This is the eleventh of 17 posts, which are collectively Eternity, etc.
......How closely would such interventions as we might expect under Open Theism have to resemble Mawson’s scenario (see previous post)? Why, to begin with, should the world’s aggregate happiness have decreased? The immediate consequence of Adolf’s birth was a little more joy in the Hitler household. And surely God would have intended to intervene further, as necessary to ensure that aggregate’s continued increase, if that had been His motivation. (Making such interventions would hardly cause further problems, as simply making evermore planets or heavens of inherently happy animals or angels might suffice.)
......But in any case, a more plausible motivation for an Open divine intervention would be that aggregate’s eventual perfection [i], e.g. by our becoming a communion of saints. Rather than the Open God intervening to ensure a baby’s birth [ii], He would more plausibly have answered Mrs. Hitler’s prayers in order to help her to relate to Him more fully [iii]. And had He done that, then the satisfaction of His desire would hardly have depended upon how her child grew up. It would have depended upon her free choices—to some extent (He would definitely have so helped her)—but that amounting to luck is generally rejected by libertarians [iv]. Furthermore, even if Mrs. Hitler did not respond by becoming a saint, the Open God could surely try again, and again. And His attempts might become irresistible, as Mrs. Hitler wised up, or perhaps she might become very undeserving.
......So in short, Mawson’s scenario did not show that the satisfaction of the Open God’s most beneficial desires—perhaps that everyone (who is not too undeserving) should end up somewhere heavenly forever—could not be inevitable. So we are left with no reason why we should think of the Open God (of any variety) as a “well-intentioned buffoon”[v], rather than as Jesus [vi], and hence no reason why God should know all about the future (cf. end of section IV). So although there are statements about the future that would not be known by the Presentist Open God despite them being in a sense correct, that sense has not been shown to be significant enough to obstruct divine omniscience.
......Notes:
......[i] Keith Ward, Divine Action (Flame, 1990), pp. 134–9.
......[ii] Swinburne, Is There a God? pp. 114–5.
......[iii] Robert M. Adams, “Theodicy and Divine Intervention,” in Thomas F. Tracy (ed.), The God Who Acts: Philosophical and theological explorations (Penn. State Univ. Press, 1994), pp. 31–40.
......[iv] Timothy O’Connor, “Is It All Just a Matter of Luck?” Philosophical Explorations 10 (2007): 157–61.
......[v] Mawson, “Divine eternity,” p. 48.
......[vi] Richard Swinburne, Was Jesus God? (Oxford Univ. Press, 2008). If Jesus is, like us, a continuant, then it’s hard to see how he could be, not just the signature, but the identity of a timeless God. But clearly an everlasting God could incarnate as fully human, e.g. if we are essentially spirits that produce human minds because we animate human brains.
Sunday, December 05, 2010
Friday, December 03, 2010
Bodging Up
This is the tenth of 17 posts, which are collectively Eternity, etc.
......Mawson’s main argument had the following preamble [i]. Early in 1936 it was, according to Mawson, vastly improbable that that year’s Man of the Year in Time magazine would be widely regarded ten years later as the most evil man ever. Mawson’s point seemed to be that if a temporal God would have known, early in 1936, that such a change was very unlikely, and if to find something so unlikely is to believe it false, which follows from Swinburne’s definition of “belief” according to Mawson [ii], then such a God would have believed that such would not happen, incorrectly (that man being Adolf Hitler).
......However, while the man in the street of early 1936 may well have found such a change unthinkable, surely the perfectly aware sustainer of the whole world might have known better. And in any case, while we do—and often should—believe things that, upon reflection, we would only regard as highly probable, the beliefs held by the Open God are presumably held infallibly. That latter observation was acknowledged by Mawson [iii], so let us now look at his main argument, which revolved around the following scenario [iv].
......The Open God answers the prayers of Mrs. Hitler by saving her unborn baby from a likely miscarriage, doing so because He wants to increase the aggregate happiness of the world. He does not know that her baby, Adolf, will eventually cause that aggregate to decrease. On the contrary, that Adolf Hitler will eventually produce terrible harm is known by Him to be fantastically unlikely. Still, terrible harm is what happened, and so His intervention did not result in greater happiness. And even if it had, He would just have got lucky.
......Of course if, were God timeless, so evil a man would never have been born, then history would be some evidence that God is not timeless [v]. But the idea behind Mawson’s scenario was that something like it must be possible under Open Theism, because the Open “God cannot will Himself to do anything under a description the truth of which depends on future free actions”[vi]. He can in the case of His own actions, however, via His constancy (see section IV), and in my next post I wonder why He would need to in our case.
......Notes:
......[i] Mawson, “Divine eternity,” p. 45.
......[ii] One’s belief that p amounts to a belief that p is more likely than q for some q, according to Richard Swinburne, Epistemic Justification (Clarendon Press, 2001), pp. 34–6. Swinburne was examining the justification of human beliefs (of that form) however, not describing God’s beliefs (as such). Mawson observed that we tend to believe that a tossed coin won’t land on its edge, even though it might. But the Lottery Paradox—I believe, of each ticket, that it won’t win, so (logically) I should believe that none will, whereas I know that one will—was addressed by Swinburne; ibid, pp. 37–8. And a natural resolution is to describe my belief that it probably won’t win at least that precisely. And in general, logical reasoning seems to involve natural language clarification procedures whose aim is an adequate bivalence. E.g. the ambiguity mentioned in note 31 might be clarified thus: Either something will definitely happen, or else it is, if not impossible, merely possible.
......[iii] Mawson, “Divine eternity,” p. 45.
......[iv] Ibid, p. 47.
......[v] Indeed, a world in which everyone always made good choices is a prima facie logical possibility, so one might wonder why a timeless God would not have created such a world, were He perfectly beneficent. For more on the atemporalist free will defense, see Mawson, Belief in God, pp. 198–271. For more discussion of theodicies, see Omniscience and the Odyssey Theodicy.
......[vi] Mawson, “Divine eternity,” p. 47.
......Mawson’s main argument had the following preamble [i]. Early in 1936 it was, according to Mawson, vastly improbable that that year’s Man of the Year in Time magazine would be widely regarded ten years later as the most evil man ever. Mawson’s point seemed to be that if a temporal God would have known, early in 1936, that such a change was very unlikely, and if to find something so unlikely is to believe it false, which follows from Swinburne’s definition of “belief” according to Mawson [ii], then such a God would have believed that such would not happen, incorrectly (that man being Adolf Hitler).
......However, while the man in the street of early 1936 may well have found such a change unthinkable, surely the perfectly aware sustainer of the whole world might have known better. And in any case, while we do—and often should—believe things that, upon reflection, we would only regard as highly probable, the beliefs held by the Open God are presumably held infallibly. That latter observation was acknowledged by Mawson [iii], so let us now look at his main argument, which revolved around the following scenario [iv].
......The Open God answers the prayers of Mrs. Hitler by saving her unborn baby from a likely miscarriage, doing so because He wants to increase the aggregate happiness of the world. He does not know that her baby, Adolf, will eventually cause that aggregate to decrease. On the contrary, that Adolf Hitler will eventually produce terrible harm is known by Him to be fantastically unlikely. Still, terrible harm is what happened, and so His intervention did not result in greater happiness. And even if it had, He would just have got lucky.
......Of course if, were God timeless, so evil a man would never have been born, then history would be some evidence that God is not timeless [v]. But the idea behind Mawson’s scenario was that something like it must be possible under Open Theism, because the Open “God cannot will Himself to do anything under a description the truth of which depends on future free actions”[vi]. He can in the case of His own actions, however, via His constancy (see section IV), and in my next post I wonder why He would need to in our case.
......Notes:
......[i] Mawson, “Divine eternity,” p. 45.
......[ii] One’s belief that p amounts to a belief that p is more likely than q for some q, according to Richard Swinburne, Epistemic Justification (Clarendon Press, 2001), pp. 34–6. Swinburne was examining the justification of human beliefs (of that form) however, not describing God’s beliefs (as such). Mawson observed that we tend to believe that a tossed coin won’t land on its edge, even though it might. But the Lottery Paradox—I believe, of each ticket, that it won’t win, so (logically) I should believe that none will, whereas I know that one will—was addressed by Swinburne; ibid, pp. 37–8. And a natural resolution is to describe my belief that it probably won’t win at least that precisely. And in general, logical reasoning seems to involve natural language clarification procedures whose aim is an adequate bivalence. E.g. the ambiguity mentioned in note 31 might be clarified thus: Either something will definitely happen, or else it is, if not impossible, merely possible.
......[iii] Mawson, “Divine eternity,” p. 45.
......[iv] Ibid, p. 47.
......[v] Indeed, a world in which everyone always made good choices is a prima facie logical possibility, so one might wonder why a timeless God would not have created such a world, were He perfectly beneficent. For more on the atemporalist free will defense, see Mawson, Belief in God, pp. 198–271. For more discussion of theodicies, see Omniscience and the Odyssey Theodicy.
......[vi] Mawson, “Divine eternity,” p. 47.
Wednesday, December 01, 2010
Theistic Presentism again
This is the ninth of 17 posts, which are collectively Eternity, etc.
......The collapse view of quantum mechanics (see previous post, also Modern Physical Probability) can help us to understand human agency [i]. But if wave-functions do not collapse then you would now be about to do everything that it was physically possible for you to do [ii], by splitting into lots of you (whereas you are a responsible agent). Furthermore, Perfect Being Theists—unlike most physicists—would not regard the question of what (or who) could collapse the universal wave-function as problematic.
......And our third reason—that there would be nothing to make all truths about the past true under Presentism—is similarly trivial under Perfect Being Theism, because God’s memory might serve as such a truth-maker [iii]. Conversely, Presentism can support Perfect Being Theism. E.g. it allows such Theists to “accept neither the timelessness nor the temporality of the being of God”[iv], insofar as “temporality” means being inside the temporal dimension or being dependent upon temporal constraints [v]. Furthermore, Presentism allows perfect goodness to become omnipresent [vi].
......Presentism is not, then, obviously implausible under Perfect Being Theism. So although there is a sense in which your earlier belief about reading on (or not) may have been correct—perhaps it seemed so with hindsight—it does not follow that an omniscient God would have known what you were going to do. Under Presentism, such a belief would not have described what was originally real—the two possibilities—accurately enough for it to have been part of divine omniscience.
......Nevertheless, it seems to me that if a God who does not know all about how things will be would be liable to bodge things up, as Mawson’s main argument claims [vii], then an omnipotent being would know them.
