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Text of the page (random words):
ess mereological sums are less fine grained than pluralities so if we require each plurality to be identical to a particular sum we lose the important distinctions that plural logic makes this suggests a better way mereological sums are abstractions from pluralities roughly speaking sums are pluralities with some distinctions ignored in particular sums are what you get by abstracting from pluralities on the relation of being coextensive analogously colors are what you get when you abstract from objects on the same color relation numbers are what you get when you abstract from pluralities on equinumerosity let s polish this up a bit take overlap as primitive and define parthood in the standard way x is part of y iff everything that overlaps x overlaps y this has a natural plural generalization the xs are covered by the ys iff everything that overlaps some x overlaps some y parthood is the limiting case of being covered when there s just one x and one y i ll identify each object with its singleton plurality we can also define an equivalence relation the xs are coextensive with the ys iff the xs cover the ys and the ys cover the xs now we can state an abstraction principle let fus be a new primitive function symbol taking one plural argument fus x fus y iff the xs are coextensive with the ys compare hume s principle x y iff the xs are equinumerous with the ys this is the main principle governing composition it isn t the only principle we ll need for all i ve said so far fusions could live in platonic heaven but we need them to participate in mereological relations the following are equivalent the ys cover the xs the ys cover fus x fus y covers the xs this guarantees that fus x really is the fusion of the xs by the standard definition of fusion there is one final assumption needed to ensure that our mereology is standard parthood is antisymmetric if x is part of y and y is part of x then x y equivalently fus x x in the singular case composition really is identity these three principles imply all of standard mereology so just how innocent are they i think they re fairly innocent given the right conception of how abstraction works i like a tame account of abstraction which doesn t introduce any new ontological commitments this means tame abstraction is too weak for frege arithmetic or for frege s basic law v this is a good thing the basic idea is that abstract terms refer indefinitely to each of their instances for example the singular term red refers indefinitely to each red thing we consider all red instances as if they were a single thing without being specific as to which semantically you can understand indefinite reference in terms of supervaluations red has the properties that all red things must share e g if any red thing must be rosier than any taupe thing then we can also say that red is rosier than taupe speaking of red doesn t commit to any new entity it s just speaking of the old entities a new way as for colors so for fusions the fusion of the xs doesn t refer to some new exotic thing it refers indefinitely to each plurality coextensive with the xs you could say it refers to the xs as long as you don t mind the difference between coextensive pluralities furthermore since whenever the xs are coextensive with the ys they stand in exactly the same covering relations principle 2 is justified principle 3 on the other hand is not entirely innocent given the definition of parthood it amounts to extensionality no distinct singular objects are coextensive i think it s right to consider this a separate serious commitment one that unlike the rest of mereology doesn t flow from the mere conception of a mereological sum it might however flow from the conception of an object if you aren t too worried about speaking completely fundamentally antisymmetry can be had cheaply by considering objects to be coextension abstractions from the basic objects in just the same way that sums are coextension abstractions from the basic pluralities so indeed the whole is nothing more than its parts it can t be identified with any particular plurality of its parts but it can be identified indefinitely with every plurality of its parts there s a technical issue for the semantics i ve alluded to here i m treating fus x as semantically plural it refers indefinitely to pluralities but it is syntactically singular in particular as a singular term it can be ascribed membership in pluralities but this means that i need the semantics to allow pluralities to be members of pluralities and so on and this isn t ordinarily allowed so it looks like i ll need to give the semantics in terms of superplurals see section 2 4 of the sep article on plural quantifiers whether this semantic richness should be reflected in the language is a separate issue i m inclined to think not but i haven t really thought it through written by jeff april 25 2009 at 12 21 pm posted in logic metaphysics tagged with abstraction mereology plurals laws before facts with 3 comments does the universe come facts first or laws first that is in terms of metaphysical priority do the non nomic facts determine what the laws of nature are or are the laws at the ground floor determining what the non nomic facts are or maybe neither grounds the other i ll ignore this view for now the best known example of a facts first theory is lewis s best system account to be a law of nature is to be a member of the set of generalizations over the non nomic facts that has the best balance of simplicity and strength here are two rough and ready arguments against an account like that the first is the circularity argument i gestured at a few weeks ago the laws explain the non nomic facts if y explains x then x does not explain y if x grounds y then x explains y so the non nomic facts don t ground the laws and this is the second the non nomic facts are many and disparate the laws are simple and few prefer metaphysical theories that are simpler and more parsimonious at the fundamental level so prefer laws first to facts first metaphysics the second premise is a methodological principle rather than a general metaphysical claim hence the imperative it s a ceteris paribus principle and so the conclusion is a ceteris paribus conclusion there is a presumption in favor of laws first accounts thoughts written by jeff april 18 2009 at 6 57 pm posted in metaphysics science tagged with explanation fundamentality laws another quick objection to tooley leave a comment in the nature of laws 1977 michael tooley claims that it is nomologically true that f s are g s just in case a certain relation r the nomological relation holds between the universal f ness and the universal g ness he claims further that this relation symbol r is a theoretical term whose referent is fixed in ramsey lewis style we specify some constraints c and then stipulate that r is the unique relation that satisfies c these are his constraints r is a two place relation on universals r is contingent there are universals f ness and g ness such that it is neither necessary that r f ness g ness nor necessary that not r f ness g ness r f ness g ness logically entails that all f s are g s i ve left out the complications that are introduced to deal with laws that have different forms such as all non f s are g s or h s tooley doesn t think there are negative or disjunctive universals but tooley thinks there is a different nomological relation associated with each syntactic construction so this doesn t make a difference here but it doesn t look at all plausible to me that these constraints pick out a unique relation assuming anything satisfies them at all look here s a non nomological relation that satisfies conditions 1 4 the relation denoted by the two place quantifier all that is the relation that holds between f ness and g ness just in case all f s are g s tooley hasn t said anything that would distinguish his nomological relation from such run of the mill categorical relations this strikes me as a serious problem am i missing something i m working through david armstrong s what is a law of nature now i ll see if he adds anything helpful edit i inadvertently left out one of tooley s constraints r is irreducibly second order you might think this might help you might say in particular that the all relation is in fact reducible to less than second order universals only since after all all f g holds iff for every x if fx then gx but this reduction involves the concept for every which plausibly involves the all relation in disguise analogously one might reduce a purported nomological relation r by pointing out that r f g holds iff it is nomologically necessary that for every x if fx then gx i guess i m not really sure what the rules are for reducing universals armstrong makes a conjecture along the same lines i speculate that the laws of nature constitute the only irreducibly second order relations between universals 84 so presumably he thinks that either there is no all relation or else that it is reducible to a lower order does anyone have an idea why he would think this written by jeff march 18 2009 at 9 26 am posted in metaphysics science tagged with laws necessity theoretical terms improbable laws with 3 comments one of my goals over spring break is to get familiar with some of the literature on laws of nature i may blog some thoughts on it as i go this afternoon i read michael tooley s the nature of laws in the anthology edited by john carroll in the section on the epistemology of laws tooley shows how we could become confident that a certain law holds in a bayesian framework he then argues that this confirmation story is a distinctive benefit of his account the dta account t here is a crucial assumption that seems reasonable if relations among universals are the truth makers for laws but not if facts about particulars are the truth makers this is the assumption that m and n the prior probabilities of certain statements of laws are not equal to zero if one takes the view that it is facts about the particulars falling under a generalization that make it a law then if one is dealing with an infinite universe it is hard to see how one can be justified in assigning any non zero probability to a generalization given evidence concerning only a finite number of instances for surely there is some non zero probability that any given particular will falsify the generalization and this entails given standard assumptions that as the number of particulars becomes infinite the probability that the generalization will be true is in the limit equal to zero in contrast if relations among universals are the truth makers for laws the truth maker for a given law is in a sense an atomic fact and it would seem perfectly justified given standard principles of confirmation theory to assign some non zero probability to this fact s obtaining this can t be right if tooley is right in the first paragraph that the probability of any universal generalization over particulars is zero then appealing to the atomicity of nomological facts is no help the problem is that on his own view the nomological relation between universals logically entails the corresponding universal generalization over particulars but this means that by monotonicity the probability of the relation can be no greater than the probability of the generalization so if the generalization has zero probability so too does the relation the upshot is that if tooley s point in the first paragraph is right then it s devastating for just about any account of the epistemology of laws because any account of laws will have it that a generalization being true by law entails it being plain old true so we d better figure out why tooley s point is wrong written by jeff march 14 2009 at 3 27 pm posted in epistemology metaphysics science tagged with laws probability non distributive explanations leave a comment this distribution principle looks awfully plausible a explains b and c iff a explains b and a explains c but i think it might be false at least in the right to left direction a potential counterexample comes from aristotle a bandit is lingering by a road and a farmer is walking home down the same road by chance as we would say they meet at place x at time t there is a telic explanation in terms of the bandit s purposes for his being at x at t and there is a telic explanation in terms of the farmer s purposes for his being at x at t but there is no telic explanation for their meeting even though i take it that their meeting just consists in both of them being at x at t the meeting is just a coincidence slightly more carefully let bp be the bandit s purposes and fp be the farmer s purposes and let bxt and fxt be the relevant location facts assuming that antecedent strengthening holds for explains this means that bp and fp telically explains bxt and bp and fp telically explains fxt but since their meeting is coincidental it seems plausible that bp and fp does not telically explain bxt and fxt if distribution fails for telic explanation then perhaps it fails for nomic explanations as well for the same kind of reason why does this matter it s relevant to my criticism last week of lewis s best system account of laws not just my criticism briefly i said on lewis s account the qualitative facts explain what the laws are but the laws should explain the qualitative facts that makes a very tight explanatory circle and that s bad a response might go it s true that the conjunction of the qualitative facts explain the laws it s also true that the laws explain each individual qualitative fact but it doesn t follow that the laws explain the conjunction of the qualitative facts since the distributive principle fails and so there is no bad explanatory circle written by jeff march 10 2009 at 4 38 pm posted in epistemology metaphysics science tagged with explanation laws magnetic laws with 7 comments i ve been thinking more about the problem of fit i posted last week specifically i m trying to work out how a response appealing to reference magnetism would go recall the puzzle how is it that when we select hypotheses that best exemplify our theoretical values we so often hit on the truth a simple example emeralds even those we haven t observed are green rather than grue and lo we believe they are green rather than believing they are grue it seems things could have been otherwise in either of two ways there might be people who project grue rather than green in a world like ours or there might be people who like us project green in a world where emeralds are grue those people are in for a shock why are we so lucky a response in the lewisian framework goes like this not all properties are created equal green is metaphysically more natural than grue in particular it is semantically privileged it is easier to have a term or thought about green than it is to have a term or thought about grue this should take care of possibility 1 if there are people who th...