Combining Texts

All the ideas for 'works', 'Frege versus Cantor and Dedekind' and 'Causation'

unexpand these ideas     |    start again     |     specify just one area for these texts


25 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait]
     Full Idea: The tendency to attack forms of expression rather than attempting to appreciate what is actually being said is one of the more unfortunate habits that analytic philosophy inherited from Frege.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], IV)
     A reaction: The key to this, I say, is to acknowledge the existence of propositions (in brains). For example, this belief will make teachers more sympathetic to pupils who are struggling to express an idea, and verbal nit-picking becomes totally irrelevant.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set was doubted, because numbering seemed to require 'units' [Tait]
     Full Idea: The conception that what can be numbered is some object (including flocks of sheep) relative to a partition - a choice of unit - survived even in the late nineteenth century in the form of the rejection of the null set (and difficulties with unit sets).
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], IX)
     A reaction: This old view can't be entirely wrong! Frege makes the point that if asked to count a pack of cards, you must decide whether to count cards, or suits, or pips. You may not need a 'unit', but you need a concept. 'Units' name concept-extensions nicely!
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
We can have a series with identical members [Tait]
     Full Idea: Why can't we have a series (as opposed to a linearly ordered set) all of whose members are identical, such as (a, a, a...,a)?
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], VII)
     A reaction: The question is whether the items order themselves, which presumably the natural numbers are supposed to do, or whether we impose the order (and length) of the series. What decides how many a's there are? Do we order, or does nature?
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis]
     Full Idea: Maybe a disposition is a more fundamental notion than a cause, in which case Lewis has from the very start erred in seeking a causal analysis, in a traditional, conceptual sense, of disposition terms.
     From: comment on David Lewis (Causation [1973]) by Alexander Bird - Nature's Metaphysics 2.2.8
     A reaction: Is this right about Lewis? I see him as reducing both dispositions and causes to a set of bald facts, which exist in possible and actual worlds. Conditionals and counterfactuals also suffer the same fate.
10. Modality / B. Possibility / 9. Counterfactuals
For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis]
     Full Idea: A counterfactual is non-vacuously true iff it takes less of a departure from actuality to make the consequent true along with the antecedent than it does to make the antecedent true without the consequent.
     From: David Lewis (Causation [1973], p.197)
     A reaction: Almost every theory proposed by Lewis hangs on the meaning of the word 'close', as used here. If you visited twenty Earth-like worlds (watch Startrek?), it would be a struggle to decide their closeness to ours in rank order.
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis]
     Full Idea: By determinism I mean that the prevailing laws of nature are such that there do not exist any two possible worlds which are exactly alike up to that time, which differ thereafter, and in which those laws are never violated.
     From: David Lewis (Causation [1973], p.196)
     A reaction: This would mean that the only way an action of free will could creep in would be if it accepted being a 'violation' of the laws of nature. Fans of free will would probably prefer to call it a 'natural' phenomenon. I'm with Lewis.
18. Thought / E. Abstraction / 2. Abstracta by Selection
Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait]
     Full Idea: If the sense of a proposition about the abstract domain is given in terms of the corresponding proposition about the (relatively) concrete domain, ..and the truth of the former is founded upon the truth of the latter, then this is 'logical abstraction'.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: The 'relatively' in parentheses allows us to apply his idea to levels of abstraction, and not just to the simple jump up from the concrete. I think Tait's proposal is excellent, rather than purloining 'abstraction' for an internal concept within logic.
Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait]
     Full Idea: Although (in Cantor and Dedekind) abstraction does not (as has often been observed) play any role in their proofs, but it does play a role, in that it fixes the grammar, the domain of meaningful propositions, and so determining the objects in the proofs.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: [compressed] This is part of a defence of abstractionism in Cantor and Dedekind (see K.Fine also on the subject). To know the members of a set, or size of a domain, you need to know the process or function which created the set.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstraction may concern the individuation of the set itself, not its elements [Tait]
     Full Idea: A different reading of abstraction is that it concerns, not the individuating properties of the elements relative to one another, but rather the individuating properties of the set itself, for example the concept of what is its extension.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], VIII)
     A reaction: If the set was 'objects in the room next door', we would not be able to abstract from the objects, but we might get to the idea of things being contain in things, or the concept of an object, or a room. Wrong. That's because they are objects... Hm.
18. Thought / E. Abstraction / 8. Abstractionism Critique
Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
     Full Idea: Why should abstraction from two equipollent sets lead to the same set of 'pure units'?
     From: William W. Tait (Frege versus Cantor and Dedekind [1996])
     A reaction: [Tait is criticising Cantor] This expresses rather better than Frege or Dummett the central problem with the abstractionist view of how numbers are derived from matching groups of objects.
If abstraction produces power sets, their identity should imply identity of the originals [Tait]
     Full Idea: If the power |A| is obtained by abstraction from set A, then if A is equipollent to set B, then |A| = |B|. But this does not imply that A = B. So |A| cannot just be A, taken in abstraction, unless that can identify distinct sets, ..or create new objects.
     From: William W. Tait (Frege versus Cantor and Dedekind [1996], V)
     A reaction: An elegant piece of argument, which shows rather crucial facts about abstraction. We are then obliged to ask how abstraction can create an object or a set, if the central activity of abstraction is just ignoring certain features.