......Notes:
......[i] Henry P. Stapp, “Quantum Interactive Dualism: An alternative to materialism,” Journal of Consciousness Studies 12 (2005): 43–58.
......[ii] Penrose, The Road to Reality, pp. 783–4, pp. 806–9.
......[iii] Alan R. Rhoda, “Presentism, Truthmakers, and God,” Pacific Philosophical Quarterly 90 (2009): 41–62. Incidentally, even the Presentist past is completely real in the sense that all statements about it have definite truth-values. Indeed, it is at least partially real in the more ontological sense that some continuants that did exist still do.
......[iv] Colin E. Gunton, The Triune Creator: A historical and systematic study (Eerdmans, 1998), p. 92.
......[v] With different senses—e.g. those of Padgett, God, Eternity and the Nature of Time—Presentism would allow us to accept both terms consistently.
......[vi] Paul Copan & William Lane Craig, Creation out of Nothing: A biblical, philosophical, and scientific exploration (Apollos, 2004), p. 162 n. 29.
......[vii] Mawson, “Divine eternity,” pp. 45–9.
......The collapse view of quantum mechanics (see previous post, also Modern Physical Probability) can help us to understand human agency [i]. But if wave-functions do not collapse then you would now be about to do everything that it was physically possible for you to do [ii], by splitting into lots of you (whereas you are a responsible agent). Furthermore, Perfect Being Theists—unlike most physicists—would not regard the question of what (or who) could collapse the universal wave-function as problematic.
......And our third reason—that there would be nothing to make all truths about the past true under Presentism—is similarly trivial under Perfect Being Theism, because God’s memory might serve as such a truth-maker [iii]. Conversely, Presentism can support Perfect Being Theism. E.g. it allows such Theists to “accept neither the timelessness nor the temporality of the being of God”[iv], insofar as “temporality” means being inside the temporal dimension or being dependent upon temporal constraints [v]. Furthermore, Presentism allows perfect goodness to become omnipresent [vi].
......Presentism is not, then, obviously implausible under Perfect Being Theism. So although there is a sense in which your earlier belief about reading on (or not) may have been correct—perhaps it seemed so with hindsight—it does not follow that an omniscient God would have known what you were going to do. Under Presentism, such a belief would not have described what was originally real—the two possibilities—accurately enough for it to have been part of divine omniscience.
......Nevertheless, it seems to me that if a God who does not know all about how things will be would be liable to bodge things up, as Mawson’s main argument claims [vii], then an omnipotent being would know them.
......Notes:
......[i] Henry P. Stapp, “Quantum Interactive Dualism: An alternative to materialism,” Journal of Consciousness Studies 12 (2005): 43–58.
......[ii] Penrose, The Road to Reality, pp. 783–4, pp. 806–9.
......[iii] Alan R. Rhoda, “Presentism, Truthmakers, and God,” Pacific Philosophical Quarterly 90 (2009): 41–62. Incidentally, even the Presentist past is completely real in the sense that all statements about it have definite truth-values. Indeed, it is at least partially real in the more ontological sense that some continuants that did exist still do.
......[iv] Colin E. Gunton, The Triune Creator: A historical and systematic study (Eerdmans, 1998), p. 92.
......[v] With different senses—e.g. those of Padgett, God, Eternity and the Nature of Time—Presentism would allow us to accept both terms consistently.
......[vi] Paul Copan & William Lane Craig, Creation out of Nothing: A biblical, philosophical, and scientific exploration (Apollos, 2004), p. 162 n. 29.
......[vii] Mawson, “Divine eternity,” pp. 45–9.
Monday, November 29, 2010
Theistic Presentism cont.
This is the eighth of 17 posts, which are collectively Eternity, etc.
......The Presentist present is not so much a time as reality. A line with dynamic (and continuous) branches may give Presentists a reasonably accurate picture of how continuants change, but that dimension is only figurative. Nothing real is literally inside it. And while it’s only common sense that we exist within time, we are dependent creatures, currently subject to physical laws in the shadow of death. By laying down our temporal constraints, the Presentist God in a sense created time as we know it, which He transcends. Furthermore He was, is or will be at all such times, and is everywhere immanent. The atemporal God also created time, of course (as a real dimension), and is in a sense spatiotemporally omnipresent [i]. So while there is a sense in which the everlasting God is inside—the timeless God outside—time, it is often more accurate to think of the former as able—the latter not liable—to change.
......As Mawson discussed atemporalist spatiotemporal omnipresence, he mentioned—the second of our three reasons—that “of course scientists are happy to talk of space and time as merely two aspects of a unity, space-time”[ii]. But to begin with, such talk is generally an unreliable guide to ontology [iii]. And in particular, the evidence for relativistic physics is quite compatible with there being an absolute present [iv]. Furthermore, many physicists are unhappy with the picture of time as quasi-spatial, because they take quantum mechanics to be describing the collapses of wave-functions that represent current physical tendencies towards the possible outcomes of such collapses [v]. Such physical possibilities interact as such, even though most won’t have been how things actually were. And that implies the current reality of (what will have been) the non-actual—in the sense of the Actual World of popular (4-Dimensionalist) Possible Worlds semantics—or in other words, that the future is partially unreal.
......Notes:
......[i] Mawson, Belief in God, pp. 48–51.
......[ii] Ibid, p. 51.
......[iii] Similarly, neuroscientists are generally happy to talk of the mind as though it was nothing but an aspect of the brain, and such talk hardly means that we are unlikely to be incarnate spirits if there is a God; ibid, pp. 93–9; Swinburne, Is There a God? pp. 70–94.
......[iv] Richard Swinburne, Space and Time, 2nd edition (Macmillan, 1981), pp. 177–205; William Lane Craig, Time and the Metaphysics of Relativity (Kluwer Academic, 2001); John Polkinghorne, “Time in Physics and Theology,” in Poe & Mattson, What God Knows, pp. 61–74; Dennis Dieks (ed.), The Ontology of Spacetime, Vol. I (Elsevier, 2006); Bourne, A Future for Presentism, pp. 141–203.
......[v] For more details, see Roger Penrose, The Road to Reality: A complete guide to the laws of the universe (Jonathan Cape, 2004), pp. 493–608; Karl R. Popper, The Open Universe: An argument for Indeterminism (Hutchinson, 1982), pp. 87–109.
......The Presentist present is not so much a time as reality. A line with dynamic (and continuous) branches may give Presentists a reasonably accurate picture of how continuants change, but that dimension is only figurative. Nothing real is literally inside it. And while it’s only common sense that we exist within time, we are dependent creatures, currently subject to physical laws in the shadow of death. By laying down our temporal constraints, the Presentist God in a sense created time as we know it, which He transcends. Furthermore He was, is or will be at all such times, and is everywhere immanent. The atemporal God also created time, of course (as a real dimension), and is in a sense spatiotemporally omnipresent [i]. So while there is a sense in which the everlasting God is inside—the timeless God outside—time, it is often more accurate to think of the former as able—the latter not liable—to change.
......As Mawson discussed atemporalist spatiotemporal omnipresence, he mentioned—the second of our three reasons—that “of course scientists are happy to talk of space and time as merely two aspects of a unity, space-time”[ii]. But to begin with, such talk is generally an unreliable guide to ontology [iii]. And in particular, the evidence for relativistic physics is quite compatible with there being an absolute present [iv]. Furthermore, many physicists are unhappy with the picture of time as quasi-spatial, because they take quantum mechanics to be describing the collapses of wave-functions that represent current physical tendencies towards the possible outcomes of such collapses [v]. Such physical possibilities interact as such, even though most won’t have been how things actually were. And that implies the current reality of (what will have been) the non-actual—in the sense of the Actual World of popular (4-Dimensionalist) Possible Worlds semantics—or in other words, that the future is partially unreal.
......Notes:
......[i] Mawson, Belief in God, pp. 48–51.
......[ii] Ibid, p. 51.
......[iii] Similarly, neuroscientists are generally happy to talk of the mind as though it was nothing but an aspect of the brain, and such talk hardly means that we are unlikely to be incarnate spirits if there is a God; ibid, pp. 93–9; Swinburne, Is There a God? pp. 70–94.
......[iv] Richard Swinburne, Space and Time, 2nd edition (Macmillan, 1981), pp. 177–205; William Lane Craig, Time and the Metaphysics of Relativity (Kluwer Academic, 2001); John Polkinghorne, “Time in Physics and Theology,” in Poe & Mattson, What God Knows, pp. 61–74; Dennis Dieks (ed.), The Ontology of Spacetime, Vol. I (Elsevier, 2006); Bourne, A Future for Presentism, pp. 141–203.
......[v] For more details, see Roger Penrose, The Road to Reality: A complete guide to the laws of the universe (Jonathan Cape, 2004), pp. 493–608; Karl R. Popper, The Open Universe: An argument for Indeterminism (Hutchinson, 1982), pp. 87–109.
Saturday, November 27, 2010
Theistic Presentism
This is the seventh of 17 posts, which are collectively Eternity, etc.
......The concept of time arises as we relate to the regular changes of such continuants as the earth, or a clock. A continuant is anything that is wholly present when it exists—e.g. you may lift up the whole clock—and which continues to be the same thing as its attributes change—you can put the same clock down later. Many of our quotidian beliefs concern such continuants as the ordinary objects around us. So our quotidian beliefs presuppose (and hence imply) something like Presentism [i]. And if you think about it, you can be justifiably certain that you are a continuant. And Presentist Theists take God to be the original continuant. So whether the Presentist Open God changes or not, He is bound to remain the same person, with the same essential attributes. He is not changeable, like a pagan god, but perfectly constant in His absolute power, and boundless love.
......Consequently He might know infallibly that He will—if He has decided that He will—sustain the earth, at least until tomorrow. It is His choice—He has the power not to—but if God determines to stay on some freely chosen course, then there being no real chance of Him deviating from it would surely confirm, rather than compromise, His perfect freedom, His omnipotence. (Cf. the classical distinction between absolute and ordained power.) Surely having the power to do X might cohere with there being no chance of X actually happening. We are, after all, regarding libertarian atemporalism as a prima facie logical possibility. So in short, it may well be false that, under Open Theism, and “given that the world’s having a future at all is dependent on God’s freely choosing to sustain it from moment to moment […] He does not have infallible knowledge of the future of the world in any respect at all”[ii].
