w a y s h a v e b e e n . W e a l l r e m e m b e r M a (...) class='Hi'> r x ' s p o l e m i c a g a i n s t P r o u d h o n , t h e Manifesto's critique of "historical action [yielding] to personal inventive action, historically created conditions of emancipation to fantastic ones, and the gradual spontaneous class organizations of the proletariat to an organization of society specially contrived by these inventors" (Marx and Engels, 1986, 64), and the numerous other occasions when the fathers of "scientific socialism" went a f t e r t h e " u t o p i a n s . " I n general this Marxian aversion to drawing up blueprints has been healthy, fueled at least in part by a respect for the concrete specificity of the revolutionary situation and for the agents engaged in revolutionary activity: it is not the business of Marxist intellectuals to tell the agents of revolution how they are to construct their postrevolutionary economy. (shrink)
In spite of vast global improvements in living standards, health, and well-being, the persistence of absolute poverty and its attendant maladies remains an unsettling fact of (...) class='Hi'>life for billions around the world and constitutes the primary cause for the failure of developing states to improve the health of their peoples. While economic development in developing countries is necessary to provide for underlying determinants of health – most prominently, poverty reduction and the building of comprehensive primary health systems – inequalities in power within the international economic order and the spread of neoliberal development policy limit the ability of developing states to develop economically and realize public goods for health. With neoliberal development policies impacting entire societies, the collective right to development, as compared with an individual rights-based approach to development, offers a framework by which to restructure this system to realize social determinants of health. The right to development, working through a vector of rights, can address social determinants of health, obligating states and the international community to support public health systems while reducing inequities in health through poverty-reducing economic growth. At an international level, where the ability of states to develop economically and to realize public goods through public health systems is constrained by international financial institutions, the implementation of the right to development enables a restructuring of international institutions and foreign-aid programs, allowing states to enter development debates with a right to cooperation from other states, not simply a cry for charity. (shrink)
Different researchers use "the philosophy of automated theorem p r o v i n g " t o cover d i f f e r e n t (...) class='Hi'> concepts, indeed, different levels of concepts. Some w o u l d count such issues as h o w to e f f i c i e n t l y i n d e x databases as part of the philosophy of automated theorem p r o v i n g . Others wonder about whether f o r m u l a s should be represented as strings or as trees or as lists, and call this part of the philosophy of automated theorem p r o v i n g . Yet others concern themselves w i t h what k i n d o f search should b e embodied i n a n y automated theorem prover, or to what degree any automated theorem prover should resemble Prolog. Still others debate whether natural deduction or semantic tableaux or resolution is " b e t t e r " , a n d c a l l t h i s a part of the p h i l o s o p h y of automated theorem p r o v i n g . Some people wonder whether automated theorem p r o v i n g should be " h u m a n oriented" or "machine o r i e n t e d " — sometimes arguing about whether the internal p r o o f methods should be " h u m a n - I i k e " or not, sometimes arguing about whether the generated proof should be output in a f o r m u n d e r s t a n d a b l e by p e o p l e , and sometimes a r g u i n g a b o u t the d e s i r a b i l i t y o f h u m a n intervention in the process of constructing a proof. There are also those w h o ask such questions as whether we s h o u l d even be concerned w i t h completeness or w i t h soundness of a system, or perhaps we should instead look at very efficient (but i n c o m p l e t e ) subsystems or look at methods of generating models w h i c h might nevertheless validate invalid arguments. A n d a l l of these have been v i e w e d as issues in the philosophy of automated theorem proving. Here, I w o u l d l i k e to step back from such i m p l e m e n t - ation issues and ask: " W h a t do we really think we are doing when we w r i t e an automated theorem prover?" My reflections are perhaps idiosyncratic, but I do think that they put the different researchers* efforts into a broader perspective, and give us some k i n d of handle on w h i c h directions we ourselves m i g h t w i s h to pursue when constructing (or extending) an automated theorem proving system. A logic is defined to be (i) a vocabulary and formation rules ( w h i c h tells us w h a t strings of symbols are w e l l - formed formulas in the logic), and ( i i ) a definition of ' p r o o f in that system ( w h i c h tells us the conditions under which an arrangement of formulas in the system constitutes a proof). Historically speaking, definitions of ' p r o o f have been given in various different manners: the most c o m m o n have been H i l b e r t - s t y l e ( a x i o m a t i c ) , Gentzen-style (consecution, or sequent), F i t c h - s t y l e (natural deduction), and Beth-style (tableaux).. (shrink)
