14 ideas
| 18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
| Full Idea: A model of a language assigns values to non-logical terms. If a sentence is true in every model, its truth doesn't depend on those non-logical terms. Hence the validity of an argument comes from its logical form. Thus models explain logical validity. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: [compressed] Thus you get a rigorous account of logical validity by only allowing the rigorous input of model theory. This is the modern strategy of analytic philosophy. But is 'it's red so it's coloured' logically valid? |
| 18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
| Full Idea: Natural language includes connectives that are not truth-functional. In order for 'p because q' to be true, both p and q have to be true, but knowing the simpler sentences are true doesn't determine whether the larger sentence is true. | |
| From: Vann McGee (Logical Consequence [2014], 2) |
| 18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
| Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification. |
| 18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
| Full Idea: We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory. |
| 18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
| Full Idea: Logically valid sentences are a species of analytic sentence, being true not just in virtue of the meanings of their words, but true in virtue of the meanings of their logical words. | |
| From: Vann McGee (Logical Consequence [2014], 4) | |
| A reaction: A helpful link between logical truths and analytic truths, which had not struck me before. |
| 18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
| Full Idea: Soundness theorems are seldom very informative, since typically we use informally, in proving the theorem, the very same rules whose soundness we are attempting to establish. | |
| From: Vann McGee (Logical Consequence [2014], 5) | |
| A reaction: [He cites Quine 1935] |
| 18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
| Full Idea: One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order. | |
| From: Vann McGee (Logical Consequence [2014], 7) | |
| A reaction: [He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation). |
| 18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
| Full Idea: If our linguistic conventions entitle us to assert a sentence, they thereby make it true, because of the maxim that 'truth is the norm of assertion'. | |
| From: Vann McGee (Logical Consequence [2014], 8) | |
| A reaction: You could only really deny that maxim if you had no belief at all in truth, but then you can assert anything you like (with full entitlement). Maybe you can assert anything you like as long as it doesn't upset anyone? Etc. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 22262 | Kant's moral law has no foundation - because that would undermine its priority [Sandel] |
| Full Idea: Given the stringent demands of the Kantian ethic, the moral law would seem almost to require a foundation in nothing, for any empirical precondition would undermine its priority. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Kantian') | |
| A reaction: The idea of a value with 'a foundation in nothing' is particular anathema to me, because my project is to find a foundation for everything (in nature, which is the Given). Kant's only foundational value seems to be rational consistency. |
| 22264 | Modern liberal rights in democracies protect individuals against the majority [Sandel] |
| Full Idea: Liberty in the modern procedural republic is defined in opposition to democracy, as an individual's guarantee against what the majority might will. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Present') | |
| A reaction: And so I should hope. Sandel is sort of criticising this view, but it seems obvious that rights of this sort must be basic to any civilised democracy. But how do you decide those rights, if not by a majoritarian decision? |
| 22261 | Liberals say rights always come first, and justice is neutral on social values [Sandel] |
| Full Idea: The liberal claim that the right is prior to the good means that individual rights cannot be sacrificed for the sake of the general good, and that the basic principles of justice cannot be premised on any particular vision of the good life. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'The right') | |
| A reaction: In Rawls, the first thesis is chosen from a neutral position, and the second is all that is needed to affirm rights as basic. These two are the target of Sandel's communitarian claims. Utilitarians will make the sacrifices. No consensus on the good life! |
| 22263 | Liberal justice means the withdrawal of the self, as transcendental or as unencumbered [Sandel] |
| Full Idea: For the liberal concept of justice we must stand to our circumstances always at a certain distance, whether as transcendental subject in the case of Kant, or as unencumbered selves in the case of Rawls. | |
| From: Michael J. Sandel (Procedural republic and unencumbered self [1984], 'Transcendental') | |
| A reaction: Maybe the only way to be unencumbered is to be transcendental. There is an insecure feeling that if the self becomes immanent or encumbered it thereby loses its objective rationality. You wake up one morning and find you are a nazi? |
| 22805 | Liberalism concerns rights, and communitarianism concerns the common good [Sandel, by Avineri/De-Shalit] |
| Full Idea: Sandel argues that liberalism is the politics of rights, while communitarianism is the politics of the common good. | |
| From: report of Michael J. Sandel (Procedural republic and unencumbered self [1984]) by Avineri,S/De-Shalit,A - Intro to 'Communitarianism and Individualism' §4 | |
| A reaction: The first thing on the agenda of the common good should be to assert and protect the rights of individual citizens. How could there be a common good which trampled on individuals? I agree that the common good is prior (e.g. in a pandemic). |