can abstract their ideas, they best can tell. For myself, I find I have a faculty of imagining, or representing to myself, only the idea of those particular things I have perceived, and of compounding and dividing them.
     From: George Berkeley (The Principles of Human Knowledge [1710], 10)
     A reaction: He is admitting mixing experiences, but always particulars, never abstract. His examples are 'man' and 'motion'. Compare Aristotle Idea 9067. Berkeley is, I think, trapped in a false imagistic view of thought. My image of Plato blurs young and old.
16. Persons / D. Continuity of the Self / 7. Self and Thinking
Ideas are perceived by the mind, soul or self [Berkeley]
     Full Idea: The thing which knows or perceives ideas is what I call mind, spirit, soul or myself.
     From: George Berkeley (The Principles of Human Knowledge [1710], §2)
     A reaction: The interest here is in making no distinction between 'mind' and 'self', which seems to ally Berkeley with Locke's view of personal identity, as continuity of consciousness. The addition of 'soul' tries to connect Locke to Christian thought.
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]
     Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes.
     From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Language is presumably for communication, and names stand for ideas [Berkeley]
     Full Idea: It is a received opinion that language has no other end but the communicating our ideas, and that every significant name stands for an idea.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §19)
     A reaction: This attitude to language has been widely discredited, partly by the observation that 'idea' is very ambiguous, and partly by the fans of meaning-as-use. Truth conditions seem to be ideas, and so are speaker's intentions.
19. Language / D. Propositions / 4. Mental Propositions
I can't really go wrong if I stick to wordless thought [Berkeley]
     Full Idea: So long as I confine my thoughts to my own ideas divested of words, I do not see how I can easily be mistaken.
     From: George Berkeley (The Principles of Human Knowledge [1710], Intro §22)
     A reaction: I think it was one of the great errors of twentieth century philosophy to say that Berkeley cannot do this, because thought needs language. Personally I think language lags along behind most our thinking, tidying up the mess. I believe in propositions.
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley]
     Full Idea: How matter should operate on a spirit, or produce any idea in it, is what no philosopher will pretend to explain; it is therefore evident there can be no use of matter in natural philosophy.
     From: George Berkeley (The Principles of Human Knowledge [1710], §50)
     A reaction: An intriguing argument for idealism, which starts in Cartesian dualism, but then discards the physical world because of the notorious interaction problem. Of course, if he had thought that matter and spirit were one (Spinoza) the problem vanishes.
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley]
     Full Idea: That food nourishes, sleep refreshes, and fire warms us; all this we know, not by discovering any necessary connexion between our ideas, but only by the observation of the settled laws of nature.
     From: George Berkeley (The Principles of Human Knowledge [1710], §31)
     A reaction: Hume is famous for this idea, but it is found in Hobbes too (Idea 2364), and is the standard empiricist view of causation. The word 'settled' I take to imply that the laws are contingent, because they could become unsettled at any time.
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
The laws of nature are mental regularities which we learn by experience [Berkeley]
     Full Idea: The set rules or established methods wherein the Mind we depend on excites in us the ideas of sense, are called the 'laws of nature'; and these we learn by experience, which teaches us that such and such ideas are attended with certain other ideas.
     From: George Berkeley (The Principles of Human Knowledge [1710], 33)
     A reaction: He observes that the ideas of sense are more regular than other mental events, and attributes the rules to an Author. He is giving the standard empirical Humean view, with his own quirky idealist slant.
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
If properties and qualities arise from an inward essence, we will remain ignorant of nature [Berkeley]
     Full Idea: An inducement to pronouncing ourselves ignorant of the nature of things is the opinion that everything includes within itself the cause of its properties; or that there is in each object an inward essence which is the source whence its qualities flow.
     From: George Berkeley (The Principles of Human Knowledge [1710], §102)
     A reaction: This remains a good objection to essentialism - that while it remains quite a plausible picture of how nature operates, it makes the task of understanding nature hopeless. We can grasp imposed regular laws, but not secret inner essences.
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
All motion is relative, so a single body cannot move [Berkeley]
     Full Idea: There cannot be any motion other than relative; …if there was one only body in being it could not possibly move.
     From: George Berkeley (The Principles of Human Knowledge [1710], §112)
     A reaction: This seems to agree with with Leibniz in denying the Newton-Clarke idea of absolute space. See Idea 2100. Suppose there were two bodies racing towards one another, when one of them suddenly vanished?
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
I cannot imagine time apart from the flow of ideas in my mind [Berkeley]
     Full Idea: Whenever I attempt to frame a simple idea of time, abstracted from the succession of ideas in my mind, which flows uniformly and is participated in by all beings, I am lost and embrangled in inextricable difficulties.
     From: George Berkeley (The Principles of Human Knowledge [1710], §98)
     A reaction: 'Embrangled'! A nice statement of the idealist view of time, as entirely mental. I know what he means. However, surely he can manage to imagine a movement which continues when he shuts he eyes? Try blinking during a horse race.
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
Particular evils are really good when linked to the whole system of beings [Berkeley]
     Full Idea: Those particular things which, considered in themselves, appear to be evil, have the nature of good, when considered as linked with the whole system of beings.
     From: George Berkeley (The Principles of Human Knowledge [1710], §153)
     A reaction: This wildly contradicts the rest of Berkeley's philosophy, which is strictly empiricist, and rests wholly on actual experience. What experience does he have of the 'whole system of beings', and its making evil into actual good?