......The underlying problem appears to be how easily Presentism is misunderstood. As we try to understand time—to see more clearly what it is like—we very naturally focus upon its quasi-spatial representation, the temporal dimension. Consequently some philosophers think that Presentism faces the dilemma—the first of our three reasons—that the present is either temporally extended, as though earlier and later could possibly be simultaneous, or else it is only an instant, at which no one could be having such sensations as we clearly are having [iii]. In fact, the Presentist present is not extended (except spatially), but enduring. Nor is it thin—as though the future rained down upon the surface of the past but only that surface was real—because it includes the whole world (as a collective continuant) and, for Presentist Theists, the whole being of God.
......Notes:
......[i] Cf. Mawson, “Divine eternity,” p. 41 n. 4.
......[ii] Ibid, p. 38. Here “world” means the whole of creation; Mawson, Belief in God, p. 10.
......[iii] For more details, see H. Scott Hestevold, “Presentism: Through Thick and Thin,” Pacific Philosophical Quarterly 89 (2008): 325–47.
......The concept of time arises as we relate to the regular changes of such continuants as the earth, or a clock. A continuant is anything that is wholly present when it exists—e.g. you may lift up the whole clock—and which continues to be the same thing as its attributes change—you can put the same clock down later. Many of our quotidian beliefs concern such continuants as the ordinary objects around us. So our quotidian beliefs presuppose (and hence imply) something like Presentism [i]. And if you think about it, you can be justifiably certain that you are a continuant. And Presentist Theists take God to be the original continuant. So whether the Presentist Open God changes or not, He is bound to remain the same person, with the same essential attributes. He is not changeable, like a pagan god, but perfectly constant in His absolute power, and boundless love.
......Consequently He might know infallibly that He will—if He has decided that He will—sustain the earth, at least until tomorrow. It is His choice—He has the power not to—but if God determines to stay on some freely chosen course, then there being no real chance of Him deviating from it would surely confirm, rather than compromise, His perfect freedom, His omnipotence. (Cf. the classical distinction between absolute and ordained power.) Surely having the power to do X might cohere with there being no chance of X actually happening. We are, after all, regarding libertarian atemporalism as a prima facie logical possibility. So in short, it may well be false that, under Open Theism, and “given that the world’s having a future at all is dependent on God’s freely choosing to sustain it from moment to moment […] He does not have infallible knowledge of the future of the world in any respect at all”[ii].
......The underlying problem appears to be how easily Presentism is misunderstood. As we try to understand time—to see more clearly what it is like—we very naturally focus upon its quasi-spatial representation, the temporal dimension. Consequently some philosophers think that Presentism faces the dilemma—the first of our three reasons—that the present is either temporally extended, as though earlier and later could possibly be simultaneous, or else it is only an instant, at which no one could be having such sensations as we clearly are having [iii]. In fact, the Presentist present is not extended (except spatially), but enduring. Nor is it thin—as though the future rained down upon the surface of the past but only that surface was real—because it includes the whole world (as a collective continuant) and, for Presentist Theists, the whole being of God.
......Notes:
......[i] Cf. Mawson, “Divine eternity,” p. 41 n. 4.
......[ii] Ibid, p. 38. Here “world” means the whole of creation; Mawson, Belief in God, p. 10.
......[iii] For more details, see H. Scott Hestevold, “Presentism: Through Thick and Thin,” Pacific Philosophical Quarterly 89 (2008): 325–47.
Thursday, November 25, 2010
Future Contingents cont.
This is the sixth of 17 posts, which are collectively Eternity, etc.
......Ordinary language is vague (see previous post), and the main thing here is that indefinite is not an unreasonable original truth-value under Presentism (given libertarianism), as follows.
......Under Presentism there would have been, before reading on, or not, those two (metaphysical) possibilities for how things could have turned out, not just the one (actual) future. So your belief about the future would not originally have concerned anything definite (insofar as your belief concerned the future directly, rather than via your intentions). The future is not completely definite under Presentism [i]; or in other words, the Presentist future is not completely real, in the sense that not all the statements about it that will ever have been correct are now true.
......As aforementioned, the future might be partially real—be what Mawson calls “real”—under Presentist Open Theism, because then it might be false (see section IV) that “there aren’t any true statements concerning future states of affairs at all”[ii]. However, the reason given by Mawson for the future being real was that some future contingency will either happen or not, and that if “we assume for the sake of argument that [it will] then that’s a fact about the future that someone could in principle have beliefs [about]”[iii]. And while it will either happen or not, as a matter of logic [iv], to presume that one of those two is already a fact is to reject (or ignore) the following picture of Presentist time, as dynamically branching.
......Presentists tend to picture the past as the trunk of a tree whose branches represent the future, one branch for each possible future [v]. If some future contingency does happen—and similarly if it does not—one could in principle look back down the single timeline of the past that includes it happening (or not), and see that fact with hindsight. Further back, and the contingency would definitely be going to happen (or not), but only with hindsight. At the time, it was one of two (metaphysical) possibilities.
......Since Mawson was right that Perfect Being Theists can, quite properly, be agnostic about theories of time [vi], and since the (logical) possibility of Presentism undermines—or at least reduces the significance of—his primary argument, the next section will further describe that possibility, and thereby answer three popular reasons for rejecting it.
......Notes:
......[i] The future is completely definite under 4-Dimensionalism (aka Eternalism); Michael Rea, “Four- Dimensionalism,” in Loux & Zimmerman, The Oxford Handbook of Metaphysics, pp. 246–80.
......[ii] Mawson, “Divine eternity,” p. 37.
......[iii] Ibid.
......[iv] The ordinary meaning of “not” is all the logic we need here. The complicating factor is that, as aforementioned, “X will happen” can mean both that X will definitely happen and that X will, as it turns out, happen. Consequently “Either X will happen or else X won’t happen” is also ambiguous. For more discussion, see Rhoda, “Generic open theism,” p. 231.
......[v] For such pictures, see Denyer, Time, Action and Necessity, p. 12; Bourne, A Future for Presentism, p. 62.
......[vi] Mawson, “Divine eternity,” pp. 40–41.
......Ordinary language is vague (see previous post), and the main thing here is that indefinite is not an unreasonable original truth-value under Presentism (given libertarianism), as follows.
......Under Presentism there would have been, before reading on, or not, those two (metaphysical) possibilities for how things could have turned out, not just the one (actual) future. So your belief about the future would not originally have concerned anything definite (insofar as your belief concerned the future directly, rather than via your intentions). The future is not completely definite under Presentism [i]; or in other words, the Presentist future is not completely real, in the sense that not all the statements about it that will ever have been correct are now true.
......As aforementioned, the future might be partially real—be what Mawson calls “real”—under Presentist Open Theism, because then it might be false (see section IV) that “there aren’t any true statements concerning future states of affairs at all”[ii]. However, the reason given by Mawson for the future being real was that some future contingency will either happen or not, and that if “we assume for the sake of argument that [it will] then that’s a fact about the future that someone could in principle have beliefs [about]”[iii]. And while it will either happen or not, as a matter of logic [iv], to presume that one of those two is already a fact is to reject (or ignore) the following picture of Presentist time, as dynamically branching.
......Presentists tend to picture the past as the trunk of a tree whose branches represent the future, one branch for each possible future [v]. If some future contingency does happen—and similarly if it does not—one could in principle look back down the single timeline of the past that includes it happening (or not), and see that fact with hindsight. Further back, and the contingency would definitely be going to happen (or not), but only with hindsight. At the time, it was one of two (metaphysical) possibilities.
......Since Mawson was right that Perfect Being Theists can, quite properly, be agnostic about theories of time [vi], and since the (logical) possibility of Presentism undermines—or at least reduces the significance of—his primary argument, the next section will further describe that possibility, and thereby answer three popular reasons for rejecting it.
......Notes:
......[i] The future is completely definite under 4-Dimensionalism (aka Eternalism); Michael Rea, “Four- Dimensionalism,” in Loux & Zimmerman, The Oxford Handbook of Metaphysics, pp. 246–80.
......[ii] Mawson, “Divine eternity,” p. 37.
......[iii] Ibid.
......[iv] The ordinary meaning of “not” is all the logic we need here. The complicating factor is that, as aforementioned, “X will happen” can mean both that X will definitely happen and that X will, as it turns out, happen. Consequently “Either X will happen or else X won’t happen” is also ambiguous. For more discussion, see Rhoda, “Generic open theism,” p. 231.
......[v] For such pictures, see Denyer, Time, Action and Necessity, p. 12; Bourne, A Future for Presentism, p. 62.
......[vi] Mawson, “Divine eternity,” pp. 40–41.
Tuesday, November 23, 2010
Future Contingents
This is the fifth of 17 posts, which are collectively Eternity, etc.
......Mawson’s primary argument against Open Theism was essentially as follows (the details differ [i]). When you finish reading this paragraph, you will either begin the next one more or less immediately, or else you will do something else for a while. And whichever it is that you actually do, if you now believe that you are going to do it, you would, it seems, be having a true belief about the future. But you might change your mind (you have libertarian freedom), so under Open Theism God should not now be certain that you are going to do it. Might He guess that apparent truth? [ii] But if the Open God knows perfectly well that He is epistemically infallible, then He is certain of whatever He believes. So this kind of argument is essentially that He is not omniscient.
......Nevertheless, it is because you have libertarian freedom that, unless your belief turned out to be false, either you just made it true by continuing to read, or else you made it true a while ago. There is therefore the conceptual possibility, at least, that your belief was originally of indefinite truth-value, neither true nor false (if very likely) [iii]; and that possibility yields one of the two or three commonest varieties of Open Theism (another being Swinburne’s) [iv]. And according to this variety, God can be (necessarily) omniscient, because not knowing something that is not true would clearly not obstruct (necessary) omniscience.
......Now, even if your belief originally had a probability between 0 (false) and 1 (true), “indefinite” might be used to denote all such probabilities (collectively or indiscriminately). So a third truth-value called “indefinite” is essentially what such an indefinite truth-value is. And those defending this variety should perhaps “motivate and defend the denial of bivalence and the attendant departure from standard logic.” [v] So note that there are many reasons for denying bivalence and moving on from our most elementary logic (e.g. see section VII) [vi].
......Swinburne retains bivalence at the cost of omniscience. Such Open Theists think that your belief was originally true or false according to how things turned out. And indeed, had you guessed correctly, your belief would—in that sense—have been correct. Still, had someone originally believed that she would read on, and later thought “I was right,” she might have meant by that only that she had read on (with no thought for how well her belief had originally described what then existed). Furthermore, since she might not have read on, there is also a sense in which her “I will read on” would originally have been false. Nevertheless, although a third variety of Open Theism does call the original truth-value “false” (and so hopes to retain bivalence as well as omniscience) [vii], her “I will read on” need not have meant that she would definitely read on (which was false), rather than that she would happen to read on (which she did), or indeed, that she would probably read on, or had intended to. Such is ordinary language.
......Notes:
......[i] For more details, see Mawson, “Divine eternity,” p. 37, pp. 44–5. For similar arguments, see Helm, Eternal God, p. 67; Swinburne, Is There a God? pp. 7–8.
......[ii] Mawson hoped to show the Open God making mistakes (see section V), but later accepted that He might be epistemically infallible; Mawson, “Divine eternity,” p. 45.
......[iii] For more details, see Elizabeth Barnes & Ross Cameron, “The Open Future: Bivalence, determinism and ontology,” Philosophical Studies 146 (2009): 291–309.
......[iv] For more on this variety, see David Kyle Johnson, “God, fatalism, and temporal ontology,” Religious Studies 45 (2009): 435–54. This variety was distinguished from Swinburne’s by Helm, Eternal God, pp. 109–21. For three varieties, see Rhoda, “Generic open theism,” pp. 229–32.
......[v] Ibid, p. 231.
......[vi] For further reasons, see Grzegorz Malinowski, “Many-valued Logic and its Philosophy,” in Dov M. Gabbay & John Woods (eds.), The Many Valued and Nonmonotonic Turn in Logic (North-Holland, 2007), pp. 13–94.
......[vii] For more details, see Alan R. Rhoda, Gregory A. Boyd & Thomas G. Belt, “Open Theism, Omniscience, and the Nature of the Future,” Faith and Philosophy 23 (2006): 432–59.
......Mawson’s primary argument against Open Theism was essentially as follows (the details differ [i]). When you finish reading this paragraph, you will either begin the next one more or less immediately, or else you will do something else for a while. And whichever it is that you actually do, if you now believe that you are going to do it, you would, it seems, be having a true belief about the future. But you might change your mind (you have libertarian freedom), so under Open Theism God should not now be certain that you are going to do it. Might He guess that apparent truth? [ii] But if the Open God knows perfectly well that He is epistemically infallible, then He is certain of whatever He believes. So this kind of argument is essentially that He is not omniscient.
......Nevertheless, it is because you have libertarian freedom that, unless your belief turned out to be false, either you just made it true by continuing to read, or else you made it true a while ago. There is therefore the conceptual possibility, at least, that your belief was originally of indefinite truth-value, neither true nor false (if very likely) [iii]; and that possibility yields one of the two or three commonest varieties of Open Theism (another being Swinburne’s) [iv]. And according to this variety, God can be (necessarily) omniscient, because not knowing something that is not true would clearly not obstruct (necessary) omniscience.
......Now, even if your belief originally had a probability between 0 (false) and 1 (true), “indefinite” might be used to denote all such probabilities (collectively or indiscriminately). So a third truth-value called “indefinite” is essentially what such an indefinite truth-value is. And those defending this variety should perhaps “motivate and defend the denial of bivalence and the attendant departure from standard logic.” [v] So note that there are many reasons for denying bivalence and moving on from our most elementary logic (e.g. see section VII) [vi].
......Swinburne retains bivalence at the cost of omniscience. Such Open Theists think that your belief was originally true or false according to how things turned out. And indeed, had you guessed correctly, your belief would—in that sense—have been correct. Still, had someone originally believed that she would read on, and later thought “I was right,” she might have meant by that only that she had read on (with no thought for how well her belief had originally described what then existed). Furthermore, since she might not have read on, there is also a sense in which her “I will read on” would originally have been false. Nevertheless, although a third variety of Open Theism does call the original truth-value “false” (and so hopes to retain bivalence as well as omniscience) [vii], her “I will read on” need not have meant that she would definitely read on (which was false), rather than that she would happen to read on (which she did), or indeed, that she would probably read on, or had intended to. Such is ordinary language.
......Notes:
......[i] For more details, see Mawson, “Divine eternity,” p. 37, pp. 44–5. For similar arguments, see Helm, Eternal God, p. 67; Swinburne, Is There a God? pp. 7–8.
......[ii] Mawson hoped to show the Open God making mistakes (see section V), but later accepted that He might be epistemically infallible; Mawson, “Divine eternity,” p. 45.
......[iii] For more details, see Elizabeth Barnes & Ross Cameron, “The Open Future: Bivalence, determinism and ontology,” Philosophical Studies 146 (2009): 291–309.
......[iv] For more on this variety, see David Kyle Johnson, “God, fatalism, and temporal ontology,” Religious Studies 45 (2009): 435–54. This variety was distinguished from Swinburne’s by Helm, Eternal God, pp. 109–21. For three varieties, see Rhoda, “Generic open theism,” pp. 229–32.
......[v] Ibid, p. 231.
......[vi] For further reasons, see Grzegorz Malinowski, “Many-valued Logic and its Philosophy,” in Dov M. Gabbay & John Woods (eds.), The Many Valued and Nonmonotonic Turn in Logic (North-Holland, 2007), pp. 13–94.
......[vii] For more details, see Alan R. Rhoda, Gregory A. Boyd & Thomas G. Belt, “Open Theism, Omniscience, and the Nature of the Future,” Faith and Philosophy 23 (2006): 432–59.
Sunday, November 21, 2010
Divine Attributes cont.
This is the fourth of 17 posts, which are collectively Eternity, etc.
......As aforementioned, God is the ground of metaphysical possibility, if He exists. Let us assume that He does (if only for the sake of agnostic argument). (And let us also assume libertarianism, if only because Mawson’s arguments do). Since God is, presumably, the greatest conceivable being, we can again follow Mawson and say that He is omnipotent, where “an omnipotent being is a being with the most power-granting set of abilities that it is logically possible anyone might have”[i]. It seems to follow that God is infallible, since being able to make mistakes would surely detract from His overall power [ii]. The Open God might be epistemically infallible, for example, in virtue of His beliefs being held by Him only insofar as they are completely justified [iii].
......Does it also follow that God is omniscient (see previous post)? Each possible fact might be associated with a power to know it. But that might be a power to know it eventually. Would it be more power-granting for God to know now all that He will ever know, or for Him to be able to know anything desired as quickly as desired? It’s hard to say, but it seems that the most powerful God is able to increase His knowledge (see section VII), which would stop Him having what Mawson calls “complete omniscience”[iv], but would not obstruct His necessary omniscience (see section VIII).
......What is relatively clear is that God is eternal, i.e. without beginning or end. That is clearly so if God transcends even the possibility of change. But even the Open God is necessarily unending, because there should never be any real (metaphysical) possibility of the ground of all good things not existing. And if the Open God had some primary state, prior to all His other states, we might regard that as time having its beginning in Him, rather than vice versa (see section IV) [v]. So, God is eternal; what is less clear is whether He is timeless or everlasting. Indeed, even that question’s terms can be questioned.
......Mawson’s terms—“atemporal” and “temporal”—were not too bad, being less biased towards atemporalism (aka Eternalism) than were the traditional terms, “eternal” and “sempiternal” (following Boethius). But whereas both “timeless” and “everlasting” connote unfading immortality, “temporal” connotes limitation. E.g. it can also mean civil or secular, as opposed to sacred or spiritual. And crucially (see section IV), the Presentist Open God does not exist inside the sort of temporal dimension that the atemporal God transcends [vi]. To avoid begging the question, and to stay apposite [vii], I suggest that we call God “timeless” if He transcends, not only spacetime, but even the possibility of change, and call Him “everlasting” if He is so involved with us that the future is open (in the sense of Open Theism).
......Notes:
......[i] Mawson, “Divine eternity,” p. 41.
......[ii] For more details, see Mawson, Belief in God, pp. 28–35.
......[iii] For a possible problem with that, see Omniscience and the Odyssey Theodicy.
......[iv] Mawson, “Divine eternity,” p. 37. “A completely omniscient being cannot learn anything,” ibid, p. 41 n. 5.
......[v] See also William Lane Craig, “God, Time, and Eternity,” in Harry Lee Poe & J. Stanley Mattson (eds.), What God Knows: Time, eternity, and divine knowledge (Baylor Univ. Press, 2005), pp. 75–93.
......[vi] See also Alan G. Padgett, God, Eternity and the Nature of Time (St. Martin’s Press, 1992).
......[vii] I am ignoring immutable temporal Deities. And according to my definitions, God would be neither timeless nor everlasting if He was able to change but had already created our future (see note v of Possible Worlds).
......As aforementioned, God is the ground of metaphysical possibility, if He exists. Let us assume that He does (if only for the sake of agnostic argument). (And let us also assume libertarianism, if only because Mawson’s arguments do). Since God is, presumably, the greatest conceivable being, we can again follow Mawson and say that He is omnipotent, where “an omnipotent being is a being with the most power-granting set of abilities that it is logically possible anyone might have”[i]. It seems to follow that God is infallible, since being able to make mistakes would surely detract from His overall power [ii]. The Open God might be epistemically infallible, for example, in virtue of His beliefs being held by Him only insofar as they are completely justified [iii].
......Does it also follow that God is omniscient (see previous post)? Each possible fact might be associated with a power to know it. But that might be a power to know it eventually. Would it be more power-granting for God to know now all that He will ever know, or for Him to be able to know anything desired as quickly as desired? It’s hard to say, but it seems that the most powerful God is able to increase His knowledge (see section VII), which would stop Him having what Mawson calls “complete omniscience”[iv], but would not obstruct His necessary omniscience (see section VIII).
......What is relatively clear is that God is eternal, i.e. without beginning or end. That is clearly so if God transcends even the possibility of change. But even the Open God is necessarily unending, because there should never be any real (metaphysical) possibility of the ground of all good things not existing. And if the Open God had some primary state, prior to all His other states, we might regard that as time having its beginning in Him, rather than vice versa (see section IV) [v]. So, God is eternal; what is less clear is whether He is timeless or everlasting. Indeed, even that question’s terms can be questioned.
......Mawson’s terms—“atemporal” and “temporal”—were not too bad, being less biased towards atemporalism (aka Eternalism) than were the traditional terms, “eternal” and “sempiternal” (following Boethius). But whereas both “timeless” and “everlasting” connote unfading immortality, “temporal” connotes limitation. E.g. it can also mean civil or secular, as opposed to sacred or spiritual. And crucially (see section IV), the Presentist Open God does not exist inside the sort of temporal dimension that the atemporal God transcends [vi]. To avoid begging the question, and to stay apposite [vii], I suggest that we call God “timeless” if He transcends, not only spacetime, but even the possibility of change, and call Him “everlasting” if He is so involved with us that the future is open (in the sense of Open Theism).
