37 ideas
| 17275 | Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K] |
| Full Idea: We may broadly distinguish between two main branches of metaphysics: the 'realist' or 'critical' branch is concerned with what is real (tense, values, numbers); the 'naive' or 'pre-critical' branch concerns natures of things irrespective of reality. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: [compressed] The 'natures' of things are presumably the essences. He cites 3D v 4D objects, and the status of fictional characters, as examples of the second type. Fine says ground is central to realist metaphysics. |
| 17282 | Truths need not always have their source in what exists [Fine,K] |
| Full Idea: There is no reason in principle why the ultimate source of what is true should always lie in what exists. | |
| From: Kit Fine (Guide to Ground [2012], 1.03) | |
| A reaction: This seems to be the weak point of the truthmaker theory, since truths about non-existence are immediately in trouble. Saying reality makes things true is one thing, but picking out a specific bit of it for each truth is not so easy. |
| 17283 | If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K] |
| Full Idea: The truth-making relation is usually explicated in modal terms, ...but this lets in far too much. Any necessary truth will be grounded by anything. ...The fact that singleton Socrates exists will be a truth-maker for the proposition that Socrates exists. | |
| From: Kit Fine (Guide to Ground [2012], 1.03) | |
| A reaction: If truth-makers are what has to 'exist' for something to be true, then maybe nothing must exist for a necessity to be true - in which case it has no truth maker. Or maybe 2 and 4 must 'exist' for 2+2=4? |
| 17286 | Logical consequence is verification by a possible world within a truth-set [Fine,K] |
| Full Idea: Under the possible worlds semantics for logical consequence, each sentence of a language is associated with a truth-set of possible worlds in which it is true, and then something is a consequence if one of these worlds verifies it. | |
| From: Kit Fine (Guide to Ground [2012], 1.10) | |
| A reaction: [compressed, and translated into English; see Fine for more symbolic version; I'm more at home in English] |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well). | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant. |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals. |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting. |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality? |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel. |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers. |
| 23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
| Full Idea: It is by the natural light that the axioms of mathematics are recognised. If we take away the same quantity from two equal things, …a thing we can easily predict without having experienced it. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], p.189) | |
| A reaction: He also says two equal weights will keep a balance level. Plato thinks his slave boy understands halving an area by the natural light, but that is just as likely to be experience. It is too easy to attribut thoughts to a 'natural light'. |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold. |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters'). |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup. |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups. |
| 17272 | 2+2=4 is necessary if it is snowing, but not true in virtue of the fact that it is snowing [Fine,K] |
| Full Idea: It is necessary that if it is snowing then 2+2=4, but the fact that 2+2=4 does not obtain in virtue of the fact that it is snowing. | |
| From: Kit Fine (Guide to Ground [2012], 1.01) | |
| A reaction: Critics dislike 'in virtue of' (as vacuous), but I can't see how you can disagree with this obvervation of Fine's. You can hardly eliminate the word 'because' from English, or say p is because of some object. We demand the right to keep asking 'why?'! |
| 17276 | If you say one thing causes another, that leaves open that the 'other' has its own distinct reality [Fine,K] |
| Full Idea: It will not do to say that the physical is causally determinative of the mental, since that leaves open the possibility that the mental has a distinct reality over and above that of the physical. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: The context is a defence of grounding, so that if we say the mind is 'grounded' in the brain, we are saying rather more than merely that it is caused by the brain. A ghost might be 'caused' by a bar of soap. Nice. |
| 17284 | An immediate ground is the next lower level, which gives the concept of a hierarchy [Fine,K] |
| Full Idea: It is the notion of 'immediate' ground that provides us with our sense of a ground-theoretic hierarchy. For any truth, we can take its immediate grounds to be at the next lower level. | |
| From: Kit Fine (Guide to Ground [2012], 1.05 'Mediate') | |
| A reaction: Are the levels in the reality, the structure or the descriptions? I vote for the structure. I'm defending the idea that 'essence' picks out the bottom of a descriptive level. |
| 17285 | 'Strict' ground moves down the explanations, but 'weak' ground can move sideways [Fine,K] |
| Full Idea: We might think of strict ground as moving us down in the explanatory hierarchy. ...Weak ground, on the other hand, may also move us sideways in the explanatory hierarchy. | |
| From: Kit Fine (Guide to Ground [2012], 1.05 'Weak') | |
| A reaction: This seems to me rather illuminating. For example, is the covering law account of explanation a 'sideways' move in explanation. Are inductive generalities mere 'sideways' accounts. Both fail to dig deeper. |
| 17288 | We learn grounding from what is grounded, not what does the grounding [Fine,K] |
| Full Idea: It is the fact to be grounded that 'points' to its ground and not the grounds that point to what they ground. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) | |
| A reaction: What does the grounding may ground all sorts of other things, but what is grounded only has one 'full' (as opposed to 'partial', in Fine's terminology) ground. He says this leads to a 'top-down' approach to the study of grounds. |
| 17281 | If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K] |
| Full Idea: In so far as ground is regarded as a relation it should be between entities of the same type, and the entities should probably be taken as worldly entities, such as facts, rather than as representational entities, such as propositions. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: That's more like it (cf. Idea 17280). The consensus of this discussion seems to point to facts as the best relata, for all the vagueness of facts, and the big question of how fine-grained facts should be (and how dependent they are on descriptions). |
| 17280 | Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K] |
| Full Idea: Ground is perhaps best regarded as an operation (signified by an operator on sentences) rather than as a relation (signified by a predicate) | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: Someone in this book (Koslicki?) says this is to avoid metaphysical puzzles over properties. I don't like the idea, because it makes grounding about sentences when it should be about reality. Fine is so twentieth century. Audi rests ground on properties. |
| 17290 | Only metaphysical grounding must be explained by essence [Fine,K] |
