24 ideas
| 192 | Only one thing can be contrary to something [Plato] |
| Full Idea: To everything that admits of a contrary there is one contrary and no more. | |
| From: Plato (Protagoras [c.380 BCE], 332c) | |
| A reaction: The sort of thing for which a modern philosopher would demand a proof (and then reject when the proof couldn't be found), where a Greek is happy to assert it as self-evident. I can't think of a counterexample. |
| 19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
| Full Idea: If truth can be explicitly defined, it can be eliminated. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
| A reaction: That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination. |
| 19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
| Full Idea: If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3) | |
| A reaction: I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction. |
| 19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
| Full Idea: Semantic approaches to truth usually necessitate the use of a metalanguage that is more powerful than the object-language for which it provides a semantics. It is usually taken to include set theory. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1) | |
| A reaction: This is a motivation for developing an axiomatic account of truth, that moves it into the object language. |
| 19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
| Full Idea: Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2) | |
| A reaction: They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth. |
| 19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
| Full Idea: If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2) | |
| A reaction: This seems like a big attraction of axiomatic theories of truth for students of metamathematics. |
| 19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
| Full Idea: If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
| A reaction: So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values? |
| 19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
| Full Idea: It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), … | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3) | |
| A reaction: It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels. |
| 19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
| Full Idea: KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4) | |
| A reaction: [summary, which I hope is correct! Stanford is not wholly clear] |
| 19121 | We can reduce properties to true formulas [Halbach/Leigh] |
| Full Idea: One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
| A reaction: [compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids. |
| 190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
| Full Idea: If someone asked me 'Is justice itself just or unjust?' I should answer that it was just, wouldn't you? I agree. | |
| From: Plato (Protagoras [c.380 BCE], 330c) |
| 19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
| Full Idea: The reduction of second-order theories (of properties or sets) to axiomatic theories of truth is a form of reductive nominalism, replacing existence assumptions (e.g. comprehension axioms) by innocuous assumptions about the truth predicate. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
| A reaction: I'm currently thinking that axiomatic theories of truth are the most exciting development in contemporary philosophy. See Halbach and Horsten. |
| 20185 | The most important things in life are wisdom and knowledge [Plato] |
| Full Idea: It would be shameful indeed to say that wisdom and knowledge are anything but the most powerful forces in human activity. | |
| From: Plato (Protagoras [c.380 BCE], 352d) | |
| A reaction: He lumps wisdom and knowledge together, and I think we can take 'knowledge' to mean something like understanding, because obviously mere atomistic propositional knowledge can be utterly trivial. |
| 20184 | The only real evil is loss of knowledge [Plato] |
| Full Idea: The only real kind of faring ill is the loss of knowledge. | |
| From: Plato (Protagoras [c.380 BCE], 345b) | |
| A reaction: This must crucially involve the intellectualist view (of Socrates) that virtuos behaviour results from knowledge, and moral wickedness is the result of ignorance. It is hard to see how forgetting a phone number is evil. |
| 191 | Everything resembles everything else up to a point [Plato] |
| Full Idea: Everything resembles everything else up to a point. | |
| From: Plato (Protagoras [c.380 BCE], 331d) |
| 203 | Courage is knowing what should or shouldn't be feared [Plato] |
| Full Idea: Knowledge of what is and is not to be feared is courage. | |
| From: Plato (Protagoras [c.380 BCE], 360d) |
| 8114 | The institutional theory says only a competent expert can decree something to be an art work [Dickie, by Gardner] |
| Full Idea: Dickie's institutional theory of art says that something is a work of art if and only if it has had that status conferred on it by a competent member of the artworld. | |
| From: report of George Dickie (Introduction to Aesthetics [1997], Ch.8) by Sebastian Gardner - Aesthetics 3.1 | |
| A reaction: The idea that a single 'competent' person can do this sounds daft, and probably circular. A consensus in the artworld sounds more plausible, but this still leaves the revolutionary genius, who - in retrospect - produced unrecognised 'art'. |
| 202 | No one willingly and knowingly embraces evil [Plato] |
| Full Idea: No one willingly goes to meet evil, or what he thinks is evil. | |
| From: Plato (Protagoras [c.380 BCE], 358d) | |
| A reaction: Presumably people who actively choose satanism can override this deep-seated attitude. But their adherence to evil usually seems to be rather restrained. A danger of tautology with ideas like this. |
| 193 | Some things are good even though they are not beneficial to men [Plato] |
| Full Idea: 'Do you mean by good those things that are beneficial to men?' 'Not only those. I call some things which are not beneficial good as well'. | |
| From: Plato (Protagoras [c.380 BCE], 333e) | |
| A reaction: Examples needed, but this would be bad news for utilitarians. Good health is not seen as beneficial if it is taken for granted. Not being deaf. |
| 197 | Some pleasures are not good, and some pains are not evil [Plato] |
| Full Idea: There are some pleasures which are not good, and some pains which are not evil. | |
| From: Plato (Protagoras [c.380 BCE], 351d) | |
| A reaction: Sadism and child birth. Though Bentham (I think) says that there is nothing good about the pain, since the event would obviously be better without it. |
| 200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
| Full Idea: The only reason the common man disapproves of pleasures is if they lead to pain and deprive us of future pleasures. | |
| From: Plato (Protagoras [c.380 BCE], 354a) | |
| A reaction: Plato has a strong sense that some pleasures are just innately depraved and wicked. If those pleasure don't hurt anyone, it is very hard to pinpoint what is wrong with them. |
| 188 | Socrates did not believe that virtue could be taught [Plato] |
| Full Idea: Socrates: I do not believe that virtue can be taught. | |
| From: Plato (Protagoras [c.380 BCE], 320b) |
| 204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
| Full Idea: Socrates is contradicting himself by saying virtue is not teachable, and yet trying to demonstrate that every virtue is knowledge. | |
| From: Plato (Protagoras [c.380 BCE], 361b) |
| 189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
| Full Idea: Athenians inflict punishment on wrong-doers, which shows that they too think it possible to impart and teach goodness. | |
| From: Plato (Protagoras [c.380 BCE], 324c) |