......Notes:
......[i] Mawson, “Divine eternity,” p. 41.
......[ii] For more details, see Mawson, Belief in God, pp. 28–35.
......[iii] For a possible problem with that, see Omniscience and the Odyssey Theodicy.
......[iv] Mawson, “Divine eternity,” p. 37. “A completely omniscient being cannot learn anything,” ibid, p. 41 n. 5.
......[v] See also William Lane Craig, “God, Time, and Eternity,” in Harry Lee Poe & J. Stanley Mattson (eds.), What God Knows: Time, eternity, and divine knowledge (Baylor Univ. Press, 2005), pp. 75–93.
......[vi] See also Alan G. Padgett, God, Eternity and the Nature of Time (St. Martin’s Press, 1992).
......[vii] I am ignoring immutable temporal Deities. And according to my definitions, God would be neither timeless nor everlasting if He was able to change but had already created our future (see note v of Possible Worlds).
Friday, November 19, 2010
Divine Attributes
This is the third of 17 posts, which are collectively Eternity, etc.
......I shall, then (see previous post), be arguing that Open Theists can accept God’s necessary omniscience, in the sense of His being bound to know each truth whenever it exists (insofar as truths exist). Richard Swinburne—the Open Theist that Mawson focused upon—disagrees; or rather, Swinburne thinks that because of future contingents (see section III) we should “understand God being omniscient as God knowing at any time all that [it] is logically possible to know at that time”[i]. But let us follow Mawson, and “say that a being is omniscient just if it is the case that for all statements, if a statement is true, then that being knows that it is true”[ii].
......It would be natural for atemporalists to take truth to be timeless, however. (Indeed, even Swinburne seems to do so.) So Mawson may well have meant, by the phrase “if a statement is true” in his definition, if a statement is ever true. But there are many reasons, e.g. Cantor’s Paradox [iii], why truth is not timeless. And whatever the merits of such arguments, our question here is whether God—who may well be the ground of truth—must be timeless. We should therefore avoid begging the question, as we use Mawson’s definition, by not also assuming that statements cannot change their truth-values.
......Of course, Swinburne’s position is, to say the least, not obviously incoherent. So I would not say that the Open God’s omniscience (in our sense) is logically necessary. A logical possibility is primarily a coherent conceptual possibility, logic being the study of correct reasoning. What I will be defending is the logical possibility—indeed, the plausibility—of a variety of Open Theism under which God is bound, of metaphysical necessity, to be omniscient. Metaphysical necessity generalizes the natural (non-Humean) laws of physics so as to allow for such non-physical things as spirits and to allow for miracles and other possible creations (e.g. a new earth) [iv]. And if there is a God, then all metaphysical possibilities would be grounded in Him.
......Notes:
......[i] Swinburne, Is There a God? p. 8.
......[ii] Mawson, Belief in God, p. 35.
......[iii] If there was a set of all the other sets, then via Cantor’s Diagonal Argument (see section VII), there would be more subsets than there are sets; but each subset is a set, so there is no set of all the other sets. That would be paradoxical if “set” meant things referred to collectively. And since for each set there are such truths as what its members are, so there is no set of all truths; Patrick Grim, “There Is No Set of All Truths,” Analysis 44 (1984): 206–8. The result that truth is not timeless follows if “set” is given its informal meaning, of an immutably complete collection. For other arguments to that effect, see Nicholas Denyer, Time, Action and Necessity: A proof of free will (Duckworth, 1981), pp. 79–82; Richard Sorabji, Time, Creation and the Continuum: Theories in antiquity and the early Middle Ages (Duckworth, 1983), pp. 132–5.
......[iv] For more details, see Mawson, Belief in God, pp. 65–7.
......I shall, then (see previous post), be arguing that Open Theists can accept God’s necessary omniscience, in the sense of His being bound to know each truth whenever it exists (insofar as truths exist). Richard Swinburne—the Open Theist that Mawson focused upon—disagrees; or rather, Swinburne thinks that because of future contingents (see section III) we should “understand God being omniscient as God knowing at any time all that [it] is logically possible to know at that time”[i]. But let us follow Mawson, and “say that a being is omniscient just if it is the case that for all statements, if a statement is true, then that being knows that it is true”[ii].
......It would be natural for atemporalists to take truth to be timeless, however. (Indeed, even Swinburne seems to do so.) So Mawson may well have meant, by the phrase “if a statement is true” in his definition, if a statement is ever true. But there are many reasons, e.g. Cantor’s Paradox [iii], why truth is not timeless. And whatever the merits of such arguments, our question here is whether God—who may well be the ground of truth—must be timeless. We should therefore avoid begging the question, as we use Mawson’s definition, by not also assuming that statements cannot change their truth-values.
......Of course, Swinburne’s position is, to say the least, not obviously incoherent. So I would not say that the Open God’s omniscience (in our sense) is logically necessary. A logical possibility is primarily a coherent conceptual possibility, logic being the study of correct reasoning. What I will be defending is the logical possibility—indeed, the plausibility—of a variety of Open Theism under which God is bound, of metaphysical necessity, to be omniscient. Metaphysical necessity generalizes the natural (non-Humean) laws of physics so as to allow for such non-physical things as spirits and to allow for miracles and other possible creations (e.g. a new earth) [iv]. And if there is a God, then all metaphysical possibilities would be grounded in Him.
......Notes:
......[i] Swinburne, Is There a God? p. 8.
......[ii] Mawson, Belief in God, p. 35.
......[iii] If there was a set of all the other sets, then via Cantor’s Diagonal Argument (see section VII), there would be more subsets than there are sets; but each subset is a set, so there is no set of all the other sets. That would be paradoxical if “set” meant things referred to collectively. And since for each set there are such truths as what its members are, so there is no set of all truths; Patrick Grim, “There Is No Set of All Truths,” Analysis 44 (1984): 206–8. The result that truth is not timeless follows if “set” is given its informal meaning, of an immutably complete collection. For other arguments to that effect, see Nicholas Denyer, Time, Action and Necessity: A proof of free will (Duckworth, 1981), pp. 79–82; Richard Sorabji, Time, Creation and the Continuum: Theories in antiquity and the early Middle Ages (Duckworth, 1983), pp. 132–5.
......[iv] For more details, see Mawson, Belief in God, pp. 65–7.
Wednesday, November 17, 2010
Introduction
This is the second of 17 posts, which are collectively Eternity, etc.
......In this debate, “God” refers to the perfect person—or Trinity (but nothing impersonal)—who created everything else ex nihilo [i]. If such a God exists, He (they, she) created us, so such Theists naturally think of Him as the greatest conceivable being; and Open Theists are no exception [ii]. Open Theists are so-called because they believe that God keeps some of His options open, as He relates to us [iii]. Such divine openness follows from the sort of freedom (responsibility, creativity) God gave to those made in His image. Open Theists take a libertarian view of free will. And atemporalists—who think that God transcends even the possibility of change—can also take that view [iv], according to Mawson:
......I argue in section IV that Presentism is not implausible under Perfect Being Theism. Mawson’s primary argument—that because of future contingents (see section III), the Open God lacks some infallible knowledge of the future—therefore lacks the significance attached to it by Mawson. Under Presentism, the Open God can be infallibly omniscient (see section III). Presentism can also explain why the Open God is essentially constant, and hence why Mawson should not have thought of the Open God as having no infallible knowledge of the future. And Mawson’s main argument—that by being incompletely omniscient, the Open God is liable to make mistakes—was based on a misunderstanding of Open divine action, according to section V.
......Section VI initiates a more direct comparison of Presentist Open Theism with libertarian atemporalism. Section VII is based on Cantor’s Paradox and is an informal mathematical argument that the numbers of things within possible creations are indefinitely extensible. God’s omnipotence therefore indicates that His knowledge of whole numbers is forever increasing. And I also suggest in section VIII that under Presentism He could, even so, be necessarily omniscient.
......Notes:
......[i] Mawson, Belief in God, pp. 9–27.
......[ii] Richard Swinburne, Is There a God? (Oxford University Press, 1996), pp. 3–19; Alan R. Rhoda, “The Philosophical Case for Open Theism,” Philosophia 35 (2007): 301–11; Alan R. Rhoda, “Generic open theism and some varieties thereof,” Religious Studies 44 (2008): 225–34.
......[iii] For more details, see Charles H. Pinnock, Most Moved Mover: A theology of God’s openness (Baker Academic, 2001).
......[iv] Not all atemporalists do, e.g. see Paul Helm, Eternal God: A study of God without time (Clarendon Press, 1988).
......[v] Mawson, “Divine eternity,” p. 40. For more details, see Timothy O’Connor, “Dualist and Agent-Causal Theories,” in Robert Kane (ed.), The Oxford Handbook of Free Will (Oxford Univ. Press, 2002), pp. 337–55.
......[vi] Rhoda, “Generic open theism,” p. 234 n. 22. For more details, see Thomas M. Crisp, “Presentism,” in Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics (Oxford Univ. Press, 2003), pp. 211–245; Craig Bourne, A Future for Presentism (Oxford Univ. Press, 2007).
......In this debate, “God” refers to the perfect person—or Trinity (but nothing impersonal)—who created everything else ex nihilo [i]. If such a God exists, He (they, she) created us, so such Theists naturally think of Him as the greatest conceivable being; and Open Theists are no exception [ii]. Open Theists are so-called because they believe that God keeps some of His options open, as He relates to us [iii]. Such divine openness follows from the sort of freedom (responsibility, creativity) God gave to those made in His image. Open Theists take a libertarian view of free will. And atemporalists—who think that God transcends even the possibility of change—can also take that view [iv], according to Mawson:
On the libertarian view of free will (as it is standardly construed), all that has to be true for you to be free in the future in your choice to do X is that you have the power at that time to do something other than X and on atemporalism you can have this power—have the power to make God either have the atemporal belief that you do X or the atemporal belief that you don’t do X—without having the power to make any belief He actually has false. [v]The future being what Mawson calls “real” (“that some statements concerning what is now the future are true”) is relatively uncontroversial. Even Presentist Open Theists might think it true that, for example, the earth will still be here tomorrow. “Presentism is the view that only what exists now has any reality”[vi], but what exists now—e.g. an egg falling—could determine how something will be—e.g. the egg breaking—via the laws of nature, and God’s constancy (see section IV), and so make it true now that such will be the case.
