17 ideas
10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
Full Idea: The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1) | |
A reaction: This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything. |
10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
Full Idea: Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
A reaction: This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008. |
9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
Full Idea: There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related? | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1) | |
A reaction: A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first? |
10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
Full Idea: There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four'). | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1) | |
A reaction: Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers. |
10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
Full Idea: Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2) | |
A reaction: His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects. |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
Full Idea: I argue for an internalist conception of arithmetic. Arithmetic is not about a domain of entities, not even quantified entities. Quantifiers over natural numbers occur in their inferential-role reading in which they merely generalize over the instances. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
A reaction: Hofweber offers the hope that modern semantics can disentangle the confusions in platonist arithmetic. Very interesting. The fear is that after digging into the semantics for twenty years, you find the same old problems re-emerging at a lower level. |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
Full Idea: That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2) | |
A reaction: This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them. |
10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
Full Idea: Determiner uses of number words may disappear on analysis. This is inspired by Russell's elimination of the word 'the'. The number becomes blocks of first-order quantifiers at the level of semantic representation. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2) | |
A reaction: [compressed] The proposal comes from platonists, who argue that numbers cannot be analysed away if they are objects. Hofweber says the analogy with Russell is wrong, as 'the' can't occur in different syntactic positions, the way number words can. |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
Full Idea: Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
A reaction: This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting. |
10004 | Our minds are at their best when reasoning about objects [Hofweber] |
Full Idea: Our minds mainly reason about objects. Most cognitive problems we are faced with deal with particular objects, whether they are people or material things. Reasoning about them is what our minds are good at. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.3) | |
A reaction: Hofweber is suggesting this as an explanation of why we continually reify various concepts, especially numbers. Very plausible. It works for qualities of character, and explains our tendency to talk about universals as objects ('redness'). |
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). |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |