46 ideas
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can. |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132) | |
| A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature. |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages. |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic? |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148) | |
| A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system. |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them? |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142) | |
| A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers? |
| 3942 | I do not believe in the existence of anything, if I see no reason to believe it [Berkeley] |
| Full Idea: It is to me a sufficient reason not to believe the existence of anything, if I see no reason for believing it. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.205) | |
| A reaction: This may just be a reasonable application of Ockham's Razor, but I fear that Berkeley painted himself into corner by demanding too many 'reasons' for everything. |
| 3952 | I know that nothing inconsistent can exist [Berkeley] |
| Full Idea: I know that nothing inconsistent can exist. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.224) | |
| A reaction: Fine, but the problem is to assess with confidence what is inconsistent. Human imagination seems to be the test for existence. But what else can we do? |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146) | |
| A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers. |
| 3959 | There is no other substance, in a strict sense, than spirit [Berkeley] |
| Full Idea: There is no other substance, in a strict sense, than spirit. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.257) | |
| A reaction: A nice clear statement of idealism. Why is he so confident of making this assertion. Note the addition, though, of 'in a strict' sense. He is presenting an epistemological claim as if it was an ontological one. |
| 3946 | A thing is shown to be impossible if a contradiction is demonstrated within its definition [Berkeley] |
| Full Idea: A thing is shown to be impossible when a repugnancy is demonstrated between the ideas comprehended in its definition. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.214) | |
| A reaction: The problem is always that imagination is needed to see the 'repugnancy', and that is relative and limited. |
| 3958 | Since our ideas vary when the real things are said to be unchanged, they cannot be true copies [Berkeley] |
| Full Idea: As our ideas are perpetually varied, without any change in the supposed real things, it necessarily follows that they cannot all be true copies of them. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.239) | |
| A reaction: This seems a good objection to any direct or naïve realist view. Colours get darker as the sun goes down, and objects become blurred as they recede into the distance. |
| 3943 | If existence is perceived directly, by which sense; if indirectly, how is it inferred from direct perception? [Berkeley] |
| Full Idea: Either you perceive the being of matter immediately, or mediately; if immediately, pray inform me by which of the senses you perceive it; if mediately, let me know by what reasonings it is inferred from those things which you perceive immediately. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.208) | |
| A reaction: A problem for strong empiricists, and he is right that existence can't be directly perceived, but it seems a good explanation (for which some reason can be shown), and supports a more rationalist view. |
| 3931 | Sensible objects are just sets of sensible qualities [Berkeley] |
| Full Idea: Sensible things are nothing else but so many sensible qualities. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.154) | |
| A reaction: As it stands this is phenomenalism, but Berkeley eventually votes for idealism. He should acknowledge possible sensations which aren't actually experienced. |
| 5192 | Berkeley did not deny material things; he merely said they must be defined through sensations [Berkeley, by Ayer] |
| Full Idea: Berkeley did not (as we are commonly told) deny the reality of material things. ..What Berkeley discovered was that material things must be defined in terms of sense-contents. | |
| From: report of George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by A.J. Ayer - Language,Truth and Logic Ch.2 | |
| A reaction: This seems to be a rather debatable attempt to claim that Berkeley was a phenomenalist (like Ayer), rather than an idealist. Try ideas 3942, 3944, 3945, 3957, 3959 in this database. |
| 5174 | Berkeley needed a phenomenalist account of the self, as well as of material things [Ayer on Berkeley] |
| Full Idea: The considerations which make it necessary, as Berkeley saw, to give a phenomenalist account of material things, make it necessary also, as Berkeley did not see, to give a phenomenalist account of the self. | |
| From: comment on George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by A.J. Ayer - Language,Truth and Logic Ch.7 | |
| A reaction: Phenomenalism involves 'possible' experiences as well as actual ones. That could add up to quite a rich and stable account of the self, as opposed to Hume's notorious introspection, which only saw an actual shifting 'bundle' of experience. |
| 1103 | 'To be is to be perceived' is a simple confusion of experience with its objects [Russell on Berkeley] |
| Full Idea: Berkeley thinks 'to be is to be perceived', and only God provides continuity. He has simply confused the experience of perception with the thing being perceived. Ideas have content. | |
| From: comment on George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by Bertrand Russell - Problems of Philosophy |
| 6403 | For Berkelely, reality is ideas and a community of minds, including God's [Berkeley, by Grayling] |
| Full Idea: Berkeley's thesis is that reality ultimately consists of a community of minds and their ideas; one of the minds (God) is infinite, and causes most of the ideas. | |
