50 ideas
| 1708 | In "Callias is just/not just/unjust", which of these are contraries? [Aristotle] |
| Full Idea: Take, for example, "Callias is just", "Callias is not just", and "Callias is unjust"; which of these are contraries? | |
| From: Aristotle (On Interpretation [c.330 BCE], 23a31) |
| 18405 | A 'teepee' argument has several mutually supporting planks to it [Cappelen/Dever] |
| Full Idea: In a 'teepee' argument, a number of argumentative planks intersupport each other. No plank is sufficiently strong to establish the position, but each lends credibility to the others because there is the appearance of a unified phenomenon. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 01.5) | |
| A reaction: To attack it, they say, you have to identify the separate planks of the argument. It is a moot point whether the teepee might be so imprecise that it is better described as 'coherence'. There is a background support, as well as the planks. |
| 1703 | It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle] |
| Full Idea: It is not necessary for a sea-battle to take place tomorrow, nor for one not to take place tomorrow - though it is necessary for one to take place OR not take place tomorrow. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a30) |
| 1704 | Statements are true according to how things actually are [Aristotle] |
| Full Idea: Statements are true according to how things actually are. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a33) |
| 22272 | Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle] |
| Full Idea: When Aristotle moved from basic name+verb (in 'De Interpretatione') to noun+noun logic...names had to be treated as special cases, so that 'Socrates' is treated as short for 'everything that is Socrates'. | |
| From: comment on Aristotle (On Interpretation [c.330 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Supp' | |
| A reaction: Just the sort of rewriting that Russell introduced for definite descriptions. 'Twas ever the logicians' fate to shoehorn ordinary speech into awkward containers. |
| 9405 | Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle] |
| Full Idea: Square of Opposition: horizontals - 'contraries' can't both be true, and 'subcontraries' can't both be false; verticals - 'subalternatives' have downwards-only implication; diagonals - 'contradictories' have opposite truth values. | |
| From: Aristotle (On Interpretation [c.330 BCE], Ch.12-13) | |
| A reaction: This is still used in modern discussion (e.g. by Stalnaker against Kripke), and there is a modal version of it (Fitting and Mendelsohn p.7). Corners read: 'All F are G', 'No F are G', 'Some F are G' and 'Some F are not G'. |
| 9728 | Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 1: 'It is necessary that P' and 'It is not possible that not P' are the contraries (not both true) of 'It is necessary that not P' and 'It is not possible that P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12a) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9729 | Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 2: 'It is not necessary that not P' and 'It is possible that P' are the subcontraries (not both false) of 'It is not necessary that P' and 'It is possible that not P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12b) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9730 | Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 3: 'It is necessary that P' and 'It is not possible that not P' are the contradictories (different truth values) of 'It is not necessary that P' and 'It is possible that not P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12c) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9731 | Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 4: 'It is necessary that not P' and 'It is not possible that P' are the contradictories (different truth values) of 'It is not necessary that not P' and 'It is possible that P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12d) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9732 | Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 5: 'It is necessary that P' and 'It is not possible that not P' are the subalternatives (first implies second) of 'It is not necessary that not P' and 'It is possible that P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12e) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 9733 | Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn] |
| Full Idea: Modal Square of Opposition 6: 'It is necessary that not P' and 'It is not possible that P' are the subalternatives (first implies second) of 'It is not necessary that P' and 'It is possible that not P'. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12f) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4 |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| Full Idea: The axiom of choice has a troubled history, but is now standard in mathematics. It could be replaced with a principle of comprehension for functions), or one could omit the variables ranging over functions. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], n 3) |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| Full Idea: Early study of first-order logic revealed a number of important features. Gödel showed that there is a complete, sound and effective deductive system. It follows that it is Compact, and there are also the downward and upward Löwenheim-Skolem Theorems. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| Full Idea: Some authors argue that second-order logic (with standard semantics) is not logic at all, but is a rather obscure form of mathematics. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| Full Idea: If the goal of logical study is to present a canon of inference, a calculus which codifies correct inference patterns, then second-order logic is a non-starter. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be because it is not 'complete'. However, moves like plural quantification seem aimed at capturing ordinary language inferences, so the difficulty is only that there isn't a precise 'calculus'. |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| Full Idea: Informally, logical consequence is sometimes defined in terms of the meanings of a certain collection of terms, the so-called 'logical terminology'. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: This seems to be a compositional account, where we build a full account from an account of the atomic bits, perhaps presented as truth-tables. |
| 21593 | In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson] |
| Full Idea: Unlike Aristotle, Stoics did not reject Bivalence for future contingencies; it is true or false that there will be a sea-fight tomorrow. | |
| From: report of Aristotle (On Interpretation [c.330 BCE], 19a31) by Timothy Williamson - Vagueness 1.2 | |
| A reaction: I'd never quite registered this simple account of the sea-fight. As Williamson emphasises, one should not lightly reject the principle of bivalence. Has Aristotle entered a slippery slope? Stoics disagreed with Aristotle. |
| 1701 | A prayer is a sentence which is neither true nor false [Aristotle] |
| Full Idea: A prayer is a sentence which is neither true nor false. | |
| From: Aristotle (On Interpretation [c.330 BCE], 17a01) |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| Full Idea: Second-order variables can range over properties, sets, or relations on the items in the domain-of-discourse, or over functions from the domain itself. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| Full Idea: Upward Löwenheim-Skolem: if a set of first-order formulas is satisfied by a domain of at least the natural numbers, then it is satisfied by a model of at least some infinite cardinal. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| Full Idea: Both of the Löwenheim-Skolem Theorems fail for second-order languages with a standard semantics | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.3.2) |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorem is usually taken as a sort of defect (often thought to be inevitable) of the first-order logic. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.4) | |
| A reaction: [He is quoting Wang 1974 p.154] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| Full Idea: Downward Löwenheim-Skolem: a finite or denumerable set of first-order formulas that is satisfied by a model whose domain is infinite is satisfied in a model whose domain is the natural numbers | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| Full Idea: Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.1) | |
| A reaction: [he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point? |
| 1706 | Non-existent things aren't made to exist by thought, because their non-existence is part of the thought [Aristotle] |
| Full Idea: It is not true to say that what is not, since it is thought about, is something that is; for what is thought about it is not that it is, but that it is not. | |
| From: Aristotle (On Interpretation [c.330 BCE], 21a31) | |
| A reaction: At least there has been one philosopher who was quite clear about the distinction between a thought and what the thought is about (its content). Often forgotten! |
| 1707 | Maybe necessity and non-necessity are the first principles of ontology [Aristotle] |
| Full Idea: Perhaps the necessary and non-necessary are first principles of everything's either being or not being. | |
| From: Aristotle (On Interpretation [c.330 BCE], 23a18) |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| Full Idea: In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably. | |
| From: Stewart Shapiro (Higher-Order Logic [2001], 2.2.1) | |
| A reaction: Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties. |
| 18422 | Prioprioception focuses on your body parts, not on your self, or indexicality [Cappelen/Dever] |
| Full Idea: Proprioception is not focused single-mindedly on the self, but is focused on a number of objects - the component bodily parts that belong to the self. There is no obvious need for a concept of the self, or of indexicality. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 07.2) |
| 18425 | We can acquire self-knowledge with mirrors, not just with proprioception and introspection [Cappelen/Dever] |
| Full Idea: Imagine a being that learns everything about itself by watching itself in mirrors, rather than by proprioception and introspection. Surely it can get wet in a storm, even though allegedly distinctive routes of self-knowledge are not available to it? | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 09.3) | |
