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8210
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Deconstructing philosophy gives the history of concepts, and the repressions behind them [Derrida]
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Full Idea:
To 'deconstruct' philosophy would be to think the structured genealogy of philosophy's concepts, but at the same time determine what this history has been able to dissimulate or forbid, making itself into history by this motivated repression.
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From:
Jacques Derrida (Implications [1967], p.5)
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A reaction:
All of this type of philosophy is motivated by what I think of as (I'm afraid!) a rather adolescent belief that we are all being 'repressed', and that somehow, if we think hard enough, we can all become 'free', and then everything will be fine.
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8211
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The movement of 'différance' is the root of all the oppositional concepts in our language [Derrida]
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Full Idea:
The movement of 'différance', as that which produces different things, that which differentiates, is the common root of all the oppositional concepts that mark our language, such as sensible/intelligible, intuition/signification, nature/culture etc.
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From:
Jacques Derrida (Implications [1967], p.7)
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A reaction:
'Différance' is a word coined by Derrida, and his most famous concept. At first glance, the concept of a thing which is the source of all differentiation sounds like a fiction.
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10007
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Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
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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.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
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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.
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9998
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What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
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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?
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1)
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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?
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10002
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'2 + 2 = 4' can be read as either singular or plural [Hofweber]
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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').
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1)
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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.
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10003
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Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
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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.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2)
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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.
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10008
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Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
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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.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
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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.
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10005
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Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
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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.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2)
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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.
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10000
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We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
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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.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2)
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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.
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10006
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First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
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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.
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From:
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
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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.
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8430
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Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim]
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Full Idea:
The function of causal statements is 1) to explain events, 2) for predictive usefulness, 3) to help control events, 4) with agents, to attribute moral responsibility, 5) in physical theory. We should judge causal theories by how they account for these.
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From:
Jaegwon Kim (Causes and Counterfactuals [1973], p.207)
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A reaction:
He suggests that Lewis's counterfactual theory won't do well on this test. I think the first one is what matters. Philosophy aims to understand, and that is achieved through explanation. Regularity and counterfactual theories explain very little.
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8429
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Counterfactuals can express four other relations between events, apart from causation [Kim]
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Full Idea:
Counterfactuals can express 'analytical' dependency, or the fact that one event is part of another, or an action done by doing another, or (most interestingly) an event can determine another without causally determining it.
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From:
Jaegwon Kim (Causes and Counterfactuals [1973], p.205)
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A reaction:
[Kim gives example of each case] Counterfactuals can even express a relation that involves no dependency. Or they might just involve redescription, as in 'If Scott were still alive, then the author of "Waverley" would be too'.
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4781
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Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos]
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Full Idea:
Kim gives a range of examples of counterfactual dependence without causation, as: 'if yesterday wasn't Monday, today wouldn't be Tuesday', and 'if my sister had not given birth, I would not be an uncle'.
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From:
report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3
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A reaction:
This is aimed at David Lewis. The objection seems like commonsense. "If you blink, the cat gets it". Causal claims involve counterfactuals, but they are not definitive of what causation is.
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