19. Language / D. Propositions / 2. Abstract Propositions / b. Propositions as possible worlds
A proposition is a set of possible worlds where it is true [Lewis]
     Full Idea: I identify a proposition with the set of possible worlds where it is true.
     From: David Lewis (Causation [1973], p.193)
     A reaction: As it stands, I'm baffled by this. How can 'it is raining' be a set of possible worlds? I assume it expands to refer to the truth-conditions, among possibilities as well as actualities. 'It is raining' fits all worlds where it is raining.
26. Natural Theory / C. Causation / 5. Direction of causation
A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H]
     Full Idea: Lewis thinks it is a major defect in a theory of causation that it builds in the condition that the time of the cause precede that of the effect: that cause precedes effect is something we ought to explain (which his counterfactual theory claims to do).
     From: report of David Lewis (Causation [1973]) by Hartry Field - Causation in a Physical World
     A reaction: My immediate reaction is that the chances of explaining such a thing are probably nil, and that we might as well just accept the direction of causation as a given. Even philosophers balk at the question 'why doesn't time go backwards?'
I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis]
     Full Idea: One might stipulate that a cause must always precede its effect, but I reject this solution. It won't solve the problem of epiphenomena, it rejects a priori any backwards causation, and it trivializes defining time-direction through causation.
     From: David Lewis (Causation [1973], p.203)
     A reaction: [compressed] Not strong arguments, I would say. Maybe apparent causes are never epiphenomenal. Maybe backwards causation is impossible. Maybe we must use time to define causal direction, and not vice versa.
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis]
     Full Idea: We sometimes single out one among all the causes of some event and call it 'the' cause. ..We may select the abnormal causes, or those under human control, or those we deem good or bad, or those we want to talk about. This is invidious discrimination.
     From: David Lewis (Causation [1973])
     A reaction: This is the standard view expressed by Mill - presumably the obvious empiricist line. But if we specify 'the pre-conditions' for an event, we can't just mention ANY fact prior to the effect - there is obvious relevance. So why not for 'the' cause as well?
The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis]
     Full Idea: In present-day regularity analyses, a cause is defined (roughly) as any member of any minimal set of actual conditions that are jointly sufficient, given the laws, for the existence of the effect.
     From: David Lewis (Causation [1973], p.193)
     A reaction: This is the view Lewis is about to reject. It seem to summarise the essence of the Mackie INUS theory. This account would make the presence of oxygen a cause of almost every human event.
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis]
     Full Idea: In the regularity analysis of causes, instead of c causing e, c might turn out to be an effect of e, or an epiphenomenon, or an inefficacious effect of a genuine cause, or a pre-empted cause (by some other cause) of e.
     From: David Lewis (Causation [1973], p.194)
     A reaction: These are Lewis's reasons for rejecting the general regularity account, in favour of his own particular counterfactual account. It is unlikely that c would be regularly pre-empted or epiphenomenal. If we build time's direction in, it won't be an effect.
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird]
     Full Idea: The Humean idea, developed by Lewis, is that rather than being sufficient for their effects, causes are (counterfactual) necessary for their effects.
     From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.162
Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird]
     Full Idea: Lewis's basic account has a basic causal relation, counterfactual dependence, and the general causal relation is the ancestral of this basic one. ...This is motivated by counterfactual dependence failing to be general because of the pre-emption problem.
     From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.161
     A reaction: It is so nice when you struggle for ages with a topic, and then some clever person summarises it clearly for you.
Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis]
     Full Idea: Some counterfactuals are based on non-causal laws, such as Newton's Third Law of Motion. 'If no force one way, then no force the other'. Lewis's counterfactual analysis implies that one force causes the other, which is not the case.
     From: comment on David Lewis (Causation [1973]) by Michael Tooley - Causation and Supervenience 5.2
     A reaction: So what exactly does 'cause' my punt to move forwards? Basing causal laws on counterfactual claims looks to me like putting the cart before the horse.
My counterfactual analysis applies to particular cases, not generalisations [Lewis]
     Full Idea: My (counterfactual) analysis is meant to apply to causation in particular cases; it is not an analysis of causal generalizations. Those presumably quantify over particulars, but it is hard to match natural language to the quantifiers.
     From: David Lewis (Causation [1973], p.195)
     A reaction: What authority could you have for asserting a counterfactual claim, if you only had one observation? Isn't the counterfactual claim the hallmark of a generalisation? For one case, 'if not-c, then not-e' is just a speculation.
One event causes another iff there is a causal chain from first to second [Lewis]
     Full Idea: One event is the cause of another iff there exists a causal chain leading from the first to the second.
     From: David Lewis (Causation [1973], p.200)
     A reaction: It will be necessary to both explain and identify a 'chain'. Some chains are extremely tenuous (Alexander could stop a barrel of beer). Go back a hundred years, and the cause of any present event is everything back then.
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis]
     Full Idea: Lewis can elucidate the logic of counterfactuals on the assumption that you are not at all puzzled about what a law of nature is. But if you are puzzled about this, it cannot contribute anything towards resolving your puzzlement.
     From: comment on David Lewis (Causation [1973]) by L. Jonathan Cohen - The Problem of Natural Laws p.219
     A reaction: This seems like a penetrating remark. The counterfactual theory is wrong, partly because it is epistemological instead of ontological, and partly because it refuses to face the really difficult problem, of what is going on out there.
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.