27 ideas
| 19215 | Arguers often turn the opponent's modus ponens into their own modus tollens [Merricks] |
| Full Idea: There is a seasoned method of turning your opponent's modus ponens into your own modus tollens. | |
| From: Trenton Merricks (Propositions [2015], 5.VII) | |
| A reaction: That is, they say 'if he's coming he'll be hear by now, and he's definitely coming', to which you say 'I'm afraid he's not here, so he obviously isn't coming after all'. They say if-A-then-B, and A, so B. You say not-B, so you're wrong about A. |
| 19205 | 'Snow is white' only contingently expresses the proposition that snow is white [Merricks] |
| Full Idea: It is contingently true that 'snow is white' expresses the proposition that snow is white. | |
| From: Trenton Merricks (Propositions [2015], 1.V n14) | |
| A reaction: Tarski stuck to sentences, but Merricks rightly argues that truth concerns propositions, not sentences. Sentences are subservient entities - mere tools used to express what matters, which is our thoughts (say I). |
| 19209 | Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks] |
| Full Idea: Logical consequence guarantees preservation of truth. The Converse Barcan, a theorem of Simple Quantified Modal Logic, says that an obvious truth implies an obvious falsehood. So SQML gets logical consequence wrong. So SQML is mistaken. | |
| From: Trenton Merricks (Propositions [2015], 2.V) | |
| A reaction: I admire this. The Converse Barcan certainly strikes me as wrong (Idea 19208). Merricks grasps this nettle. Williamson grasps the other nettle. Most people duck the issue, I suspect. Merricks says later that domains are the problem. |
| 19208 | The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks] |
| Full Idea: The Converse Barcan Formula has a startling result. Simple Quantified Modal Logic (SQML) has the following as a theorem: □∀xFx → ∀x□Fx. So 'everything exists necessarily' is a consequence of 'necessarily, everything exists'. | |
| From: Trenton Merricks (Propositions [2015], 2.V) | |
| A reaction: He says this is blatantly wrong. Williamson is famous for defending it. I think I'm with Merricks on this one. |
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| Full Idea: Quine ends up with the logic that is maximally justified by experience, ...but a large number of the core principles of logic will have to be used to select the logic that is maximally justified by experience. | |
| From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Paul Boghossian - Knowledge of Logic p.233 | |
| A reaction: In order to grasp some core principles of logic, you will probably need a certain amount of experience. I take logic to be an abstracted feature of reality (unless it is extended by pure fictions). Some basic logic may be hard wired in us. |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| Full Idea: Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand. |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| Full Idea: Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false. | |
| From: report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5 | |
| A reaction: One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter. |
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| Full Idea: Quine said a logical truth is a truth in which only logical constants occur essentially, ...but then a fruitful definition of 'logical constant' is called for. | |
| From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Ian Hacking - What is Logic? §02 |
| 19207 | Sentence logic maps truth values; predicate logic maps objects and sets [Merricks] |
| Full Idea: The models for sentential logic map sentences to truth-values. The models for predicate logic map parts of sentences to objects and sets. | |
| From: Trenton Merricks (Propositions [2015], 2.II) | |
| A reaction: Logic books rarely tell you important things like this. That is why this database is so incredibly important! You will never understand the subject if you don't collect together the illuminating asides of discussion. They say it all so much more simply. |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| Full Idea: Unlike elementary logic, the truths of set theory are not obvious. Set theory was straining at the leash of intuition ever since Cantor discovered higher infinites; and with the added impetus of the paradoxes of set theory the leash snapped. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: This problem seems to have forced Quine into platonism about sets, because he felt they were essential for mathematics and science, but couldn't be constructed with precision. So they must be real, but we don't quite understand them. |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| Full Idea: We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic. |
| 14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
| Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition. | |
| From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3 | |
| A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers? |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
| Full Idea: One's hypothesis as to there being universals is at bottom just as arbitrary or pragmatic a matter as one's adoption of a new brand of set theory or even a new system of bookkeeping. | |
| From: Willard Quine (Carnap and Logical Truth [1954], x) | |
| A reaction: This spells out clearly the strongly pragmatist vein in Quine's thinking. |
| 19214 | In twinning, one person has the same origin as another person [Merricks] |
| Full Idea: Origin essentialists claim that parental union results in a person, and that person could not have resulted from any other union. However, if the fertilised egg undergoes twinning, at least one of the resultant persons is not the original person. | |
| From: Trenton Merricks (Propositions [2015], 5.V) | |
| A reaction: Merricks says that therefore that origin could have just produced the second twin, rather than the original person. This is interesting, but doesn't seem to threaten the necessity of origin thesis. Once I'm here, I have that origin, despite my twin. |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| Full Idea: When Kant's arithmetical examples of a priori synthetic judgements were sweepingly disqualified by Frege's reduction of arithmetic to logic, attention moved to the less tendentious and logically prior question 'How is logical certainty possible?' | |
| From: Willard Quine (Carnap and Logical Truth [1954], I) | |
| A reaction: A nice summary of the story so far, from someone who should know. This still leaves the question open of whether any synthetic truths can be derived from the logical certainties which are available. |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| Full Idea: In trying to make sense of the role of convention in a priori knowledge, the very distinction between a priori and empirical begins to waver and dissolve. | |
| From: Willard Quine (Carnap and Logical Truth [1954], VI) | |