......I argue in section IV that Presentism is not implausible under Perfect Being Theism. Mawson’s primary argument—that because of future contingents (see section III), the Open God lacks some infallible knowledge of the future—therefore lacks the significance attached to it by Mawson. Under Presentism, the Open God can be infallibly omniscient (see section III). Presentism can also explain why the Open God is essentially constant, and hence why Mawson should not have thought of the Open God as having no infallible knowledge of the future. And Mawson’s main argument—that by being incompletely omniscient, the Open God is liable to make mistakes—was based on a misunderstanding of Open divine action, according to section V.
......Section VI initiates a more direct comparison of Presentist Open Theism with libertarian atemporalism. Section VII is based on Cantor’s Paradox and is an informal mathematical argument that the numbers of things within possible creations are indefinitely extensible. God’s omnipotence therefore indicates that His knowledge of whole numbers is forever increasing. And I also suggest in section VIII that under Presentism He could, even so, be necessarily omniscient.
......Notes:
......[i] Mawson, Belief in God, pp. 9–27.
......[ii] Richard Swinburne, Is There a God? (Oxford University Press, 1996), pp. 3–19; Alan R. Rhoda, “The Philosophical Case for Open Theism,” Philosophia 35 (2007): 301–11; Alan R. Rhoda, “Generic open theism and some varieties thereof,” Religious Studies 44 (2008): 225–34.
......[iii] For more details, see Charles H. Pinnock, Most Moved Mover: A theology of God’s openness (Baker Academic, 2001).
......[iv] Not all atemporalists do, e.g. see Paul Helm, Eternal God: A study of God without time (Clarendon Press, 1988).
......[v] Mawson, “Divine eternity,” p. 40. For more details, see Timothy O’Connor, “Dualist and Agent-Causal Theories,” in Robert Kane (ed.), The Oxford Handbook of Free Will (Oxford Univ. Press, 2002), pp. 337–55.
......[vi] Rhoda, “Generic open theism,” p. 234 n. 22. For more details, see Thomas M. Crisp, “Presentism,” in Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics (Oxford Univ. Press, 2003), pp. 211–245; Craig Bourne, A Future for Presentism (Oxford Univ. Press, 2007).
Monday, November 15, 2010
Eternity
This is the first of 17 posts that, collectively, defend Open Theism against Mawson’s Divine eternity (2008). As I write them, I shall be polishing up what I was writing over the summer, i.e. Eternity, Mawson’s belief and Cantor’s paradox, which was itself the result of a very slow revision of the first half of my 2008 reply to Mawson, Omniscience and the Odyssey Theodicy. The Abstract for the current paper is:
............I Introduction
............II Divine Attributes
............II Divine Attributes cont.
............III Future Contingents
............III Future Contingents cont.
............IV Theistic Presentism
............IV Theistic Presentism cont.
............IV Theistic Presentism again
............V Bodging Up
............V Bodging Up cont.
............VI Possible Worlds
............VII Cantor’s Paradox
............VII Cantor’s Paradox cont.
............VII Cantor’s Paradox again
............VIII Omniscience Again
............VIII Omniscience Again cont....
P.S.: Two years later, that unpublishable paper became Divine Eternity Revisited
T. J. Mawson believes that the God of Open Theism is liable to bodge things up, by not infallibly knowing all about the future. But I argue that Mawson misconstrued the Open Theist view of divine action. And since the God of Presentist Open Theism ould infallibly know all there is to know, I also argue that Presentism, whose falsity Mawson presupposed, is not implausible if God is the Perfect Being. Furthermore, if God can create arbitrarily many things, then because of Cantor’s Paradox, His knowledge of whole numbers is plausibly growing forever. Yet even such a powerful and hence changing God could, under Presentism, know all the truths of arithmetic. I conclude that the Presentist Open God could be the Perfect Being.According to T. J. Mawson [i], even those Perfect Being Theists who take a libertarian view of free will should reject Open Theism, so long as they accept what he calls “the reality of the future,” i.e. “that some statements concerning what is now the future are true.” [ii] Mawson argued that because of future contingents, the Open God lacks “infallible knowledge of at least some aspects of the future,” [iii] and that such incomplete omniscience makes “whatever goodness (in the sense of beneficence, not just benevolence) God has a matter of luck.” [iv] I will be uncovering several lacunae in Mawson’s reasoning (in sections III to V), and then arguing more directly (in sections VI to VIII) for my conclusion, that such Theists should not reject Open Theism. The underlying question concerns how God is eternal (sections I and II). The 16 posts will be:
............I Introduction
............II Divine Attributes
............II Divine Attributes cont.
............III Future Contingents
............III Future Contingents cont.
............IV Theistic Presentism
............IV Theistic Presentism cont.
............IV Theistic Presentism again
............V Bodging Up
............V Bodging Up cont.
............VI Possible Worlds
............VII Cantor’s Paradox
............VII Cantor’s Paradox cont.
............VII Cantor’s Paradox again
............VIII Omniscience Again
............VIII Omniscience Again cont....
Notes:
......[i] T. J. Mawson, “Divine eternity,” International Journal for Philosophy of Religion 64 (2008): 35–50.
......[ii] Ibid, p. 37. Statements are basically possible assertions. For more details, see T. J. Mawson, Belief in God: An introduction to the philosophy of religion (Oxford Univ. Press, 2005), p. 239 n. 6. Questions of truth are essentially questions of how well our words describe the world, of course.
......[iii] Mawson, “Divine eternity,” p. 37.......[iv] Ibid, p. 49.
......[i] T. J. Mawson, “Divine eternity,” International Journal for Philosophy of Religion 64 (2008): 35–50.
......[ii] Ibid, p. 37. Statements are basically possible assertions. For more details, see T. J. Mawson, Belief in God: An introduction to the philosophy of religion (Oxford Univ. Press, 2005), p. 239 n. 6. Questions of truth are essentially questions of how well our words describe the world, of course.
......[iii] Mawson, “Divine eternity,” p. 37.......[iv] Ibid, p. 49.
P.S.: Two years later, that unpublishable paper became Divine Eternity Revisited
Saturday, November 13, 2010
The Alternative to Naturalism
...is Philosophy, which revolves around debates between Naturalists and Theists. It is a few centuries since Philosophy was the alternative to Theism, but the mainstream of analytical philosophy remains Naturalism, which is essentially atheistic. Science, which Naturalists emphasise, is not atheistic, however, but agnostic. Indeed, the particular sciences are not just agnostic about God, but about most other things too, so that scientists make the most interesting connexions. But Naturalists, no less than Theists, aim not so much to join up the sciences, but to find holes in each others’ arguments.
......As a mathematician, I am quite interested in seeing how mathematics would differ from standard set theory were we created by a Perfect Being. Indeed, I suspect there is an argument from 2 + 2 = 4 to the existence of a Perfect Being who created us. Mainstream philosophy of mathematics takes ‘2 + 2 = 4’ to be what mainstream mathematics—whose foundation is axiomatic set theory—says it is, and aims to develop an atheistic epistemology of set theory. As they do so, their concepts become implausible (whence the possibility of such an argument).
......Ironically, it is because I am essentially a mathematician that my approach to philosophical problems would strike most analytical philosophers as insufficiently mathematical (formal). And incidentally, there is a famous story that:
......As a mathematician, I am quite interested in seeing how mathematics would differ from standard set theory were we created by a Perfect Being. Indeed, I suspect there is an argument from 2 + 2 = 4 to the existence of a Perfect Being who created us. Mainstream philosophy of mathematics takes ‘2 + 2 = 4’ to be what mainstream mathematics—whose foundation is axiomatic set theory—says it is, and aims to develop an atheistic epistemology of set theory. As they do so, their concepts become implausible (whence the possibility of such an argument).
......Ironically, it is because I am essentially a mathematician that my approach to philosophical problems would strike most analytical philosophers as insufficiently mathematical (formal). And incidentally, there is a famous story that:
Czarina Catherine the Great of Russia was concerned about the deleterious effect the philosopher Diderot was having on the religious faith of the nobility who were listening to him hold forth on atheism in her court. She encouraged famous mathematician Leonard Euler to confront him, and he did, with the following challenge: “Sir, (a + bn)/z = x, hence God exists—reply!” Diderot, who, according to the story, was completely mystified by all things mathematical, fled the court and Russia in deep humiliation. Diderot and Euler actually were in Russia at the same time, both at the invitation of the Czarina, but this is a joke at Diderot’s expense that neither Euler the man nor Euler the mathematician would have made. Even if it had been, Diderot—who was actually a fairly capable mathematician himself—would not have been stumped.
Saturday, October 30, 2010
Two Contraries of Naturalism
Naturalists are analytical philosophers who take the natural sciences to be giving us the best foundation for our thoughts. As philosophers, they don’t usually trust scientists to interpret their own discoveries, however, so I wonder what Naturalists contribute to the scientific enterprise. Is it logical rigour and coherence, or just the opposite?
......Naturalists emphasise the very careful observations that scientists make. And indeed, it is important that we be sure of our facts. But when it comes to the most certain thing in the world—that we are conscious entities—they favour materialistic theories that reduce such things away. They may justify their preference on the grounds of ontological parsimony, or overall theoretical elegance, or the fact that natural scientists don’t usually include subjective stuff in their scientific observations. But Naturalists rightly regard as unscientific those who would explain away such less obvious facts as the fossil record on similar grounds (e.g. not needing all those aeons of inhumanity, and there being no mention of such things in a favoured account of reality).
......Naturalists criticise religion for giving too-easy answers. And it is indeed important to get the right answers to the questions the world raises, not just the most convenient ones. But Naturalists like theories that are based on standard logic, which is simple and popular. And standard logic takes a timeless view from nowhere, which is a bit unrealistic. E.g. consider how the Copenhagen interpretation of quantum mechanics, by having an observer-shaped hole in its description of reality, is less tidy but clearly more realistic than those no-collapse interpretations that would have us doing everything it was physically possible for us to do by splitting into lots of different people all the time.
......Naturalists emphasise the very careful observations that scientists make. And indeed, it is important that we be sure of our facts. But when it comes to the most certain thing in the world—that we are conscious entities—they favour materialistic theories that reduce such things away. They may justify their preference on the grounds of ontological parsimony, or overall theoretical elegance, or the fact that natural scientists don’t usually include subjective stuff in their scientific observations. But Naturalists rightly regard as unscientific those who would explain away such less obvious facts as the fossil record on similar grounds (e.g. not needing all those aeons of inhumanity, and there being no mention of such things in a favoured account of reality).
