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All the ideas for 'Matter and Memory', 'Number Determiners, Numbers, Arithmetic' and 'Value Theory'

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26 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
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.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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?
'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.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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.
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
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.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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.
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
Bergson was a rallying point, because he emphasised becomings and multiplicities [Bergson, by Deleuze]
     Full Idea: Bergson was a rallying point for all the opposition, …not so much because of the theme of duration, as of the theory and practice of becoming of all kinds, of coexistent multiplicities.
     From: report of Henri Bergson (Matter and Memory [1896]) by Gilles Deleuze - A Conversation: what is it? What is it for? I
     A reaction: The three heroes of Deleuze are Spinoza, Nietzsche and Bergson. All philosophers are either of Being, or of Becoming, I suggest.
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi]
     Full Idea: It is no part of supervenience that 'if p then q' entails 'if not p then not q'. To avoid such misunderstandings, it is common (though not more accurate) to describe supervenience in negative terms: no difference in A without a difference in B.
     From: Francesco Orsi (Value Theory [2015], 5.2)
     A reaction: [compressed] In other words it is important to avoid the presupposition that the given supervenience is a two-way relation. The paradigm case of supervenience is stalking.
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Bergson showed that memory is not after the event, but coexists with it [Bergson, by Deleuze]
     Full Idea: Bergson has shown that memory is not an actual image which forms after the object has been perceived, but a virtual image coexisting with the actual perception of the object.
     From: report of Henri Bergson (Matter and Memory [1896]) by Gilles Deleuze - The Actual and the Virtual p.114
     A reaction: It strikes me as plausible to say that all conscious life is memory. Perceiving the present instant is only possible because it endures for a tiny moment.
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
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').
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi]
     Full Idea: Many have suggested alternative roles or sorts of reasons, which are not mandatory. Dancy says some reasons are 'enticing' rather than peremptory; Raz makes options 'eligible' rather than required; Gert says they justify rather than require action.
     From: Francesco Orsi (Value Theory [2015], 6.4)
     A reaction: The third option is immediately attractive - but then it would only justify the action because it was a good reason, which would need explaining. 'Enticing' captures the psychology in a nice vague way.
22. Metaethics / A. Value / 1. Nature of Value / a. Nature of value
Final value is favoured for its own sake, and personal value for someone's sake [Orsi]
     Full Idea: Final value is to be favoured for its own sake; personal value is to be favoured for someone's sake.
     From: Francesco Orsi (Value Theory [2015], 7.2)
     A reaction: This gives another important dimension for discussions of value. I like the question 'what gives rise to this value?', but we can also ask (given the value) why we should then promote it. Health isn't a final value, and truth isn't a personal value?
Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi]
     Full Idea: Examples of value-maker concepts are courageous, honest, cowardly, corrupt, elegant, tacky, melodious, insightful. Employing these concepts normally means both evaluating and describing the thing or person one way or another.
     From: Francesco Orsi (Value Theory [2015], 1.2)
     A reaction: The point being that they tell you two things - that this thing has a particular value, and also why it has that value. Since I am flirting with the theory that all values must have 'value-makers' this is very interesting.
The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi]
     Full Idea: The '-able' concepts, such as valuable, enviable, contemptible, wear on their sleeve the idea that the thing so evaluated merits or is worth a certain attitude or response (of valuing, envying, despising).
     From: Francesco Orsi (Value Theory [2015], 1.2)
     A reaction: Compare Idea 18666. Hence some concepts point to the source of value in the thing, and others point to the source of the value in the normative attitude of the speaker. Interesting.
Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi]
     Full Idea: If a certain object is valuable, then something other than its being valuable must make it so. ...One is always in principle entitled to an answer as to why it is good or bad.
     From: Francesco Orsi (Value Theory [2015], 5.2)
     A reaction: What Orsi calls the 'chemistry' of value. I am inclined to think that this is the key to a philosophical study of value. Without this assumption the values float free, and we drift into idealised waffle. Note that here he only refers to 'objects'.