| A reaction: This is the next stage in the argument after Wittgenstein presents the apriori as nothing more than what arises from truth tables. The rationalists react by taking us back to the original 'natural light of reason' view. Then we go round again... |
| 19217 | I don't accept that if a proposition is directly about an entity, it has a relation to the entity [Merricks] |
| Full Idea: The Aboutness Assumption says that necessarily, if a proposition is directly about an entity, then that proposition stands in a relation to the entity. I shall argue that the Assumption is false. | |
| From: Trenton Merricks (Propositions [2015], 5.VII) | |
| A reaction: This feels sort of right, though the nature of aboutness remains elusive. He cites denials of existence. I take speech to be fairly internal, even though its main role is communication. Maybe its a Cambridge relation, as far as the entity is concerned. |
| 19203 | A sentence's truth conditions depend on context [Merricks] |
| Full Idea: A sentence has truth conditions only in a context of use. And the truth conditions of many sentences can differ from one context of use to another (as in 'I am a philosopher'). | |
| From: Trenton Merricks (Propositions [2015], 1.II) | |
| A reaction: He is building a defence of propositions, because they are eternal, and have their truth conditions essentially. I too am a fan of propositions. |
| 19200 | Propositions are standardly treated as possible worlds, or as structured [Merricks] |
| Full Idea: The thesis that propositions are sets of possible worlds is one of the two leading accounts of the nature of propositions. The other leading account endorses structured propositions. | |
| From: Trenton Merricks (Propositions [2015], Intro) | |
| A reaction: Merricks sets out to reject both main views. I take the idea that propositions actually are sets of possible worlds to be ridiculous (though they may offer a way of modelling them). The idea that they have no structure at all strikes me as odd. |
| 19206 | 'Cicero is an orator' represents the same situation as 'Tully is an orator', so they are one proposition [Merricks] |
| Full Idea: The proposition expressed by 'Cicero is an orator' represents things as being exactly the same way as does the proposition expressed by 'Tully is an orator'. Hence two sentences express the same proposition. Fregeans about names deny this. | |
| From: Trenton Merricks (Propositions [2015], 2.II) | |
| A reaction: Merricks makes the situation in the world fix the contents of the proposition. I don't agree. I would expand the first proposition as 'The person I know as 'Cicero' was an orator', but I might never have heard of 'Tully'. |
| 19202 | Propositions are necessary existents which essentially (but inexplicably) represent things [Merricks] |
| Full Idea: My account says that each proposition is a necessary existent that essentially represents things as being a certain way, ...and there is no explanation of how propositions do that. | |
| From: Trenton Merricks (Propositions [2015], Intro) | |
| A reaction: Since I take propositions to be brain events, I don't expect much of an explanation either. The idea that propositions necessarily exist strikes me as false. If there were no minds, there would have been no propositions. |
| 19204 | True propositions existed prior to their being thought, and might never be thought [Merricks] |
| Full Idea: 1,000 years ago, no sentence had ever expressed, and no one had believed, the true proposition 'a water molecule has two hydrogen and one oxygen atoms'. There are surely true propositions that have never been, and never will be, expressed or believed. | |
| From: Trenton Merricks (Propositions [2015], 1.V) | |
| A reaction: 'Surely'? Surely not! How many propositions exist? Where do they exist? What are they made of? If they already exist when we think them, how do we tune into them? When did his example come into existence? Before water did? No! No! |
| 19210 | The standard view of propositions says they never change their truth-value [Merricks] |
| Full Idea: The standard view among philosophers nowadays seems to be that propositions do not and even cannot change in truth-value. But my own view is that some propositions can, and do, change in truth value. | |
| From: Trenton Merricks (Propositions [2015], 3.VII) | |
| A reaction: He gives 'that A sits' as an example of one which can change, though 'that A sits at time t' cannot change. I take Merricks to be obviously right, and cannot get my head round the 'standard' view. What on earth do they think a proposition is? |
| 19201 | Propositions can be 'about' an entity, but that doesn't make the entity a constituent of it [Merricks] |
| Full Idea: If a singular proposition is 'directly about' an entity, I argue that a singular proposition does not have the entity that it is directly about as a constituent. | |
| From: Trenton Merricks (Propositions [2015], Intro) | |
| A reaction: This opposes the view of the early Russell, that propositions actually contain the entities they are about, thus making propositions real features of the external world. I take that view of Russell's to be absurd. |
| 19211 | Early Russell says a proposition is identical with its truthmaking state of affairs [Merricks] |
| Full Idea: I describe Russell's 1903 account of propositions as the view that each proposition is identical with the state of affairs that makes that proposition true. That is, a proposition is identical with its 'truthmaking' state of affairs. | |
| From: Trenton Merricks (Propositions [2015], 4.II) | |
| A reaction: Russell soon gave this view up (false propositions proving tricky), and I'm amazed anyone takes it seriously. I take it as axiomatic that if there were no minds there would be no propositions. Was the Big Bang a set of propositions? |
| 19212 | Unity of the proposition questions: what unites them? can the same constituents make different ones? [Merricks] |
| Full Idea: What binds the constituents of a structured proposition together into a single unity, a proposition? Can the very same constituents constitute two distinct propositions? These are questions about 'the unity of the proposition'. | |
| From: Trenton Merricks (Propositions [2015], 4.II) | |
| A reaction: Merricks solves it by saying propositions have no structure. The problem is connected to the nature of predication (instantiation, partaking). You can't just list objects and their properties. Objects are united, and thus propositions are too. |
| 19213 | We want to explain not just what unites the constituents, but what unites them into a proposition [Merricks] |
| Full Idea: A successful account of the unity of the proposition tells us what unites the relevant constituents not merely into some entity or other, but into a proposition. | |
| From: Trenton Merricks (Propositions [2015], 4.X) | |
| A reaction: Merrickes takes propositions to be unanalysable unities, but their central activity is representation, so if they needed uniting, that would be the place to look. Some people say that we unite our propositions. Others say the world does. I dunno. |