......Naturalists criticise religion for giving too-easy answers. And it is indeed important to get the right answers to the questions the world raises, not just the most convenient ones. But Naturalists like theories that are based on standard logic, which is simple and popular. And standard logic takes a timeless view from nowhere, which is a bit unrealistic. E.g. consider how the Copenhagen interpretation of quantum mechanics, by having an observer-shaped hole in its description of reality, is less tidy but clearly more realistic than those no-collapse interpretations that would have us doing everything it was physically possible for us to do by splitting into lots of different people all the time.
Friday, October 29, 2010
Valid Enough
The essence of analytical philosophy is the presentation of a valid argument. But often the result is a lot of boring nonsense, many of us find. Why? Well, the reason may be that we are encouraged to work with an absurd definition of ‘valid’. A technically valid argument is, for example, since x and y, therefore x.
......But what about, since the sky is blue, and there’s little wind, I won’t need my umbrella? Technically, that’s invalid because it’s not impossible that it suddenly clouds over and rains. Some philosophers would therefore call it an induction. But I don’t see any generalisation over lots of observations there. And while such a generalisation may well be one of the argument’s many implicit premises, surely it is all the obvious implicit premises that make the argument sufficiently valid for human communication.
......Or, for a more philosophical example, consider Moore’s argument: Since that looks like a tree, therefore that is a tree. Now, we usually make such a deduction subconsciously, but nevertheless, surely such arguments are usually valid enough. And even in more rigorous contexts, how else are we to do science except by taking our readings to be as we read them? What would make such arguments invalid is something like bad lighting, not the mere possibility that we’ve just been taken into the Matrix.
......Indeed, even if we had been, our argument might be valid enough, because we would then be using words in a new external world, and ‘tree’ would usually refer to the new object. Our argument would only be invalidated if we were aware that we were in the Matrix, and if that aspect of our situation was the most apposite.
......But what about, since the sky is blue, and there’s little wind, I won’t need my umbrella? Technically, that’s invalid because it’s not impossible that it suddenly clouds over and rains. Some philosophers would therefore call it an induction. But I don’t see any generalisation over lots of observations there. And while such a generalisation may well be one of the argument’s many implicit premises, surely it is all the obvious implicit premises that make the argument sufficiently valid for human communication.
......Or, for a more philosophical example, consider Moore’s argument: Since that looks like a tree, therefore that is a tree. Now, we usually make such a deduction subconsciously, but nevertheless, surely such arguments are usually valid enough. And even in more rigorous contexts, how else are we to do science except by taking our readings to be as we read them? What would make such arguments invalid is something like bad lighting, not the mere possibility that we’ve just been taken into the Matrix.
......Indeed, even if we had been, our argument might be valid enough, because we would then be using words in a new external world, and ‘tree’ would usually refer to the new object. Our argument would only be invalidated if we were aware that we were in the Matrix, and if that aspect of our situation was the most apposite.
Tuesday, October 19, 2010
Definite enough
Reference occurs when someone refers another person to something—or to some things (the first thing that Russell looked at, after thinking about Cantor’s paradox, was reference). Reference is fundamental to language (and mathematics). And even before creatures had language, there was being seen to be looking at something. There was pointing and then naming and thinking. But for Russell, names were definite descriptions, and vagueness was a logical problem. I think that vagueness is not so much a problem in logic, as the possibility of a logical solution to most if not all of the philosophical problems in logic. Consider, for example, the Lottery paradox:
......Quite generally, the power of natural language lies in its flexibility, which derives from the inherent vagueness of its terms: our words arrive sufficiently well defined for their usual uses, but they can always be defined with more precision if that becomes necessary. The ubiquity of vagueness in natural language is not a logical problem (as Russell believed), it is the possibility of a logical solution to most if not all of our philosophical problems.
......Philosophers have a strong bias towards bivalence because as we philosophize we clarify, aiming to maintain an adequate bivalence. But intuitions that logic ought to be bivalent are therefore quite compatible with logic not being perfectly bivalent. After all, questions of truth are essentially questions of how well our words describe the world; so, the logical primitive is not True (or T, in some mathematical model of logical reasoning) but True Enough. When we say “that’s true” we usually mean that it’s true enough. And it is implausible that statements are bound to be either true enough or else sufficiently false.
If I believe, of each ticket, that it won’t win, then I believe that none of the tickets will win. Whereas, I know that one of them will win.But I actually believe, of each ticket, that it very probably won’t win, and when I describe those beliefs with that amount of precision, there is no paradox. What about the Preface paradox; or more simply, the likelihood of some of my beliefs being wrong? I certainly believe all of my beliefs, so my belief that some of them are likely to be wrong might appear paradoxical. However, as soon as I come to the realisation that some of my beliefs are likely to be wrong, I find that I am holding those beliefs less strongly. For a more epistemological problem:
I can see very clearly that there is a horse trotting past a tree, outside my window (I live in a village in Bedfordshire), so I know that there is a horse there. I could conceivably be looking at a painted zebra that is about to be eaten by an alien stick-insectoid, though: that is a logical possibility. And if I don’t know how rare such creatures are, how can I know how unlikely this possibility is?Well, I can simply assume that it is unlikely, until I get evidence to the contrary. We naturally assume that things remain more or less the same, in the absence of evidence to the contrary, when we name things. And we only have to be definite enough for the purposes of communication. We do not need a precise definition of “horse” in order to know that something is a horse, so why would we need to rule out all conceivable stick-insectoids?
......Quite generally, the power of natural language lies in its flexibility, which derives from the inherent vagueness of its terms: our words arrive sufficiently well defined for their usual uses, but they can always be defined with more precision if that becomes necessary. The ubiquity of vagueness in natural language is not a logical problem (as Russell believed), it is the possibility of a logical solution to most if not all of our philosophical problems.
......Philosophers have a strong bias towards bivalence because as we philosophize we clarify, aiming to maintain an adequate bivalence. But intuitions that logic ought to be bivalent are therefore quite compatible with logic not being perfectly bivalent. After all, questions of truth are essentially questions of how well our words describe the world; so, the logical primitive is not True (or T, in some mathematical model of logical reasoning) but True Enough. When we say “that’s true” we usually mean that it’s true enough. And it is implausible that statements are bound to be either true enough or else sufficiently false.
Thursday, October 07, 2010
Do Inconsistent Objects Exist?
Mark Colyvan (2009: ‘Applying Inconsistent Mathematics,’ in Otávio Bueno & Øystein Linnebo, New Waves in Philosophy of Mathematics, Palgrave Macmillan, pp. 160–172), while looking at Inconsistent Mathematics, tentatively suggested that (p. 163): ‘There are times when we ought to believe in inconsistent objects.’
......His example was the infinitesimals of the early calculus, which are widely believed to have been inconsistent. E.g. they were equated to both zero and non-zero quantities (while Newton’s fluxions varied but were inconsistently equated to constants). Nevertheless, the early calculus was widely applied throughout the eighteenth century. So if, as many philosophers assert, ‘we should be committed to the existence of all and only the entities that are indispensible to our best scientific theories’ (p. 162), then it seems that Colyvan’s suggestion makes sense.
......But can we know what our best theories are, without hindsight? Epicycles, for example, were an arbitrarily effective way of coping with real-world ellipses, given a mathematical language of circles. So the astronomy of Copernicus, with his circular orbits and no epicycles, was originally less accurate than Ptolemaic astronomy. But of course, the former was a better theory. It was a step in the right direction. If we can’t, then, know what our best theories are without the benefit of hindsight, then insofar as we now have better theories without such inconsistencies in them, perhaps we should now say that we should not then have believed in such objects. After all, we could always take inconsistencies to be good indications that we need a better theory.
......It is perhaps easier to see that asking if inconsistent objects exist is a bit like asking if impossible things can happen. And of course, if something happens then it must have been possible. Nevertheless, things that seem impossible can happen. And similarly, existing objects may well have descriptions that, while true enough individually (for our usual purposes), are collectively inconsistent (at least on the surface). An apparent inconsistency usually means that our descriptions stand in need of more precision. But it doesn’t mean that they’re too bad to use most of the time. Nor does it mean that the objects so described don’t exist.
......For a ubiquitous example, light as we sense it can be bright (or dull), but photons are dense (or sparse). Our word ‘light’ equivocates between our sensations of light and the light itself. Furthermore, light itself is lots of photons, but it’s also electromagnetic waves, and waves aren’t particles. But it isn’t that light doesn’t exist, of course, and eventually quantum physics described such behaviour consistently enough. It certainly makes sense for us to believe that photons exist (and to be even surer that light exists). And although light also behaves according to relativity physics, which may well be inconsistent with quantum physics, such inconsistency may just be a reason to pursue an even better theory (of light).
......For a more apposite example, the infinitesimals of the early calculus, more precisely described, may be the so-called irreal infinitesimals that were informally introduced in my To Continue with Continuity (pp. 105–107). Suppose there are such continua as I describe in that paper (e.g. space, perhaps). And let x be a real number (e.g. pi), in the sense of an integer (e.g. 3) plus, after the decimal point, an endless sequence of digits in all the decimal places: the first (e.g. 1), the second (4), the third (1) and so forth (59265...). While that isn’t the standard definition of a real number, it’s a definite enough concept, and highly applicable.
......And since the standard axiom of infinity—which says that the natural numbers are collectively a standard set—goes well beyond the Peano axioms, and is rather prone to paradox (e.g. Levy’s paradox), let us further suppose that the natural numbers are collectively indefinitely extensible. If that’s indeed the case, then x is an (infinitesimally) imprecise description of many (infinitesimally) different lengths.
......So if l is a non-zero irreal infinitesimal then x + l = x because, quite generally, infinitesimals are smaller than 1/n for any natural number n, so that adding them to x affects x in none of its decimal places. (And incidentally, the word ‘infinitesimal’ derives from a Latin word that originally meant the infiniteth term in a sequence.) There are, then, consistent (if informal) mathematical objects—irreal infinitesimals—that for the purposes of the early calculus could be adequately described by its descriptions of its infinitesimals.