The symbolism introduced earlier provides a convenient vehicle for examining the status and consistency of Aristotle's three diverse justifications and for explaining how he means to (...) class='Hi'>avoid Protagorean relativism without embracing Platonic absolutism. When the variables ‘ x ’ and ‘ y ’ are allowed to range over the groups of free men in a given polis as well as over individual free men, the formula for the Aristotelian conception of justice expresses the major premiss of Aristotle's three justifications: (1) (∀ x )(∀ y ) (P(x)·W(x)/P(y)·W(y)=V(T(x))/V(T(y)))Democracy is justified by adding a minor premiss to the effect that as a group the many ( m ) are superior (>) in virtue and wealth to the few best men ( f ): 85 (2 d ) (P(m) · W(m)) > (P(f) · W(f)) (3 d ) V(T(m))>V(T(f))Absolute kingship is justified when a godlike man ( g ) appears in a polis who is incommensurably superior (≫) in virtue and wealth to all the remaining free men ( r ): (2 k ) (P(g) · W(g)) ≫ (P(r) · W(r)) (3 k ) V(T(g)) ≫ V(T(r))True aristocracy requires a more complex justification, which was symbolized in Section 4. These justifications are compatible with each other since they apply to different situations. The polises where democracy and true aristocracy are justified contain no godlike men, and the polis in which democracy is justified differs from that in which true aristocracy is justified in containing a large group of free men who individually have little virtue ( Pol. III.11.1281b23-25, 1282a25-26). Each of the justifications is a valid deductive argument. Aristotle affirms the major premiss they share on the basis of a twofold appeal to nature. The principle of distributive justice, the concept as distinguished from the various conceptions of distributive justice, is itself according to nature ( Pol. VII.3.1325b7-10) and so too is one particular standard of worth, the standard of the best polis. Consequently, the question of the status of these three justifications, whether they are purely hypothetical or not, is a question about the minor premiss or premisses of each. In the case of the democratic premiss Aristotle's answer is straightforward: it is sometimes but not always true ( Pol. III.11.1281bl5-21). Hence the justification of democracy is not purely hypothetical. Nor is the justification of absolute kingship. The man who is “like a god among men” ( Pol. III.13.1284a10-11) would be a man of heroic virtue (see VII.14.1332bl6-27); and such a man, Aristotle says, is “rare” ( σπávιoη ) (not nonexistent) ( E.N. VII.1.1145a27-28). The minor premisses of the aristocratic argument describe a situation where all of the free men in a given polis have sufficient wealth for the exercise of the moral and intellectual virtues and where all of the older free men of the polis are men of practical wisdom. In the Politics Aristotle makes only the modest claim that such a situation is possible: It is not possible for the best constitution to come into being without appropriate equipment [that is, the appropriate quality and quantity of territory and of citizens and noncitizens]. Hence one must presuppose many things as one would wish them to be, though none of them must be impossible ( Pol. VII.4.1325b37-38; see also II.6.1265al7-18). But Aristotle appears to subscribe to the principle that every possibility is realized at some moment of time ( Top. 11.11.115bl7-18, Met. Θ.4.1047b3-6, N.2.1088b23-25). This principle together with the claim that the situation described is possible entails that the situation sometimes occurs. Thus even Aristotle's justification of true aristocracy is not purely hypothetical. The final question is Aristotle's way of avoiding Protagorean relativism without embracing Platonic absolutism. The relativist, along with everyone else ( E.N. V.3.1131a13-14, Pol. III.12.1282bl8), can accept the principle of distributive justice: Q(x)/Q(y) = V(T(x))/V(T(y)) And he can concede that particular instances of this principle, particular conceptions of justice, accurately describe the modes of distributing political authority that appear just to particular polises and to particular philosophers. What he denies is that there is any basis for ranking these various conceptions of justice or for singling one out as the best (Plato, Theaet. 