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Philosophers
Mortimer Adler Rogers Albritton Alexander of Aphrodisias Samuel Alexander William Alston Anaximander G.E.M.Anscombe Anselm Louise Antony Thomas Aquinas Aristotle David Armstrong Harald Atmanspacher Robert Audi Augustine J.L.Austin A.J.Ayer Alexander Bain Mark Balaguer Jeffrey Barrett William Belsham Henri Bergson George Berkeley Isaiah Berlin Richard J. Bernstein Bernard Berofsky Robert Bishop Max Black Susanne Bobzien Emil du Bois-Reymond Hilary Bok Laurence BonJour George Boole émile Boutroux F.H.Bradley C.D.Broad Michael Burke C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Ernst Cassirer David Chalmers Roderick Chisholm Chrysippus Cicero Randolph Clarke Samuel Clarke Anthony Collins Antonella Corradini Diodorus Cronus Jonathan Dancy Donald Davidson Mario De Caro Democritus Daniel Dennett Jacques Derrida René Descartes Richard Double Fred Dretske John Dupré John Earman Laura Waddell Ekstrom Epictetus Epicurus Herbert Feigl John Martin Fischer Owen Flanagan Luciano Floridi Philippa Foot Alfred Fouilleé Harry Frankfurt Richard L. Franklin Michael Frede Gottlob Frege Peter Geach Edmund Gettier Carl Ginet Alvin Goldman Gorgias Nicholas St. John Green H.Paul Grice Ian Hacking Ishtiyaque Haji Stuart Hampshire W.F.R.Hardie Sam Harris William Hasker R.M.Hare Georg W.F. Hegel Martin Heidegger Heraclitus R.E.Hobart Thomas Hobbes David Hodgson Shadsworth Hodgson Baron d'Holbach Ted Honderich Pamela Huby David Hume Ferenc Huoranszki William James Lord Kames Robert Kane Immanuel Kant Tomis Kapitan Jaegwon Kim William King Hilary Kornblith Christine Korsgaard Saul Kripke Andrea Lavazza Keith Lehrer Gottfried Leibniz Leucippus Michael Levin George Henry Lewes C.I.Lewis David Lewis Peter Lipton C. Lloyd Morgan John Locke Michael Lockwood E. Jonathan Lowe John R. Lucas Lucretius Alasdair MacIntyre Ruth Barcan Marcus James Martineau Storrs McCall Hugh McCann Colin McGinn Michael McKenna Brian McLaughlin John McTaggart Paul E. Meehl Uwe Meixner Alfred Mele Trenton Merricks John Stuart Mill Dickinson Miller G.E.Moore Thomas Nagel Otto Neurath Friedrich Nietzsche John Norton P.H.Nowell-Smith Robert Nozick William of Ockham Timothy O'Connor Parmenides David F. Pears Charles Sanders Peirce Derk Pereboom Steven Pinker Plato Karl Popper Porphyry Huw Price H.A.Prichard Protagoras Hilary Putnam Willard van Orman Quine Frank Ramsey Ayn Rand Michael Rea Thomas Reid Charles Renouvier Nicholas Rescher C.W.Rietdijk Richard Rorty Josiah Royce Bertrand Russell Paul Russell Gilbert Ryle Jean-Paul Sartre Kenneth Sayre T.M.Scanlon Moritz Schlick Arthur Schopenhauer John Searle Wilfrid Sellars Alan Sidelle Ted Sider Henry Sidgwick Walter Sinnott-Armstrong J.J.C.Smart Saul Smilansky Michael Smith Baruch Spinoza L. Susan Stebbing Isabelle Stengers George F. Stout Galen Strawson Peter Strawson Eleonore Stump Francisco Suárez Richard Taylor Kevin Timpe Mark Twain Peter Unger Peter van Inwagen Manuel Vargas John Venn Kadri Vihvelin Voltaire G.H. von Wright David Foster Wallace R. Jay Wallace W.G.Ward Ted Warfield Roy Weatherford William Whewell Alfred North Whitehead David Widerker David Wiggins Bernard Williams Timothy Williamson Ludwig Wittgenstein Susan Wolf Scientists Michael Arbib Walter Baade Bernard Baars Gregory Bateson John S. Bell Charles Bennett Ludwig von Bertalanffy Susan Blackmore Margaret Boden David Bohm Niels Bohr Ludwig Boltzmann Emile Borel Max Born Satyendra Nath Bose Walther Bothe Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle S. H. Burbury Donald Campbell Anthony Cashmore Eric Chaisson Jean-Pierre Changeux Arthur Holly Compton John Conway John Cramer E. P. Culverwell Charles Darwin Terrence Deacon Lüder Deecke Louis de Broglie Max Delbrück Abraham de Moivre Paul Dirac Hans Driesch John Eccles Arthur Stanley Eddington Paul Ehrenfest Albert Einstein Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher Joseph Fourier Philipp Frank Lila Gatlin Michael Gazzaniga GianCarlo Ghirardi J. Willard Gibbs Nicolas Gisin Paul Glimcher Thomas Gold A.O.Gomes Brian Goodwin Joshua Greene Jacques Hadamard Patrick Haggard Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman John-Dylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Art Hobson Jesper Hoffmeyer E. T. Jaynes William Stanley Jevons Roman Jakobson Pascual Jordan Ruth E. Kastner Stuart Kauffman Martin J. Klein Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovà? Rolf Landauer Alfred Landé Pierre-Simon Laplace David Layzer Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Ulrich Mohrhoff Jacques Monod Emmy Noether Abraham Pais Howard Pattee Wolfgang Pauli Massimo Pauri Roger Penrose Steven Pinker Colin Pittendrigh Max Planck Susan Pockett Henri Poincaré Daniel Pollen Ilya Prigogine Hans Primas Adolphe Quételet Juan Roederer Jerome Rothstein David Ruelle Erwin Schrödinger Aaron Schurger Claude Shannon David Shiang Herbert Simon Dean Keith Simonton B. F. Skinner Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark William Thomson (Kelvin) Peter Tse Vlatko Vedral Heinz von Foerster John von Neumann John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss John Wheeler Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson H. Dieter Zeh Ernst Zermelo Wojciech Zurek Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium |
Modality
Logic is an
There is nothing material about logic. It is purely abstract and Where symbols in ordinary language are notoriously ambiguous, logic is an attempt to formalize the allowed terms, the rules by which they are assembled into statements, and the principles for deductively reasoning from some statements (premises) to others (conclusions), such that true premises lead to true (valid) conclusions. It was the vision of the great rationalist philosopher Gottfried Leibniz that we could develop an ambiguity-free language for logic and mathematics. That dream was pursued by Bertrand Russell, Ludwig Wittgenstein, Rudolf Carnap, and others. Their logical truth-functional analyses are severely limited by the principle of bivalence, the excluded middle, that the only possible values are true and false. But the world is not limited to truth and falsity. Attempts to develop three-valued or many-valued logics have largely failed.
Modal The use of "necessity" and "impossibility" to describe the physical world should be guarded and understood to describe events or "states of affairs" that have extremely high or low probability. The term certainty, when used about knowledge of the physical world, normally represents only extremely high probability.
Possibility and contingency are not easily constrained to the binary values of true and false. To begin with, possibility is normally understood to include necessity. If something is necessary, it is The modal operators are a box '?' for necessity and a diamond ' ◇ ' for possibility. Impossibility is the negation of possibility, ?◇, and contingency must negate necessity and also negate impossibility, so it is the logical conjunction of "not necessity" and "possibility" (?? ∧ ◇).
Mathematically, contingency is a continuum of values But physically, contingency is the closed interval, including the endpoints of necessity (1) and impossibility (0). Theoretical physics today is often described as probabilistic and statistical, which is sometimes misunderstood to exclude perfect certainties like 0 and 1, but this is not the case. Even quantum physics, the basis of ontological chance in the universe, sometimes predicts certain outcomes, as explained by Paul Dirac.
With its four modes, necessity, possibility, impossibility, and contingency, modal analyses simply contain more than can be confined to two-valued truth-functions, whether in logic, usually called Truth is a binary relation of ideas, true or false. Facts of the matter have a continuous value somewhere between 0 and 1, with plus or minus estimates of the standard deviation of probable errors around that value.
In analytic language philosophy, we need more than the "truth" of statements and propositions with their apparent claims about "necessary"
Although we distinguish the
All facts about the world are (necessarily?) empirical and
We therefore conclude that the logical empiricist's idea that the laws of nature can be described with linguistic statements or propositions is simply wrong. This is particularly the case for the laws of modern physics, which are now irreducibly
The "evidence" that "verifies" or validates a physical theory is gathered from a very large number of experiments. No single measurement can establish a fact in the way that a single valid argument can assert the "truth" of an analytic statement. The large number of measurements means that evidence is statistical. Indeed, physical theories make predictions that are probabilities. Theories are confirmed when the
Information philosophy considers claims such as "If P, then P is true" to be redundant, adding no information to the (true) assertion of the statement or proposition "P." Further redundancies are equally vacuous, such as "If P is true, then P is necessarily true" and "If P is true, then P is necessarily true in all possible worlds." Logically necessary and analytic statements are tautological and carry no new information. This is the paradox of analyticity. The statement "A is A" tells us nothing. The statement "A is B" is informative. Adding "is true" and the like also add no new information. They cannot change the fundamental nature of a statement. For example, they cannot change a contingent statement into a necessary one. Consider the statement "A is contingently B." Prepending the necessity operator, we have "Necessarily, A is contingently B." It changes nothing.