| From: report of George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: I think Russell nicely pinpoints what is wrong with Berekely, which is that he confuses ideas with their contents. If I think about my garden, the garden is real (probably), which is the content, and they idea is just a way of thinking. |
| 3936 | Time is measured by the succession of ideas in our minds [Berkeley] |
| Full Idea: Time is measured by the succession of ideas in our minds. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.172) | |
| A reaction: But we distinguish between subjective time (which flies when you are having fun), and objective time, judged from observation of clocks and nature. |
| 3930 | There is no such thing as 'material substance' [Berkeley] |
| Full Idea: That there is no such thing as what philosophers call 'material substance', I am seriously persuaded. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.150) | |
| A reaction: I'm sorry, but I can't do with this. It confuses epistemology with ontology. Ontology is a matter of judgement; epistemology is the evidence on which we base it. We know sensations; personally I judge that there are material substances. What about you? |
| 3939 | I conceive a tree in my mind, but I cannot prove that its existence can be conceived outside a mind [Berkeley] |
| Full Idea: I may conceive in my own thoughts the idea of a tree, but that is all. And this is far from proving that I can conceive it existing out of the minds of all spirits. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.184) | |
| A reaction: If Berkeley has based a world view on this point, then his mistake is to require a 'proof'. Aristotle explained why you can't prove everything (not to mention Gödel). |
| 3945 | There is nothing in nature which needs the concept of matter to explain it [Berkeley] |
| Full Idea: I challenge you to show me that thing in nature which needs matter to explain or account for it. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.212) | |
| A reaction: I disagree. Physics is a good theory for explaining why we have perceptions. Failing that there is not even a glimmer of an explanation of our experiences. |
| 3947 | Perceptions are ideas, and ideas exist in the mind, so objects only exist in the mind [Berkeley] |
| Full Idea: Wood, fire, water, flesh, iron, are things that I know, and only known because I perceive them by my senses; these are immediately perceived, and so are ideas; ideas cannot exist without the mind; their existence consists therefore in being perceived. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.220) | |
| A reaction: This makes no distinction between an idea and its content. Berkeley fails to grasp the weird concept of intentionality. Trees aren't in my head, just because I think about them! |
| 3933 | Primary qualities (such as shape, solidity, mass) are held to really exist, unlike secondary qualities [Berkeley] |
| Full Idea: Sensible qualities are by philosophers divided into primary and secondary; the former are extension, figure, solidity, gravity, motion and rest, which exist really in bodies. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.169) | |
| A reaction: A crucial distinction, which anti-realists such as Berkeley end up denying. I think it is a good distinction, and philosophers should fight to preserve it. |
| 3934 | A mite would see its own foot as large, though we would see it as tiny [Berkeley] |
| Full Idea: A mite must be supposed to see his own foot as a body of some considerable dimension, though they appear to you scarcely discernible. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.170) | |
| A reaction: Berkeley is confused. Hot is secondary, but temperature is primary. Bigness is secondary, size primay. Midgets and tall people don't disagree over the size of a table. |
| 3935 | The apparent size of an object varies with its distance away, so that can't be a property of the object [Berkeley] |
| Full Idea: As we approach to or recede from an object, the visible extension varies, being at one distance ten or a hundred times greater than at another; doth it not follow that it is not really inherent in the object? | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.171) | |
| A reaction: Berkeley is confused, because he is too literally empirical. Qualities are not self-evidently primary or secondary, but are judged so after comparisons (e.g. with testimony, or with the other senses). |
| 3937 | 'Solidity' is either not a sensible quality at all, or it is clearly relative to our senses [Berkeley] |
| Full Idea: By 'solidity' either you do not mean any sensible quality, and so it is beside our enquiry; or if you do, it must be hardness or resistance, which are plainly relative to our senses. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.173) | |
| A reaction: Berkeley fails to recognise that a quality can have primary and secondary aspects (hot/high temperature). He is right that primary qualities are not directly perceived. They are judgements. |
| 3940 | Distance is not directly perceived by sight [Berkeley] |
| Full Idea: Distance is not properly and immediately perceived by sight. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.186) | |
| A reaction: Interestingly, if secondary qualities are not strictly perceptions of the object, and primary qualities are not directly perceived, then we don't seem to perceive anything at all. Perhaps we should drop the concept of 'perception'? |
| 3957 | Immediate objects of perception, which some treat as appearances, I treat as the real things themselves [Berkeley] |
| Full Idea: Those immediate objects of perception, which, according to you, are only appearances of things, I take to be the real things themselves. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.237) | |
| A reaction: If that is a judgement, which it seems to be, it is a strange one. Realists offer a much better explanation of perceptions. |
| 3953 | Real things and imaginary or dreamed things differ because the latter are much fainter [Berkeley] |
| Full Idea: The difference between real things, and chimeras formed by the imagination, or the visions of a dream, is that the latter are faint and indistinct. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.225) | |
