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All the ideas for 'Realism in Mathematics', 'The Question of Realism' and 'De Legibus Naturae'

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27 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K]
     Full Idea: If there is no way of settling metaphysical questions, then who cares whether or not they make sense?
     From: Kit Fine (The Question of Realism [2001], 4 n20)
     A reaction: This footnote is aimed at logical positivists, who seemed to worry about whether metaphysics made sense, and also dismissed its prospects even if it did make sense.
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K]
     Full Idea: The 'quietist' view of metaphysics says that realist metaphysics should be abandoned, not because its questions cannot be framed, but because their answers cannot be found. The real world of metaphysics is akin to Kant's noumenal world.
     From: Kit Fine (The Question of Realism [2001], 4)
     A reaction: [He cites Blackburn, Dworkin, A.Fine, and Putnam-1987 as quietists] Fine aims to clarify the concepts of factuality and of ground, in order to show that metaphysics is possible.
2. Reason / A. Nature of Reason / 7. Status of Reason
If a decision is in accord with right reason, everyone can agree with it [Cumberland]
     Full Idea: No decision can be in accord with right reason unless all can agree on it.
     From: Richard Cumberland (De Legibus Naturae [1672], Ch.V.XLVI)
     A reaction: Personally I think anyone who disagrees with this should get out of philosophy (and into sociology, fantasy fiction, ironic game-playing, crime…). Of course 'can' agree is not the same as 'will' agree. You must have faith that good reasons are persuasive.
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
     Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
     A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
     Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members.
     From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties
     A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
     Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3
     A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
     Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience.
     From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5
     A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory.
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K]
     Full Idea: My main objection to Fine's notion of grounding as fundamental is that it violates 'purity' - that fundamental truths should involve only fundamental notions.
     From: comment on Kit Fine (The Question of Realism [2001]) by Theodore Sider - Writing the Book of the World 08.2
     A reaction: [p.106 of Sider for 'purity'] The point here is that to define a grounding relation you have to mention the 'higher' levels of the relationship (as in a 'city' being grounded in physical stuff), which doesn't seem fundamental enough.
Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider]
     Full Idea: When p 'grounds' q then q holds in virtue of p's holding; q's holding is nothing beyond p's holding; the truth of p explains the truth of q in a particularly tight sense (explanation of q by p in this sense requires that p necessitates q).
     From: report of Kit Fine (The Question of Realism [2001], 15-16) by Theodore Sider - Writing the Book of the World 08.1
     A reaction: This proposal has become a hot topic in current metaphysics, as attempts are made to employ 'grounding' in various logical, epistemological and ontological contexts. I'm a fan - it is at the heart of metaphysics as structure of reality.
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
Grounding relations are best expressed as relations between sentences [Fine,K]
     Full Idea: I recommend that a statement of ground be cast in the following 'canonical' form: Its being the case that S consists in nothing more than its being the case that T, U... (where S, T, U... are particular sentences).
     From: Kit Fine (The Question of Realism [2001], 5)
     A reaction: The point here is that grounding is to be undestood in terms of sentences (and 'its being the case that...'), rather than in terms of objects, properties or relations. Fine thus makes grounding a human activity, rather than a natural activity.
7. Existence / C. Structure of Existence / 2. Reduction
Reduction might be producing a sentence which gets closer to the logical form [Fine,K]
     Full Idea: One line of reduction is logical analysis. To say one sentence reduces to another is to say that they express the same proposition (or fact), but the grammatical form of the second is closer to the logical form than the grammatical form of the first.
     From: Kit Fine (The Question of Realism [2001], 3)
     A reaction: Fine objects that S-and-T reduces to S and T, which is two propositions. He also objects that this approach misses the de re ingredient in reduction (that it is about the things themselves, not the sentences). It also overemphasises logical form.
Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K]
     Full Idea: A second line of reduction is semantic, and holds in virtue of the meaning of the sentences. It should then be possible to acquire an understanding of the reduced sentence on the basis of understanding the sentences to which it reduces.
     From: Kit Fine (The Question of Realism [2001], 3)
     A reaction: Fine says this avoids the first objection to the grammatical approach (see Reaction to Idea 15050), but still can't handle the de re aspect of reduction. Fine also doubts whether this understanding qualifies as 'reduction'.
Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K]
     Full Idea: The third, more recent, approach to reduction is a modal matter. A class of propositions will reduce to - or supervene upon - another if, necessarily, any truth from the one is entailed by truths from the other.
     From: Kit Fine (The Question of Realism [2001], 3)
     A reaction: [He cites Armstrong, Chalmers and Jackson for this approach] Fine notes that some people reject supervenience as a sort of reduction. He objects that this reduction doesn't necessarily lead to something more basic.
The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K]
     Full Idea: The notion of ground should be distinguished from the strict notion of reduction. A statement of reduction implies the unreality of what is reduced, but a statement of ground does not.
     From: Kit Fine (The Question of Realism [2001], 5)
     A reaction: That seems like a bit of a caricature of reduction. If you see a grey cloud and it reduces to a swarm of mosquitoes, you do not say that the cloud was 'unreal'. Fine is setting up a stall for 'ground' in the metaphysical market. We all seek structure.
7. Existence / D. Theories of Reality / 3. Reality
What is real can only be settled in terms of 'ground' [Fine,K]
     Full Idea: Questions of what is real are to be settled upon the basis of considerations of ground.
     From: Kit Fine (The Question of Realism [2001], Intro)
     A reaction: This looks like being one of Fine's most important ideas, which is shifting the whole basis of contemporary metaphysics. Only Parmenides and Heidegger thought Being was the target. Aristotle aims at identity. What grounds what is a third alternative.
Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K]
     Full Idea: I conclude that there is a primitive metaphysical concept of reality, one that cannot be understood in fundamentally different terms.
     From: Kit Fine (The Question of Realism [2001], Intro)
     A reaction: Fine offers arguments to support his claim, but it seems hard to disagree with. The only alternative I can see is to understand reality in terms of our experiences, and this is the road to metaphysical hell.
Why should what is explanatorily basic be therefore more real? [Fine,K]
     Full Idea: We may grant that some things are explanatorily more basic than others, but why should that make them more real?
     From: Kit Fine (The Question of Realism [2001], 8)
     A reaction: This is the question asked by the 'quietist'. Fine's answer is that our whole conception of Reality, with its intrinsic structure, is what lies at the basis, and this is primitive.
In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K]
     Full Idea: The first main approach says metaphysical reality is to be identified with what is 'objective' or 'factual'. ...According to the second conception, metaphysical reality is to be identified with what is 'irreducible' or 'fundamental'.
     From: Kit Fine (The Question of Realism [2001], 1)
     A reaction: Fine is defending the 'fundamental' approach, via the 'grounding' relation. The whole structure, though, seems to be reality. In particular, a complete story must include the relations which facilitate more than mere fundamentals.
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K]
     Full Idea: As long as colour terms pick out fundamental physical properties, I would be willing to countenance their use in the description of Reality in itself, ..even if they are based on a peculiar form of sensory awareness.
     From: Kit Fine (The Question of Realism [2001], 8)
     A reaction: This seems to explain why metaphysicians are so fond of using colour as their example of a property, when it seems rather subjective. There seem to be good reasons for rejecting Fine's view.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K]
     Full Idea: The main sources of evidence for judgments of ground are intuitive and explanatory. The relationship of ground is a form of explanation, ..explaining what makes a proposition true, which needs simplicity, breadth, coherence, non-circularity and strength.
     From: Kit Fine (The Question of Realism [2001], 7)
     A reaction: My thought is that not only must grounding explain, and therefore be a good explanation, but that the needs of explanation drive our decisions about what are the grounds. It is a bit indeterminate which is tail and which is dog.
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K]
     Full Idea: We take ground to be an explanatory relation: if the truth that P is grounded in other truths, then they account for its truth; P's being the case holds in virtue of the other truths' being the case. ...It is the ultimate form of explanation.
     From: Kit Fine (The Question of Realism [2001], 5)
     A reaction: To be 'ultimate' that which grounds would have to be something which thwarted all further explanation. Popper, for example, got quite angry at the suggestion that we should put a block on further investigation in this way.
19. Language / D. Propositions / 5. Unity of Propositions
A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K]
     Full Idea: A proposition essentially contains a given constituent if its replacement by some other constituent induces a shift in truth value. Thus Socrates is essential to the proposition that Socrates is a philosopher, but not to Socrates is self-identical.
     From: Kit Fine (The Question of Realism [2001], 6)
     A reaction: In this view the replacement of 'is' by 'isn't' would make 'is' (or affirmation) part of the essence of most propositions. This is about linguistic essence, rather than real essence. It has the potential to be trivial. Replace 'slightly' by 'fairly'?
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
Natural law is supplied to the human mind by reality and human nature [Cumberland]
     Full Idea: Some truths of natural law, concerning guides to moral good and evil, and duties not laid down by civil law and government, are necessarily supplied ot the human mind by the nature of things and of men.
     From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.I)
     A reaction: I agree that some moral truths have the power of self-evidence. If you say they are built into the mind, we now ask what did the building, and evolution is the only answer, and hence we distance ourselves from the truths, seeing them as strategies.
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
If there are different ultimate goods, there will be conflicting good actions, which is impossible [Cumberland]
     Full Idea: If there be posited different ultimate ends, whose causes are opposed to each other, then there will be truly good actions likewise opposed to each other, which is impossible.
     From: Richard Cumberland (De Legibus Naturae [1672], Ch.V.XVI)
     A reaction: A very interesting argument for there being one good rather than many, and an argument which I don't recall in any surviving Greek text. A response might be to distinguish between what is 'right' and what is 'good'. See David Ross.
23. Ethics / E. Utilitarianism / 1. Utilitarianism
The happiness of individuals is linked to the happiness of everyone (which is individuals taken together) [Cumberland]
     Full Idea: The happiness of each person cannot be separated from the happiness of all, because the whole is no different from the parts taken together.
     From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.VI)
     A reaction: Sounds suspiciously like the fallacy of composition (Idea 6219). An objection to utilitarianism is its assumption that a group of people have a 'total happiness' that is different from their individual states. Still, Cumberland is on to utilitarianism.
The happiness of all contains the happiness of each, and promotes it [Cumberland]
     Full Idea: The common happiness of all contains the greatest happiness for each, and most effectively promotes it. …There is no path leading anyone to his own happiness, other than the path which leads all to the common happiness.
     From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.VI)
     A reaction: I take this as a revolutionary idea, which leads to utilitarianism. It is doing what seemed to the Greeks unthinkable, which is combining hedonism with altruism. There is no proof for it, but it is a wonderful clarion call for building a civil society.
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Natural law is immutable truth giving moral truths and duties independent of society [Cumberland]
     Full Idea: Natural law is certain propositions of immutable truth, which guide voluntary actions about the choice of good and avoidance of evil, and which impose an obligation to act, even without regard to civil laws, and ignoring compacts of governments.
     From: Richard Cumberland (De Legibus Naturae [1672], Ch.I.I)
     A reaction: Not a popular view, but I am sympathetic. If you are in a foreign country and find a person lying in pain, there is a terrible moral deficiency in anyone who just ignores such a thing. No legislation can take away a person's right of self-defence.