We adopt Ludwig Wittgenstein's terminology from "The world is all that is the case."
In fact, that is to say in the empirical world, any fact F is at best probably "the case," with the probability approaching certainty in cases that are adequately determined. And, in any case, any past F was contingent and could possibly have been otherwise. The idea of a "possible world" is best understood as a way this actual world could have been.
There is, "in fact," only one
See Saul Kripke,
The "sample space" of modern probability theory and the "phase space" of statistical physics are spaces for possible worlds. The 36 ways that two dice can be thrown, the 64 squares where a pawn can be located on a chessboard, the coarse-grained cells for gas particles in position-momentum space, and the minimum uncertainty volumes Naming and Necessity, 1981, p.19.
Δp Δx = ℏ of quantum physics, all can be used to describe possible worlds, how worlds can be, and thus how our world might be.
Information philosophy maintains that ontologically real possibilities "exist" or subsist as ideas, as pure abstract information, at the present time, alongside "actual" material objects. The ontological or existential status of ideas has always been a controversial question in metaphysics. The exact status of their "existence" in the past and future is equally controversial, and likely asymmetrical in the past and the future.
Actual Possibles and Possible Possibles
Possibilities in the past may be described as having been "actual possibles." Possibilities in the future are merely "possible possibles."
Possibilities in the past, for example the past alternatives for human actions or the past outcomes of experiments in probabilistic quantum physics, were mostly "roads not taken" and were condemned to "non-being," as the existentialists described it. But they were actual as possibilities in the past that were never "really" actualized. Thus, we can say they
The existence of alternative possibilities in the future raises the famous problem of
But what can be said about the existential status of these future alternative possibilities in the present time? What can "actual possibles" mean metaphysically? We shall show that possibilities are ideas, abstract entities, which from the time they are embodied in a physical system or in a human mind become "actual possibles." At later times, we are justified in describing them as past "actual possibles" that were never Whenever one of many actual possibles is actualized, it does not mean that alternatives that existed as abstract entities at that moment are no longer possibly actualizable in the future. Unless they are forgotten, they remain as "actual possibles"for future use. We can now describe the many possible worlds that exist within our actual world. They are ways our actual world may be.
If you see a connection between quantum chance and "free" human decisions, there is one but it does not make our decisions random
Information philosophy provides two examples of future "possible possibles" that are transformed when one is actualized into past "actual possibles." One comes from the world of quantum physics (the source of ontological chance), the other from the human mind when evaluating alternatives and making a decision.
The Many Possible Worlds in Our Actual World
We distinguish three kinds of information structures and processes in our world, the physical, the biological, and the particularly human. All such processing systems can have multiple possibilities for the next step in their processes. These possibilities are abstract bits of information ("ideas") that must be embodied physically to be available as "actual possibles."
At the physical level, quantum events that are amplified to the macroscopic world start new causal chains in "adequately determined" physical processes. Biological possibilities include sexual selection, where chromosomes for the zygote are randomly selected from the sperm and egg, as a genuinely new individual is created and novel information enters the universe. For human beings, possibilities are ideas in minds about what to do next. Many of these ideas are constantly available in the normal repertoire of behaviors. That one is chosen over others does not remove the others from future actualization. They remain as "actual possibles" unless they are forgotten. Human minds also create genuinely new information, like that created in biological evolution, when they mentally consider an idea never before thought as an "actual possible." Although our metaphysically actual possibles are not as numerous as the plurality of worlds of David Lewis or the many worlds of Hugh Everett III, they are plentiful enough. With ten billion humans, millions of other species, some with trillions of individuals that have behavioral repertoires, the numbers of possibilities being actualized in the world each second is vast. There are many ways that our world may be. It is thus very strange that modal logicians, especially those who are necessitists, assume our actual world has only one way to be and all possibilities are found in worlds that are physically inaccessible, though modally accessible.
Necessity of Identity and the Limits of Necessitism
David Wiggins and Saul Kripke claimed that the proof of the necessity of identity appeared to make contingent identity impossible. Wiggins also argued against Peter Geach's idea of relative identity.