| A reaction: In Hume this becomes 'impressions' and 'ideas'. It does raise the question of WHY some ideas are not as faint as others. |
| 3938 | Geometry is originally perceived by senses, and so is not purely intellectual [Berkeley] |
| Full Idea: Figures and extension, being originally perceived by sense, do not belong to pure intellect. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.176) | |
| A reaction: Is the square root of 169 less 'pure' in my mind if I learn it from laying out bricks instead of by thinking about numbers? Confusion of how you learn with what you learn? |
| 3944 | It is possible that we could perceive everything as we do now, but nothing actually existed. [Berkeley] |
| Full Idea: We might perceive all things just as we do now, though there was no matter in the world. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.209) | |
| A reaction: An old Greek argument. Now we have an explanation of experience, but we wouldn't if nothing existed. Which doesn't prove that anything exists. Is some explanation always preferable to none? Cf. religion. |
| 3932 | A hot hand and a cold hand will have different experiences in the same tepid water [Berkeley] |
| Full Idea: Suppose now one of your hands hot, and the other cold, and that they are both at once put into the same vessel of water, in an intermediate state; will not the water seem cold to one hand, and warm to the other? | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.158) | |
| A reaction: A nice clear example of how some relativism must be acknowledged. It feels hot, but what is its temperature in degrees C? |
| 3948 | Experience tells me that other minds exist independently from my own [Berkeley] |
| Full Idea: It is plain that other minds have an existence exterior to my mind, since I find them by experience to be independent of it. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.220) | |
| A reaction: This is a surprising claim from Berkeley. If trees only exist through their experience in my mind, why don't other minds exist in the same way? |
| 3941 | How can that which is unthinking be a cause of thought? [Berkeley] |
| Full Idea: How can that which is unthinking be a cause of thought? | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.203) | |
| A reaction: Presumably, though, he thinks that thought can cause 'that which is unthinking' to move'. He likes one half of the interaction problem (which supports dualism), but avoids the other half. |
| 5374 | Berkeley probably used 'idea' to mean both the act of apprehension and the thing apprehended [Russell on Berkeley] |
| Full Idea: Berkeley seems to have confused the colour of the thing apprehended with the act of apprehension; probably either of these would have been called an 'idea' be Berkeley. | |
| From: comment on George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by Bertrand Russell - Problems of Philosophy | |
| A reaction: If we are saying that Berkeley's error was entirely verbal, there is a chicken-and-egg problem. He was an idealist, so he wouldn't have thought that there were two separate concepts behind the word 'idea'. Russell merely asserts that there are. |
| 3954 | Immorality is not in the action, but in the deviation of the will from moral law [Berkeley] |
| Full Idea: Sin or moral turpitude doth not consist in the outward physical action or motion, but in the internal deviation of the will from the laws of reason and religion. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.227) | |
| A reaction: A Kantian view (that the only good thing is a good will). It is a very empiricist (and anti-Greek) view to deny that actions have any intrinsic value. |
| 3950 | There must be a God, because all sensible things must be perceived by him [Berkeley] |
| Full Idea: I immediately and necessarily conclude the being of a God, because all sensible things must be perceived by him. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.198) | |
| A reaction: Daft. This contradicts Berkeley's whole empiricist position, that existence depends on known experience. Who knows whether God is thinking about trees? |
| 3951 | There must be a God, because I and my ideas are not independent [Berkeley] |
| Full Idea: From the dependency I find in myself and my ideas, I do by an act of reason necessarily infer the existence of a God. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.222) | |
| A reaction: No. Hume answered this, by showing how big abstract ideas are built up from experience. This is a future bishop's wish-fulfilment. |
| 3949 | It has been proved that creation is the workmanship of God, from its beauty and usefulness [Berkeley] |
| Full Idea: Divines and philosophers have proved beyond all controversy, from the beauty and usefulness of the several parts of creation, that it was the workmanship of God. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.198) | |
| A reaction: Not convincing. Beauty is probably a sublimation of sexual desire (or an echo of the human mind in the external world, in music), and utility is relative to homo sapiens, I presume. |
| 3956 | People are responsible because they have limited power, though this ultimately derives from God [Berkeley] |
| Full Idea: Thinking rational beings, in the production of motions, have the use of limited powers, ultimately derived from God, but immediately under the direction of their own wills, which is sufficient to entitle them to all the guilt of their own actions. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.228) | |
| A reaction: An episcopal evasion. A classic attempt to have cake and eat it. Either God is in charge or he isn't. |
| 3955 | If sin is not just physical, we don't consider God the origin of sin because he causes physical events [Berkeley] |
| Full Idea: If sin doth not consist of purely physical actions, the making God a cause of all such actions, is not making him the author of sin. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.227) | |
| A reaction: An equivocation. If responsibility resides in consciousness, God is presumably conscious, and we can judge the events he causes. |