A complex value is not just the sum of the values of the parts [Orsi]
     Full Idea: The whole 'being pleased by cats being tortured' is definitely not better, and is likely worse, than cats being tortured. So its value cannot result from a sum of the intrinsic values of the parts.
     From: Francesco Orsi (Value Theory [2015], 5.3)
     A reaction: This example is simplistic. It isn't a matter of just adding 'pleased' and 'tortured'. 'Pleased' doesn't have a standalone value. Only a rather gormless utilitarian would think it was always good if someone was pleased. I suspect values don't sum at all.
Trichotomy Thesis: comparable values must be better, worse or the same [Orsi]
     Full Idea: It is natural to assume that if we can compare two objects or states of affairs, X and Y, then X is either better than, or worse than, or as good as Y. This has been called the Trichotomy Thesis.
     From: Francesco Orsi (Value Theory [2015], 6.2)
     A reaction: This is the obvious starting point for a discussion of the difficult question of the extent to which values can be compared. Orsi says even if there was only one value, like pleasure, it might have incommensurable aspects like duration and intensity.
The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi]
     Full Idea: The main claims of the Fitting Attitude view of value are Reduction: values such are goodness are reduced to fitting attitudes, having reasons, and Normative Redundancy: goodness provides no reasons for attitudes beyond the thing's features.
     From: Francesco Orsi (Value Theory [2015], 8.2)
     A reaction: Orsi's book is a sustained defence of this claim. I like the Normative Redundancy idea, but I am less persuaded by the Reduction.
22. Metaethics / A. Value / 1. Nature of Value / c. Objective value
Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi]
     Full Idea: A support for the fittingness account (against the buck-passing reasons account) is the 'wrong kind of reasons' problem. There are many reasons for positive attitudes towards things which are not good. We might admire a demon because he threatens torture.
     From: Francesco Orsi (Value Theory [2015], 1.4)
     A reaction: [compressed] I like the Buck-Passing view, but was never going to claim that all reasons for positive attitudes bestow value. I only think that there is no value without a reason
22. Metaethics / A. Value / 1. Nature of Value / f. Ultimate value
A thing may have final value, which is still derived from other values, or from relations [Orsi]
     Full Idea: Many believe that final values can be extrinsic: objects which are valuable for their own sake partly thanks to their relations to other objects. ...This might depend on the value of other things...or an object's relational properties.
     From: Francesco Orsi (Value Theory [2015], 2.3)
     A reaction: It strikes me that virtually nothing (or even absolutely nothing) has final value in total isolation from other things (Moore's 'isolation test'). Values arise within a tangled network of relations. Your final value is my instrumental value.
22. Metaethics / A. Value / 2. Values / a. Normativity
The Buck-Passing view of normative values says other properties are reasons for the value [Orsi]
     Full Idea: Version two of the normative view of values is the Buck-Passing account, which says that 'x is good' means 'x has the property of having other properties that provide reasons to favour x'.
     From: Francesco Orsi (Value Theory [2015], 1.4)
     A reaction: [He cites Scanlon 1998:95-8] I think this is the one to explore. We want values in the world, bridging the supposed 'is-ought gap', and not values that just derive from the way human beings are constituted (and certainly not supernatural values!).
Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi]
     Full Idea: Version one of the normative view of values is the Fitting Attitude account, which says that 'x is good' means 'it is fitting to respond favourably to (or 'favour') x'.
     From: Francesco Orsi (Value Theory [2015], 1.4)
     A reaction: Brentano is mentioned. Orsi favours this view. The rival normative view is Scanlon's [1998:95-8] Buck-Passing account, in Idea 18670. I am interested in building a defence of the Buck-Passing account, which seems to suit a naturalistic realist like me.
Truths about value entail normative truths about actions or attitudes [Orsi]
     Full Idea: My guiding assumption is that truths about value, at least, regularly entail normative truths of some sort about actions or attitudes.
     From: Francesco Orsi (Value Theory [2015], 1.4)
     A reaction: Not quite as clear as it sounds. If I say 'the leaf is green' I presume a belief that it is green, which is an attitude. If I say 'shut the door' that implies an action with no value. One view says that values are entirely normative in this way.