Combining Texts

All the ideas for 'Mathematics without Numbers', 'Four Decades of Scientific Explanation' and 'Ontological Dependence'

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


35 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
We understand things through their dependency relations [Fine,K]
     Full Idea: We understand a defined object (what it is) through the objects on which it depends.
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: This places dependency relations right at the heart of our understanding of the world, and hence shifts traditional metaphysics away from existence and identity. The notion of explanation is missing from Fine's account.
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics deals with the existence of things and with the nature of things [Fine,K]
     Full Idea: Metaphysics has two main areas of concern: one is with the nature of things, with what they are; and the other is with the existence of things, with whether they are.
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: This paper is part of a movement which has shifted metaphysics to a third target - how things relate to one another. The possibility that this third aim should be the main one seems quite plausible to me.
2. Reason / D. Definition / 4. Real Definition
Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K]
     Full Idea: In Wooster as the witless bachelor and Jeeves as the crafty manservant, and one valet to the other, we will have the counterpart, within the framework of real definition, to the simultaneous definition of two terms.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: This is wonderful grist to the mill of scientific essentialism, which endeavours to produce an understanding through explanation of the complex interactions of nature.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
     Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3
     A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'?
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
     Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort.
     From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3
     A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world).
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
     Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us.
     From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3
     A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities?
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K]
     Full Idea: It seems wrong to identify the 'being' of an object, its being what it is, with its existence. In one respect existence is too weak; for there is more to an object than mere existence; also too strong, for an object's nature need not include existence.
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: The word 'being' has been shockingly woolly, from Parmenides to Heidegger, but if you identify it with a thing's 'nature' that strikes me as much clearer (even if a little misty).
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K]
     Full Idea: An object 'weakly' depends upon another if it is ineliminably involved in one of its definitions; and it 'strongly' depends upon the other if it is ineliminably involved in all of its definitions.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: It is important to remember that a definition can be very long, and not just what might go into a dictionary.
A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K]
     Full Idea: A natural account of dependence in terms of modality and existence is that one thing x will depend on another thing y just in case it is necessary that y exists if x exists (or in the symbolism of modal logic, □(Ex→Ey).
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: He is going to criticise this view (which he traces back to Aristotle and Husserl). It immediately seems possible that there might be counterexamples. x might depend on y, but not necessarily depend on y. Necessities may not produce dependence.
An object depends on another if the second cannot be eliminated from the first's definition [Fine,K]
     Full Idea: The objects upon which a given object depends, according to the present account, are those which must figure in any of the logically equivalent definitions of the object. They will, in a sense, be ineliminable.
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: This is Fine's main proposal for the dependency relationship, with a context of Aristotelian essences understood as definitions. Sounds pretty good to me.
Dependency is the real counterpart of one term defining another [Fine,K]
     Full Idea: The notion of one object depending upon another is the real counterpart to the nominal notion of one term being definable in terms of another.
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: This begins to fill out the Aristotelian picture very nicely, since definitions are right at the centre of the nature of things (though a much more transitional part of the story than Fine seems to think).
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
We should understand identity in terms of the propositions it renders true [Fine,K]
     Full Idea: We should understand the identity or being of an object in terms of the propositions rendered true by its identity rather than the other way round.
     From: Kit Fine (Ontological Dependence [1995], I)
     A reaction: Behind this is an essentialist view of identity, rather than one connected with necessary properties.
9. Objects / D. Essence of Objects / 2. Types of Essence
How do we distinguish basic from derived esssences? [Fine,K]
     Full Idea: How and where are we to draw the line between what is basic to the essence and what is derived?
     From: Kit Fine (Ontological Dependence [1995], II)
     A reaction: He calls the basic essence 'constitutive' and the rest the 'consequential' essence. This question is obviously very challenging for the essentialist. See Idea 22.
Maybe some things have essential relationships as well as essential properties [Fine,K]
     Full Idea: It is natural to suppose, in the case of such objects as Wooster and Jeeves, that in addition to possessing constitutive essential properties they will also enter into constitutive essential relationships.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: I like this. If we are going to have scientific essences as structures of intrinsic powers, then the relationships between the parts of the essence must also be essential. That is the whole point - that the powers dictate the relationships.