172A-B). Aristotle, following in Plato's track ( Laws X.888D7-890D8), maintains against the relativist that nature provides such a basis. But he departs from Plato in his conception of nature. For Plato “the just by nature” ( τó ρυσει δίκ↑oν }) ( Rep. VI.501B2) is the Form of justice, an incorporeal entity ( Phdo. 65D4-5, Soph. 246B8) that exists beyond time and space ( Tim. 37C6-38C3, 51E6-52B2), whereas for Aristotle the sensible world is the realm of nature ( Met. A.1.1069a30-b2). Thus in appealing to nature Aristotle does not appeal to a transcendent standard. Nor does he appeal to his main criterion of the natural, namely, happening always or for the most part. Aristotle's theory of justice is anchored to nature by means of the polis described in Politics VII and VIII, and he regards this polis as natural because it fosters the true end of human life and because its social and political structure reflects the natural hierarchy of human beings and the natural stages of life. Thus the nature that Aristotle's theory of justice is ultimately founded on is human nature. (shrink)
In a recent paper [1], O. F. de Alcantara Bonfim, J. Florencio, and F. C. S´ a Barreto claim to have found numerical evidence of chaos in (...) the motion of a Bohmian quantum particle in a double square-well potential, for a wave function that is a superposition of five energy eigenstates. But according to the result proven here, chaos for this motion is impossible. We prove in fact that for a particle on the line in a superposition of n + 1 energy eigenstates, the Bohm motion x(t) is always quasiperiodic, with (at most) n frequencies. This means that there is a function F (y1, . . . , yn) of period 2π in each of its variables and n frequencies ω1, . . . , ωn such that x(t) = F (ω1t, . . . , ωnt). The Bohm motion for a quantum particle of mass m with wave function ψ = ψ(x, t), a solution to Schrödinger’s equation, is defined by.. (shrink)
A is for Alice and astronomers arguing about acceleration -- B is for Bernard's body-exchange machine -- C is for the Catholic cannibal -- D is for Maxwell (...) class='Hi'>'s demon -- E is for evolution (and an embarrassing problem with it) -- F is for the forms lost forever to the prisoners of the cave -- G is for Galileo's gravitational balls -- H is for Hume's shades -- I is for the identity of indiscernibles -- J is for Henri Poincaré and alternative geometries -- K is for the Kritik and Kant's kind of thought experiments -- L is for Lucretius' spear -- M is for Mach's motionless chain -- N is for Newton's bucket -- O is for Olbers' paradox -- P is for Parfit's person -- Q is for the questions raised by thought experiments quotidiennes -- R is for the rule-ruled room -- S is for Salvatius' ship, sailing along its own space-time line -- T is for the time-travelling twins -- U is for the universe, and Einstein's attempts to understand it -- V is for the vexed case of the violinist -- W is for Wittgenstein's beetle -- X is for xenophanes and thinking by examples -- Y is for counterfactuals and a backwards approach to history -- Z is for Zeno and the mysteries of infinity. (shrink)
A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n (...) class='Hi'>)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov function, which assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)
The main thrust of my argument was that ad hoc su gge s ti ons of ch a ri ty cannot replace a systematic and theoreti c (...) a lly inform ed approach to poverty rel i ef . Ch a ri t a ble don a ti on som eti m e s h elps—and som etimes harm s — but is no general solution to global poverty, and can be po s i tively dangerous wh en pre s en ted as such. We need to consider, and often choose, other routes to helping the poor—including ethical to u rism and fair trade in lu x u ry goods. We will not be able to invest in such feasible routes if we give away all our extra income, as Singer recommends. Sticking to donation above all, when a combination of other strategies is necessary, is highly likely to harm the poor. Si n ger doe s n’t re a lly en ga ge my argumen t . In s te ad , he cari c a tu res our “f u n d a m ental disa greem en t” :a pp a ren t ly, Si n ger rej ects va ri o u s policies because he takes into account the “f act s” ; wh ereas Ku per is the one seeking a “f a i t h ,” a “po l i tical ph i l o s ophy. . . i m mune to ref ut a ti on on the basis of evi den ce .” Anyon e who has re ad my arti cle (pp. 1 07 - 2 0) must fin d this puzzling. The arti cle explains at len g t h wh i ch kinds of b ack ground theories help us to d i s cern and re s pon s i bly con s i der the rel eva n t f act s . I show that Si n ger sel ects and uses fact s u n c ri ti c a lly prec i s ely because he has no po l i tical econ omy, no po l i tical soc i o l ogy, and no t h eory of ju s ti ce . We are seri o u s ly misled if we do not draw adequ a tely on the wi s dom and.. (shrink)