| Full Idea: If the grounding relation is not metaphysical (such as normative or natural grounding), there is no need for there to be an explanation of its holding in terms of the essentialist nature of the items involved. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) | |
| A reaction: He accepts that some things have partial grounds in different areas of reality. |
| 17274 | Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K] |
| Full Idea: For philosophers interested in explanation - of what accounts for what - it is largely through the notion of ontological ground that such questions are to be pursued. Ground, if you like, stands to philosophy as cause stands to science. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: Why does the ground have to be 'ontological'? It isn't the existence of the snow that makes me cold, but the fact that I am lying in it. Better to talk of 'factual' ground (or 'determinative' ground), and then causal grounds are a subset of those? |
| 17278 | We can only explain how a reduction is possible if we accept the concept of ground [Fine,K] |
| Full Idea: It is only by embracing the concept of a ground as a metaphysical form of explanation in its own right that one can adequately explain how a reduction of the reality of one thing to another should be understood. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: I love that we are aiming to say 'how' a reduction should be understood, and not just 'that' it exists. I'm not sure about Fine's emphasis on explaining 'realities', when I think we are after more like structural relations or interconnected facts. |
| 17287 | Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K] |
| Full Idea: Given any facts, there will be a fusion of those facts. Given the facts that the ball is red and that it is round, there is a fused fact that it is 'red and round'. | |
| From: Kit Fine (Guide to Ground [2012], 1.10) | |
| A reaction: This is how we make 'units' for counting. Any type of thing which can be counted can be fused, such as the first five prime numbers, forming the 'first' group for some discussion. Any objects can be fused to make a unit - but is it thereby a 'unity'? |
| 13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
| Full Idea: That which is necessary for something does not constitute its essence. Air is necessary for our life, but our life is something other than air. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: Bravo. Why can't modern philosophers hang on to this distinction? They seem to think that because they don't believe in traditional essences they can purloin the word for something else. Same with the word 'abstraction'. |
| 17279 | Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K] |
| Full Idea: Even the three-dimensionalist might be willing to admit that material things have temporal parts. For given any persisting object, he might suppose that 'in thought' we could mark out its temporal segments or parts. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: A big problem with temporal parts is how thin they are. Hawley says they are as fine-grained as time itself, but what if time has no grain? How thin can you 'think' a temporal part to be? Fine says imagined parts are grounded in things, not vice versa. |
| 17273 | Each basic modality has its 'own' explanatory relation [Fine,K] |
| Full Idea: I am inclined to the view that ....each basic modality should be associated with its 'own' explanatory relation. | |
| From: Kit Fine (Guide to Ground [2012], 1.01) | |
| A reaction: He suggests that 'grounding' connects the various explanatory relations of the different modalities. I like this a lot. Why assert any necessity without some concept of where the necessity arises, and hence where it is grounded? You've got to eat. |
| 17289 | Every necessary truth is grounded in the nature of something [Fine,K] |
| Full Idea: It might be held as a general thesis that every necessary truth is grounded in the nature of certain items. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) | |
| A reaction: [He cites his own 1994 for this] I'm not sure if I can embrace the 'every' in this. I would only say, more cautiously, that I can only make sense of necessity claims when I see their groundings - and I don't take a priori intuition as decent grounding. |
| 19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
| Full Idea: Intelligible truth is independent of the truth or of the existence outside us of sensible and material things. ....It is generally true that we only know necessary truths by the natural light [of reason] | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: A nice quotation summarising a view for which Leibniz is famous - that there is a tight correlation between necessary truths and our a priori knowledge of them. The obvious challenge comes from Kripke's claim that scientists can discover necessities. |
| 19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
| Full Idea: We use the external senses ...to make us know their particular objects ...but they do not make us know what those sensible qualities are ...whether red is small revolving globules causing light, heat a whirling of dust, or sound is waves in air. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: These seems to be exactly the concept of secondary qualities which Locke was promoting. They are unreliable information about the objects we perceive. Primary qualities are reliable information. I like that distinction. |
| 19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
| Full Idea: It can be said that there is nothing in the understanding which does not come from the senses, except the understanding itself, or that which understands. | |
| From: Gottfried Leibniz (Letters to Queen Charlotte [1702], 1702) | |
| A reaction: Given that Leibniz is labelled as a 'rationalist', this is awfully close to empiricism. Not Locke's 'tabula rasa' perhaps, but Hume's experiences plus associations. Leibniz has a much loftier notion of understanding and reason than Hume does. |
| 17291 | We explain by identity (what it is), or by truth (how things are) [Fine,K] |
| Full Idea: I think it should be recognised that there are two fundamentally different types of explanation; one is of identity, or of what something is; and the other is of truth, or of how things are. | |
| From: Kit Fine (Guide to Ground [2012], 1.11) |
| 17271 | Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K] |
| Full Idea: In addition to scientific or causal explanation, there maybe a distinctive kind of metaphysical explanation, in which explanans and explanandum are connected, not through some causal mechanism, but through some constitutive form of determination. | |
| From: Kit Fine (Guide to Ground [2012], Intro) | |
| A reaction: I'm unclear why determination has to be 'constitutive', since I would take determination to be a family of concepts, with constitution being one of them, as when chess pieces determine a chess set. Skip 'metaphysical'; just have Determinative Explanation. |
| 17277 | If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K] |
| Full Idea: It is not enough to require that the mental should modally supervene on the physical, since that still leaves open the possibility that the physical is itself ultimately to be understood in terms of the mental. | |
| From: Kit Fine (Guide to Ground [2012], 1.02) | |
| A reaction: See Horgan on supervenience. Supervenience is a question, not an answer. The first question is whether the supervenience is mutual, and if not, which 'direction' does it go in? |