26 ideas
14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
Full Idea: Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], I) | |
A reaction: The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree. |
14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
Full Idea: It is an anacoluthon to say that a proposition is impossible because it is self-contradictory. It rather is thought so to appear self-contradictory because the ideal induction has shown it to be impossible. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) |
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. |
13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
Full Idea: The laws of logic - which are constituted by atemporal thoughts and atemporal subject matter - provide universal prescriptions of how one ought to think, given that one's thinking has the function of attaining truth. | |
From: Tyler Burge (Frege on Knowing the Third Realm [1992], p.316) | |
A reaction: Burge is giving, and endorsing, Frege's view. Burge is fighting a rearguard action, when logical systems keep proliferating. See Idea 10282. I sympathise with the dream of Burge and Frege. |
14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) |
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. |
14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV) | |
A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities. |
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. |
14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
Full Idea: Many say everything is logically possible which involves no contradiction. In this sense two contradictory propositions may be severally possible. In the substantive sense, the contradictory of a possible proposition is impossible (if we were omniscient). | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) |
14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
Full Idea: If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898]) | |
A reaction: Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience. |
14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
Full Idea: The real world is the world of sensible experience, and it is part of the process of sensible experience to locate its facts in the world of ideas. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) | |
A reaction: This is the neatest demolition of the sharp dividing line between empiricism and rationalism that I have ever encountered. |
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. |
14784 | Ethics is the science of aims [Peirce] |
Full Idea: Ethics is the science of aims. | |
From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) | |
A reaction: Intriguing slogan. He is discussing the aims of logic. I think what he means is that ethics is the science of value. 'Science' may be optimistic, but I would sort of agree with his basic idea. |