| A reaction: [compressed] |
| 18421 | Proprioception is only immune from error if you are certain that it represents the agent [Cappelen/Dever] |
| Full Idea: The guarantee of immunity from error in prioprioception is only as strong as the guarantee that proprioception only ever represents the proprioceiving agent. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 07.1) | |
| A reaction: This is part of an interesting and sustained attack on the idea that self-knowledge is immune from error. They are thinking of science-fictiony situations where I am wired up to experience your leg movement. My experiences usually track me, that's all. |
| 18419 | Folk Functionalism is a Ramsification of our folk psychology [Cappelen/Dever] |
| Full Idea: According to Folk Functionalism, mental states are theoretically defined by Ramsifying on our folk-psychological theory. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 06.2) |
| 18404 | It is assumed that indexical content is needed to represent the perspective of perception [Cappelen/Dever] |
| Full Idea: Because our perceptual states typically represent the world as seen from a perspective, it is sometimes thought that some distinctively indexical kind of content is needed to characterise those states. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 01.4) | |
| A reaction: They are summarising this view precisely so that they can oppose it, and I think they are right. |
| 18426 | All information is objective, and purely indexical information is not much use [Cappelen/Dever] |
| Full Idea: Fundamentally, all information is objective information. ...[176] What we want is fully portable information, and information that co-ordinates on the world, rather than on us, is best suited for the task. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 10) | |
| A reaction: I agree entirely with their thesis. We just pick up information about ourselves, such as who and where we are, which is just like equivalent information about other people. It is isn't a special type of information. |
| 18427 | If some of our thought is tied to its context, it will be hard to communicate it [Cappelen/Dever] |
| Full Idea: It is bad news if some of our contents are essentially tied to particular contexts. ...If information needs to be assessed relative to some ur-context, later recipients won't know what to do with it. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 10) |
| 18428 | You don't remember your house interior just from an experienced viewpoint [Cappelen/Dever] |
| Full Idea: When you recall the look of the inside of your house ....where things are relative to one another is what persists in memory, not where they were relative to you when seen. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 10) | |
| A reaction: This seems to be a very telling example, though you could postulate some system which converts perspectival input into objective information. But why bother? We seek objective information, not perspectives. |
| 18429 | Our beliefs and desires are not organised around ourselves, but around the world [Cappelen/Dever] |
| Full Idea: Our view on the world is not primarily a view from a perspective. Our beliefs and desires are not organized around us. They are instead organized around the world itself. Our view is a view from everywhere. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 10) | |
| A reaction: Slipping in the claim that our desires are also organised around the world is not quite as persuasive as the claim about beliefs. If you want to draw a freehand straight line, focus on the far end of it. The world will guide your hand. |
| 18407 | Indexicality is not significantly connected to agency [Cappelen/Dever] |
| Full Idea: There are no interesting or distinctive explanatory connections between indexicality and agency. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 01.8) |
| 2337 | For Aristotle meaning and reference are linked to concepts [Aristotle, by Putnam] |
| Full Idea: In 'De Interpretatione' Aristotle laid out an enduring theory of reference and meaning, in which we understand a word or any other sign by associating that word with a concept. This concept determines what the word refers to. | |
| From: report of Aristotle (On Interpretation [c.330 BCE]) by Hilary Putnam - Representation and Reality 2 p.19 | |
| A reaction: Sounds right to me, despite all this Wittgensteinian stuff about beetles in boxes. When you meet a new technical term in philosophy, you must struggle to fully grasp the concept it proposes. |
| 18413 | Fregeans can't agree on what 'senses' are [Cappelen/Dever] |
| Full Idea: There is little agreement among Fregeans about what senses are. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 04.5) | |
| A reaction: I don't take this to be sufficient grounds for dismissing Fregean senses. When we look into the workings of the linguistic mind, there seems little prospect of clarity or agreement. |
| 18417 | Possible worlds accounts of content are notoriously coarse-grained [Cappelen/Dever] |