9. Objects / D. Essence of Objects / 4. Essence as Definition
An object only essentially has a property if that property follows from every definition of the object [Fine,K]
     Full Idea: We can say that an object essentially has a certain property if its having that property follows from every definition of the object, while an object will definitively have a given property if its having that property follows from some definition of it.
     From: Kit Fine (Ontological Dependence [1995], III)
     A reaction: Presumably that will be every accurate definition. This nicely allows for the fact that at least nominal definitions may not be unique, and there is even room for real definitions not to be fully determinate (thus, how far should they extend?).
11. Knowledge Aims / A. Knowledge / 2. Understanding
It is knowing 'why' that gives scientific understanding, not knowing 'that' [Salmon]
     Full Idea: Knowledge 'that' is descriptive, and knowledge 'why' is explanatory, and it is the latter that provides scientific understanding of our world.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], Intro)
     A reaction: I agree, but of course, knowing 'why' may require a lot of knowing 'that'. People with extensive knowledge 'that' things are so tend to understand why something happens more readily than the rest of us ignoramuses.
Understanding is an extremely vague concept [Salmon]
     Full Idea: Understanding is an extremely vague concept.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.3)
     A reaction: True, I suppose, but we usually recognise understanding when we encounter it, and everybody has a pretty clear notion of an 'increase' in understanding. I suspect that the concept is perfectly clear, but we lack any scale for measuring it.
14. Science / A. Basis of Science / 4. Prediction
Correlations can provide predictions, but only causes can give explanations [Salmon]
     Full Idea: Various kinds of correlations exist that provide excellent bases for prediction, but because no suitable causal relations exist (or are known), these correlations do not furnish explanation.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.3)
     A reaction: There may be problem cases for the claim that all explanations are causal, but I certainly think that this idea is essentially right. Prediction can come from induction, but inductions may be true and yet baffling.
14. Science / B. Scientific Theories / 3. Instrumentalism
For the instrumentalists there are no scientific explanations [Salmon]
     Full Idea: There is a centuries-old philosophical tradition, sometimes referred to by the name of 'instrumentalism', that has denied the claim that science has explanatory power. For the instrumentalists there are no scientific explanations.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.3)
     A reaction: [He quotes Coffa] Presumably it is just a matter of matching the world to the readings on the instruments, aiming at van Fraassen's 'empirical adequacy'. If there are no scientific explanations, does that mean that there are no explanations at all? Daft!
14. Science / C. Induction / 4. Reason in Induction
Good induction needs 'total evidence' - the absence at the time of any undermining evidence [Salmon]
     Full Idea: Inductive logicians have a 'requirement of total evidence': induction is strong if 1) it has true premises, 2) it has correct inductive form, and 3) no additional evidence that would change the degree of support is available at the time.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.4.2)
     A reaction: The evidence might be very close at hand, but not quite 'available' to the person doing the induction.
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Scientific explanation is not reducing the unfamiliar to the familiar [Salmon]
     Full Idea: I reject the view that scientific explanation involves reduction of the unfamiliar to the familiar.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], Pref)
     A reaction: Aristotle sometimes seems to imply this account of explanation, and I would have to agree with Salmon's view of it. Aristotle is also, though, aware of real explanations, definitions and essences. People are 'familiar' with some peculiar things.
Why-questions can seek evidence as well as explanation [Salmon]
     Full Idea: There are evidence-seeking why-questions, as well as explanation-seeking why-questions.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.2)
     A reaction: Surely we would all prefer an explanation to mere evidence? It seems to me that they are all explanation-seeking, but that we are grateful for some evidence when no full explanation is available. Explanation renders evidence otiose.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
The three basic conceptions of scientific explanation are modal, epistemic, and ontic [Salmon]
     Full Idea: There are three basic conceptions of scientific explanation - modal, epistemic, and ontic - which can be discerned in Aristotle, and that have persisted down the ages.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.1)
The 'inferential' conception is that all scientific explanations are arguments [Salmon]
     Full Idea: The 'inferential' conception of scientific explanation is the thesis that all legitimate scientific explanations are arguments of one sort or another.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 1.1)
     A reaction: This seems to imply that someone has to be persuaded of something, and hence seems a rather too pragmatic view. I presume an explanation might be no more than dumbly pointing at conclusive evidence of a cause. Man with smoking gun.
Ontic explanations can be facts, or reports of facts [Salmon]
     Full Idea: Proponents of the ontic conception of explanation can say that explanations exist in the world as facts, or that they are reports of such facts (as opposed to the view of explanations as arguments, or as speech acts).