......So if such continua as do exist are well enough described by such (informal) theories as mine, then surely we could take irreal infinitesimals to be the referents of ‘infinitesimal’ in the early calculus. (Points were not then the same as real numbers, and the natural numbers were widely regarded as indefinitely extensible, so that infinite space would contain infinite lengths and hence geometrical infinitesimals.) Furthermore, insofar as the natural numbers can be said to exist, we could then think of such infinitesimals as existing.
......Of course, if mathematical existence is equated with consistency, relative to some axioms, then inconsistent mathematical objects exist when, and only when, we have inconsistent axioms; and of course, such inconsistent objects shouldn’t exist because they would be too trivial.
......His example was the infinitesimals of the early calculus, which are widely believed to have been inconsistent. E.g. they were equated to both zero and non-zero quantities (while Newton’s fluxions varied but were inconsistently equated to constants). Nevertheless, the early calculus was widely applied throughout the eighteenth century. So if, as many philosophers assert, ‘we should be committed to the existence of all and only the entities that are indispensible to our best scientific theories’ (p. 162), then it seems that Colyvan’s suggestion makes sense.
......But can we know what our best theories are, without hindsight? Epicycles, for example, were an arbitrarily effective way of coping with real-world ellipses, given a mathematical language of circles. So the astronomy of Copernicus, with his circular orbits and no epicycles, was originally less accurate than Ptolemaic astronomy. But of course, the former was a better theory. It was a step in the right direction. If we can’t, then, know what our best theories are without the benefit of hindsight, then insofar as we now have better theories without such inconsistencies in them, perhaps we should now say that we should not then have believed in such objects. After all, we could always take inconsistencies to be good indications that we need a better theory.
......It is perhaps easier to see that asking if inconsistent objects exist is a bit like asking if impossible things can happen. And of course, if something happens then it must have been possible. Nevertheless, things that seem impossible can happen. And similarly, existing objects may well have descriptions that, while true enough individually (for our usual purposes), are collectively inconsistent (at least on the surface). An apparent inconsistency usually means that our descriptions stand in need of more precision. But it doesn’t mean that they’re too bad to use most of the time. Nor does it mean that the objects so described don’t exist.
......For a ubiquitous example, light as we sense it can be bright (or dull), but photons are dense (or sparse). Our word ‘light’ equivocates between our sensations of light and the light itself. Furthermore, light itself is lots of photons, but it’s also electromagnetic waves, and waves aren’t particles. But it isn’t that light doesn’t exist, of course, and eventually quantum physics described such behaviour consistently enough. It certainly makes sense for us to believe that photons exist (and to be even surer that light exists). And although light also behaves according to relativity physics, which may well be inconsistent with quantum physics, such inconsistency may just be a reason to pursue an even better theory (of light).
......For a more apposite example, the infinitesimals of the early calculus, more precisely described, may be the so-called irreal infinitesimals that were informally introduced in my To Continue with Continuity (pp. 105–107). Suppose there are such continua as I describe in that paper (e.g. space, perhaps). And let x be a real number (e.g. pi), in the sense of an integer (e.g. 3) plus, after the decimal point, an endless sequence of digits in all the decimal places: the first (e.g. 1), the second (4), the third (1) and so forth (59265...). While that isn’t the standard definition of a real number, it’s a definite enough concept, and highly applicable.
......And since the standard axiom of infinity—which says that the natural numbers are collectively a standard set—goes well beyond the Peano axioms, and is rather prone to paradox (e.g. Levy’s paradox), let us further suppose that the natural numbers are collectively indefinitely extensible. If that’s indeed the case, then x is an (infinitesimally) imprecise description of many (infinitesimally) different lengths.
......So if l is a non-zero irreal infinitesimal then x + l = x because, quite generally, infinitesimals are smaller than 1/n for any natural number n, so that adding them to x affects x in none of its decimal places. (And incidentally, the word ‘infinitesimal’ derives from a Latin word that originally meant the infiniteth term in a sequence.) There are, then, consistent (if informal) mathematical objects—irreal infinitesimals—that for the purposes of the early calculus could be adequately described by its descriptions of its infinitesimals.
......So if such continua as do exist are well enough described by such (informal) theories as mine, then surely we could take irreal infinitesimals to be the referents of ‘infinitesimal’ in the early calculus. (Points were not then the same as real numbers, and the natural numbers were widely regarded as indefinitely extensible, so that infinite space would contain infinite lengths and hence geometrical infinitesimals.) Furthermore, insofar as the natural numbers can be said to exist, we could then think of such infinitesimals as existing.
......Of course, if mathematical existence is equated with consistency, relative to some axioms, then inconsistent mathematical objects exist when, and only when, we have inconsistent axioms; and of course, such inconsistent objects shouldn’t exist because they would be too trivial.
Tuesday, October 05, 2010
Monarchy And Democracy
Yesterday's Dispatches on Channel 4 was about "the illegal phone hacking carried out at the New of World during the six years Andy Coulson was either Deputy Editor and Editor," of current interest because "by hiring Andy Coulson David Cameron has sanctioned the News of the World culture of impunity." Rupert Murdoch certainly seems to have a worrying amount of influence over our police and politics, centre-left as well as centre-right. The origin of these revelations, in a successful prosecution for hacking a conversation between our two young princes, is of course less interesting. But the consequent importance of the fact that Murdoch could neither buy off nor intimidate the Palace does make me wonder whether the left, and other democrats, should question their traditional Republicanism, in these transitional days.
Monday, October 04, 2010
Ordinary Objects
Further to the question of whether or not Chairs Exist, I notice that Amie L. Thomasson’s 2007 book Ordinary Objects is out in paperback next month. Basically, it shows how “the claim that there are ordinary objects can form part of a coherent, reflective metaphysical view built up out of our common sense way of looking at the world, in a way that avoids the philosophical problems that have long been feared to plague a common sense ontology” (pp. 7–8).
......The first problem addressed (pp. 9–24) was that if all such things are made of atoms then there’s causal redundancy, e.g. if it’s really atoms arranged stone-wise that break a window (atoms arranged window-wise) then we shouldn’t also have a stone breaking it. But of course, the former just is the stone breaking it, if all such things are made of atoms. Thomasson’s analysis was more detailed, of course, but still readable, and seems to generalize nicely (e.g. the next section addressed the related issue of epiphenomenalism in the theory of mind).
......The first problem addressed (pp. 9–24) was that if all such things are made of atoms then there’s causal redundancy, e.g. if it’s really atoms arranged stone-wise that break a window (atoms arranged window-wise) then we shouldn’t also have a stone breaking it. But of course, the former just is the stone breaking it, if all such things are made of atoms. Thomasson’s analysis was more detailed, of course, but still readable, and seems to generalize nicely (e.g. the next section addressed the related issue of epiphenomenalism in the theory of mind).
Saturday, October 02, 2010
Euler’s ‘2’
Incidentally, I’ve rewritten two of last month’s posts, and the rewrite—Did Euler’s ‘2’ refer to ZFC’s {Ø, {Ø}}?—will be appearing in next month’s issue of The Reasoner.
Friday, October 01, 2010
True Enough
What is truth? Well, snow can be brown when it is a bit muddy, and in shadows snow can be blue, but insofar as snow is white, ‘snow is white’ is true. Words are true when they are true to reality. And the obvious contrast is with falsity, with saying, of what is, that it isn’t (or of what isn’t that it is).
......But words exist in a public language and so, given how we come to acquire our linguistic skills, vague meanings are inevitably ubiquitous. Still, we invariably speak within some context, wherein we need only say enough to make our meaning clear enough. Our words can describe the world well enough—they usually do—and then what we say is true enough. And when it isn’t, we can always be more precise.
......We can even introduce new terms into our language, if we have to (as scientists and philosophers). Indeed, there seems to be no logical limit to our ability to be ever more precise. And so to say that something is true is, more precisely, to say that it’s true enough. Bivalent propositional logics—in which each sentence is either true or else false—are usefully rough approximations to the truth.
......Consider some commonplace examples: The table at which I’m typing this is flat—it isn’t warped or lopsided—but in another sense it isn’t flat, not being perfectly smooth and horizontal. To say that it’s flat is to say something that’s true enough.
......And similarly, to return to the themes of previous posts, ‘grass is green’ is true because ordinary grass (such as fills lawns and pastures) reflects the green bits of daylight (fuzzily delineated bits) ordinarily (e.g. when there’s no drought).
......And it’s insofar as chairs exist that it’s true to say of them that they do.
......And do rainbows exist? Well, in a sense they do (e.g. we can refer each other to them), but there is clearly a sense in which they don’t (much as mirages are not oases).
......What do we mean by ‘grass’ or ‘chair’? Such things form obvious kinds, which is how we come to learn such words. What most of our words have, then, are meanings that are definite enough. Indeed, such vagueness may well be logically necessary, in any possible medium of communication. But even if a more definite language was possible, it’s the vagueness we have which means that our words can be given more definite meanings as required. So a less vague language would in any case be a less useful tool in general (although it might have its uses).
......But words exist in a public language and so, given how we come to acquire our linguistic skills, vague meanings are inevitably ubiquitous. Still, we invariably speak within some context, wherein we need only say enough to make our meaning clear enough. Our words can describe the world well enough—they usually do—and then what we say is true enough. And when it isn’t, we can always be more precise.
......We can even introduce new terms into our language, if we have to (as scientists and philosophers). Indeed, there seems to be no logical limit to our ability to be ever more precise. And so to say that something is true is, more precisely, to say that it’s true enough. Bivalent propositional logics—in which each sentence is either true or else false—are usefully rough approximations to the truth.
......Consider some commonplace examples: The table at which I’m typing this is flat—it isn’t warped or lopsided—but in another sense it isn’t flat, not being perfectly smooth and horizontal. To say that it’s flat is to say something that’s true enough.
......And similarly, to return to the themes of previous posts, ‘grass is green’ is true because ordinary grass (such as fills lawns and pastures) reflects the green bits of daylight (fuzzily delineated bits) ordinarily (e.g. when there’s no drought).
......And it’s insofar as chairs exist that it’s true to say of them that they do.
......And do rainbows exist? Well, in a sense they do (e.g. we can refer each other to them), but there is clearly a sense in which they don’t (much as mirages are not oases).
......What do we mean by ‘grass’ or ‘chair’? Such things form obvious kinds, which is how we come to learn such words. What most of our words have, then, are meanings that are definite enough. Indeed, such vagueness may well be logically necessary, in any possible medium of communication. But even if a more definite language was possible, it’s the vagueness we have which means that our words can be given more definite meanings as required. So a less vague language would in any case be a less useful tool in general (although it might have its uses).
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