| Full Idea: Possible worlds accounts of content are notoriously coarse-grained. They fail to distinguish between logical or mathematical truths, ..between metaphysical equivalences, ..between coreferentials, ..and between indexicals and non-indexicals. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 05.5) | |
| A reaction: [A nice summary, very compressed] |
| 18408 | Indexicals are just non-constant in meaning, and don't involve any special concepts [Cappelen/Dever] |
| Full Idea: Once the non-constant characters of expressions has been characterised, there is no further need for additional devices like 'first-person concepts' or 'demonstrative concepts'. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 01.7) | |
| A reaction: This seems to me to be a wonderfully liberating attack on this issue. There is a kind of creepy mysticism that has been allowed to accrue around indexicals, and it's nonsense. |
| 18414 | Fregeans say 'I' differs in reference, so it must also differ in sense [Cappelen/Dever] |
| Full Idea: Fregeans tend to treat as a fundamental tenet that sense determines reference; same sense, same reference. From that it follow trivially that indexicals don't have the same sense: different uses of 'I' have different referents, so sense must differ. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 04.6) | |
| A reaction: Interesting. Since it seems implausible that 'I' is profoundly different when two people use it, this seems to be a strong argument against Frege's distinction. But I rather like Frege's distinction, while being sceptical about 'I', so I'm baffled.... |
| 18423 | All indexicals can be expressed non-indexically [Cappelen/Dever] |
| Full Idea: Whatever can be expressed indexically could be expressed by non-indexical means. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 08.1) | |
| A reaction: This is the best summary of the thesis of their book. Indexicality in non-essential. |
| 13763 | Spoken sounds vary between people, but are signs of affections of soul, which are the same for all [Aristotle] |
| Full Idea: Spoken sounds are symbols of affections in the soul, ...and just as written marks are not the same for all men, neither are spoken sounds. But what these are in the first place signs of - affections of the soul - are the same for all. | |
| From: Aristotle (On Interpretation [c.330 BCE], 16a03-08) | |
| A reaction: Loux identifies this passage as the source of the 'conceptualist' view of propositions, which I immediately identify with. The view that these propositions are 'the same for all' is plausible for normal objects, but dubious for complex abstractions. |
| 1705 | It doesn't have to be the case that in opposed views one is true and the other false [Aristotle] |
| Full Idea: It is not necessary that of every affirmation and opposite negation one should be true and the other false. For what holds for things that are does not hold for things that are not but may possibly be or not be. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a39) | |
| A reaction: Thus even if Bivalence holds, and the only truth-values are T and F, it doesn't follow that Excluded Middle holds, which says that every proposition must have one of those two values. |
| 18406 | The basic Kaplan view is that there is truth-conditional content, and contextual character [Cappelen/Dever] |
| Full Idea: In what we label 'Basic Kaplanianism', each of the sentences 'Smith is happy' and 'I am happy', as uttered by Smith, has two levels of meaning. The 'content' is a truth-conditional representation. The 'character' is a function from contexts to contents. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 01.6) | |
| A reaction: They give this as a minimal and plausible account of the situation, without reading huge significance into the indexical. I'm inclined to see the situation in terms of the underlying proposition containing both ingredients. |
| 18411 | It is proposed that a huge range of linguistic items are context-sensitive [Cappelen/Dever] |
| Full Idea: An enormous amount has been written about whether 'all', 'know', 'might', 'delicious', 'good', 'if, then', 'and', 'red', 'just', 'justified', 'probable', 'local', 'ready', and 'left-right' are context-sensitive. | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 02.3) | |
| A reaction: The clearest way to approach these things is ask what the (informal) domain of quantification is for that particular context. The domain can shift in the course of a sentence. |
| 18420 | We deny that action involves some special class of beliefs [Cappelen/Dever] |
| Full Idea: Maybe there is a class of beliefs that plays a special role in the explanation of action. We have argued against the existence of such a class (or at least any interesting such class). | |
| From: Cappelen,H/Dever,Josh (The Inessential Indexical [2013], 06.2) | |
| A reaction: The main class which has been proposed is the one that involves indexical beliefs. I agree with this idea. |
| 1702 | Things may be necessary once they occur, but not be unconditionally necessary [Aristotle] |
| Full Idea: To say that everything that is, is of necessity, when it is, is not the same as saying unconditionally that it is of necessity. | |
| From: Aristotle (On Interpretation [c.330 BCE], 19a25) |