An information analysis of identity limits perfect and total identity to cases of self-identity, which includes an object's
Kripke claims that such things, which we describe as informationally identical, are metaphysically necessary
It was the claim for the necessity of identity that led to the leading modal systems including a "rule of necessitation," that if P, then necessarily P. (P ? ? P) We should examine this claim carefully. If correct, it may only be a tautological or analytical statement about a universe of discourse, with no significance for the physical world. By contrast, our claim for The first proof of the necessity of identity, by Ruth Barcan Marcus, was little more than the substitutivity of identicals, which may be seen as begging the question of that identity! It is best seen in a simple proof by her thesis adviser, Frederick B. Fitch,
23.4 (1) a = b, (2) ?[a = a], then (3) ?[a = b], by identity elimination. (p.164)
Clearly this is mathematically and logically sound. Fitch substitutes b from (1), for a in the modal context of (2). This would be fine if these are just equations. But substitutivity in statements also requires that the substitution is intensionally meaningful. In the sense that b is actually just a, substituting b is equivalent to keeping a there, a tautology, something with no new information. To be informative and prove the necessary truth of the new statement, we must know more about b, for example, that its Most earlier identity claims showed only that a and b were references (names) for the same thing, Frege's Morning Star and Evening Star for example. But this is a new claim, that numerically distinct things are identical – in some respect.
Those earlier claims often referred to Leibniz's Law, the Identity of Indiscernibles, and Marcus in 1961, Wiggins in 1965, and Kripke in 1971 all added Leibniz's Law. But none of these changed the fact that contingent identities are merely possible, that substitution of b for a is valid if and only if you already know that a and b are If a and b refer to the same object, it is already a perfect and absolute identity. Calling it necessary adds nothing more than "is true" or "necessarily true in all possible worlds." But it is for claims about "transworld identity" of individuals that modal realists following David Lewis require the "necessity of identity."
Possible Worlds
It is critical to note that the metaphysicians proposing possible worlds are for the most part materialists and determinists who do not believe in the existence of ontological possibilities in our world.
They are mostly actualists who say that the only 'possibilities' have always been whatever it was that has actually happened. This is Dan Dennett's position, for example, not far from the original actualist, Diodorus Cronus. Moreover, all of their infinite number of worlds, e.g., David Lewis's possible worlds, are governed by deterministic laws of nature. This means that there are also no real possibilities in any of their possible worlds, only actualities there as well. Now this is quite ironic, since the invention of possible worlds was proposed as a superior way of talking about counterfactual possibilities in our world.
Since information philosophy defends the existence of alternative possibilities leading to different futures, we can adopt a form of modal discourse to describe these possibilities as Saul Kripke recommended that his "possible worlds" are best regarded as "possible states (or histories) of the world," or just "counterfactual situations," or simply "ways the world might have been." Kripke appears to endorse the idea of alternative possibilities, that things could have been otherwise. David Lewis appears to have been a materialist and determinist. The infinity is not as large as the absurdly extravagant number in David Lewis's possible worlds, which have counterparts for each and every living person with every imaginable difference in each of our counterparts, each counterpart in its own unique world. Thus there are Lewisian worlds in which your counterpart is a butcher, baker, candlestick maker, and every other known occupation. There are possible worlds in which your counterpart eats every possible breakfast food, drives every possible car, and lives in every block on every street in every city or town in the entire word. This extravagance is of course part of Lewis's appeal. It makes Hugh Everett's "many worlds" of quantum mechanics (which split the universe in two when a physicist makes a quantum measurement) minuscule, indeed quite parsimonious, by comparison. Specifically, when an Everett universe splits into two, it doubles the matter and energy in the new universe(s) – an extreme violation of the principle of the conservation of matter/energy – and it also doubles the information. Apart from that absurdity, the two universes differ by only one bit of information, for example, whether the electron spin measured up or down in the quantum measurement. Similarly, for every Lewisian universe, the change of one bit of information implies one other possible universe in which all the infinite number of other bits stay exactly the same. But Lewis imagines that every single bit in the universe may be changed at any time, an order of physical infinities that rivals the greatest number that Georg Cantor ever imagined. Is David Lewis ontologically committed to such a number?
References
Barcan, R. C. (1946). "A functional calculus of first order based on strict implication." The Journal of Symbolic Logic, 11(01), 1-16.Barcan, R. C. (1946). "The deduction theorem in a functional calculus of first order based on strict implication." The Journal of Symbolic Logic, 11(04), 115-118.Barcan, R. C. (1947). "The identity of individuals in a strict functional calculus of second order." The Journal of Symbolic Logic, 12(01), 12-15.Kripke, Saul. 1981. Naming and Necessity." Blackwell Publishing.Lewis, D. K. (1973). Counterfactuals. Oxford: Blackwell.Lewis, D. K. (1986). On the plurality of worlds. Oxford: Blackwell.Quine, W. V. 1943. "Notes on Existence and Necessity." The Journal of Philosophy, 40 (5) p.113Quine, W. V. 1947. "The Problem of Interpreting Modal Logic." The Journal of Symbolic Logic 12 (2) p.43Quine, W. V. 1980. From a Logical Point of View, 2d ed. Cambridge, MA: Harvard University Press.Wiggins, David. 2001. Sameness and Substance Renewed. Cambridge University Press.Normal | Teacher | Scholar |