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.2)
     A reaction: [compressed] I am strongly drawn to the ontic approach, but not sure whether we want facts, or reports of them. The facts are the causal nexus, but which parts of the nexus provide the main aspect of explanation? I'll vote for reports, for now.
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
We must distinguish true laws because they (unlike accidental generalizations) explain things [Salmon]
     Full Idea: The problem is to distinguish between laws and accidental generalizations, for laws have explanatory force while accidental generalizations, even if they are true, do not.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 1.1)
     A reaction: [He is discussing Hempel and Oppenheim 1948] This seems obviously right, but I can only make sense of the explanatory power if we have identified the mechanism which requires the generalisation to continue in future cases.
Deductive-nomological explanations will predict, and their predictions will explain [Salmon]
     Full Idea: The deductive-nomological view has an explanation/prediction symmetry thesis - that a correct explanation could be a scientific prediction, and that any deductive prediction could serve as a deductive-nomological explanation.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 1.1)
     A reaction: Of course, not all predictions will explain, or vice versa. Weird regularities become predictable but remain baffling. Good explanations may be of unrepeatable events. It is the 'law' in the account that ties the two ends together.
A law is not enough for explanation - we need information about what makes a difference [Salmon]
     Full Idea: To provide an adequate explanation of any given fact, we need to provide information that is relevant to the occurrence of that fact - information that makes a difference to its occurrence. It is not enough to subsume it under a general law.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.2)
     A reaction: [He cites Bromberger for this idea] Salmon is identifying this idea as the beginnings of trouble for the covering-law account of explanation, and it sounds exactly right.
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Flagpoles explain shadows, and not vice versa, because of temporal ordering [Salmon]
     Full Idea: The height of the flagpole explains the length of the shadow because the interaction between the sunlight and the flagpole occurs before the interaction between the sunlight and the ground.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.6)
     A reaction: [Bromberger produced the flagpole example] This seems to be correct, and would apply to all physical cases, but there may still be cases of explanation which are not causal (in mathematics, for example).
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
Explanation at the quantum level will probably be by entirely new mechanisms [Salmon]
     Full Idea: My basic feeling about explanation in the quantum realm is that it will involve mechanisms, but mechanisms that are quite different from those that seem to work in the macrocosm.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], Pref)
     A reaction: Since I take most explanation to be by mechanisms (or some abstraction analogous to mechanisms), then I think this is probably right (rather than being by new 'laws').
Does an item have a function the first time it occurs? [Salmon]
     Full Idea: In functional explanation, there is a disagreement over whether an item has a function the first time it occurs.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.8)
     A reaction: This question arises particularly in evolutionary contexts, and would obviously not generally arise in the case of human artefacts.
Explanations reveal the mechanisms which produce the facts [Salmon]
     Full Idea: I favour an ontic conception of explanation, that explanations reveal the mechanisms, causal or other, that produce the facts we are trying to explain.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 4.1)
     A reaction: [He also cites Coffa and Peter Railton] A structure may explain, and only be supported by causal powers, but it doesn't seem to be the causal powers that do the explaining. Is a peg fitting a hole explained causally?
14. Science / D. Explanation / 2. Types of Explanation / l. Probabilistic explanations
Can events whose probabilities are low be explained? [Salmon]
     Full Idea: Can events whose probabilities are low be explained?
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.6)
     A reaction: I take this to be one of the reasons why explanation must ultimately reside at the level of individual objects and events, rather than residing with generalisations and laws.
Statistical explanation needs relevance, not high probability [Salmon]
     Full Idea: Statistical relevance, not high probability, is the key desideratum in statistical explanation.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 2.5)
     A reaction: I suspect that this is because the explanation will not ultimately be probabilistic at all, but mechanical and causal. Hence the link is what counts, which is the relevance. He notes that relevance needs two values instead of one high value.
Think of probabilities in terms of propensities rather than frequencies [Salmon]
     Full Idea: Perhaps we should think of probabilities in terms of propensities rather than frequencies.
     From: Wesley Salmon (Four Decades of Scientific Explanation [1989], 3.2)
     A reaction: [He cites Coffa 1974 for this] I find this suggestion very appealing, as it connects up with dispositions and powers, which I take to be the building blocks of all explanation. It is, of course, easier to render frequencies numerically.