Justified True Belief

(●) Composition infers that a whole has a property because its parts do, and division runs the same inference backwards. + One mistake with two directions. What is true of the parts and what is true of the whole are different questions. (1) The move hands a property between the parts and the whole. - Mr. Ellis is loading a van for his daughter's move. Every box he lifts is light, so the load is light, he decides, and he takes the hill in top gear with the springs flat on the axle. Backwards is just as easy: the van is heavy, so each box must be heavy, and he braces for the first one and nearly puts it through the ceiling. - Two words help here. The reasons someone offers are the premises, and what they are meant to support is the conclusion. Composition puts facts about the parts in the premises and a fact about the whole in the conclusion; division does the reverse. - Watch the noun. "The boxes are light" can mean each box on its own, the distributive sense, or all of them together, the collective sense. Mr. Ellis heard the first and concluded the second. That slip is why Irving Copi's textbook files the pair among the fallacies of ambiguity, arguments that work only because a word carries two meanings. (2) It tempts because the transfer usually works. - Every brick is red, so the wall is red. Nobody checks that, because plenty of properties really do spread from the parts to the whole. Call such a property expansive: if every part has it, the whole has it. - Not every property is expansive, and the mind rarely stops to ask which kind it holds. Take being invisible: no atom of a stick of chalk can be seen, and the chalk sits there in plain view. The fallacy lives in the skipped check. (3) The name is Aristotle's, and the family has two cousins. - Aristotle listed both among his thirteen fallacies in the Sophistical Refutations, around 350 BC, though he meant a trick of how words are grouped: "a man can walk while sitting" is true of a seated man, and false if it means both at once. The parts-and-wholes sense a reader meets today comes from the textbook tradition, and from Copi's Introduction to Logic of 1953. - Division with numbers is the ecological fallacy: the school's average went up, so Maya's score went up. An average can rise while half the children fall. - The nothing but move is composition in a lab coat: you are nothing but atoms, atoms have no purposes, so your life has none. Whether purpose is expansive is exactly what is in dispute. Therefore, the fallacy is not in noticing what the parts are like, or what the whole is like. It is in assuming, without checking, that one settles the other.

(●) Simple example: "Every player is the best in his position, so the team is the best in the league." + Your brother-in-law has just explained why his side cannot lose this year, and the reasoning is a headcount. (1) What is claimed and what is offered. - The claim is about the team. The support is eleven true facts about eleven players. (2) Why the support does no work. - Being the best is not expansive. A team is its players plus whatever happens between them, and the passing can be a shambles while every name on the sheet is a star. A squad of NBA stars flew to Athens in 2004 and came home with bronze. - Try the swap. "Every player was born in Spain, so the team is Spanish" is a perfectly good inference. The move is not wrong in itself, only wrong for this property. - The reverse runs the same way: "The choir is loud, so each singer must be loud." Forty people who could not fill a kitchen can fill a cathedral. (3) What the reply was really doing. - It swapped a hard question, how the parts work together, for an easy count of the parts. Counting is quicker than watching.

(●) A critic says: "Explain each thing in the universe and you have explained the universe. Asking what caused the whole is an extra question with nothing behind it." + The oldest and best form is David Hume's, and it turns up in comment threads as readily as in seminars. (1) What is being argued. - The cosmological argument is the family of arguments that reason from the existence of the world to a cause or ground of it. The charge is that its central question, what explains the whole chain of causes, is an empty one. - The published ancestor is Part IX of Hume's Dialogues Concerning Natural Religion (1779), where Cleanthes, one of its speakers, imagines twenty particles, each with its own cause: "This is sufficiently explained in explaining the cause of the parts." Paul Edwards retold it in 1959 with five Eskimos on a New York street corner. (2) Where the fallacy sits. - The slide runs from "each part has an explanation" to "the whole has an explanation", and it treats being explained as expansive. Sometimes it is. Edwards's Eskimos each came to the corner for a reason of his own, outside the group, so the group's presence really is the sum of those reasons. The chain the cosmological argument asks about is different: every link is explained by another link, and there the transfer fails. - Alexander Pruss answered it in 1998 with a cannonball, and again in The Principle of Sufficient Reason (2006). Every instant of its flight is explained by the instant before it, so on Hume's principle the whole flight is explained. And yet nobody has mentioned the cannon. - Pruss adds that Hume's principle helps itself to the very point in dispute, that a whole is nothing over and above its parts. (3) The sound version. - Cleanthes had a better suggestion in the same breath: "Why may not the material universe be the necessarily existent Being?" A necessary being is one that could not have failed to exist, and so needs nothing outside itself to explain it. Nominating the universe for that job is no fallacy. - Bertrand Russell said the same thing in 1948, "the universe is just there, and that's all", and Graham Oppy's Arguing about Gods (2006) builds it into a full position: everyone stops somewhere, and the naturalist's stopping point, he argues, is the simpler one. - The real question is whether a universe whose basic numbers (the strength of gravity, the mass of the electron) could have been otherwise is the kind of thing that could not have failed to exist. (4) How to answer it. - "You may be right that explaining every link explains the chain. But if each link is explained by the one before, we know how the chain hangs and not why anything is hanging. 'The universe is just there' answers that honestly, so let's talk about whether it answers it well." See also: Natural Theology: Leibniz' Contingency Argument Natural Theology: The Kalam Argument

(●) A Christian says: "Atoms can't think. A brain is nothing but atoms. So the brain can't think, and there has to be a soul." + The same move from our side of the table, and it tempts because the conclusion may well be true. The argument still does not reach it. (1) What is being argued. - The claim is that the mind is not the brain, so there is a soul. The support is that no atom thinks, and a pile of non-thinkers cannot think. - The point has an honourable ancestor. Leibniz, in the Monadology (1714), imagined a thinking machine blown up to the size of a mill, so that you could walk around inside it and find parts pushing on parts, never a perception. How experience could come out of arrangement is a real puzzle, and nobody on either side has solved it. (2) Where the fallacy sits. - The step from "no atom thinks" to "no arrangement of atoms thinks" assumes that thinking works the way colour does, present in the whole only if it is present in the parts. Plenty of properties do not. No atom is wet, and water is. No transistor plays chess, and the computer beats the grandmaster. - A naturalist (someone who holds that the physical world is all there is) calls thought an emergent property: one the whole has and none of its parts has. The argument as stated has not touched him; it has assumed what he denies. - Turn it around: "You're just atoms, and atoms have no purpose, so your life has none." Every Christian can see the hole in that one, and it is the same hole. - Division turns up on our side too: "The scientific establishment is naturalistic, so this scientist's finding is biased." A property of a profession is handed down to one paper, which has to be read on its own. (3) The sound version. - J. P. Moreland's Consciousness and the Existence of God (2008) does not count atoms. He argues from the kind of property consciousness is: a thought is about something, a pain feels like something from the inside, and nothing physics describes (mass, charge, position, spin) is about anything or feels like anything. - So no rearrangement of physical parts will add those features, he argues. Arrangement explains wetness and chess-playing; it does not explain aboutness or felt experience. Whether he succeeds is a live debate, but his is an argument about the property rather than a headcount of the parts. - The argument from free thinking reaches the same place by another road, from our capacity to reason freely to a self that is more than its physics. (4) How to answer it, when a fellow Christian says it. - "Dry atoms make wet water, so 'the parts can't, therefore the whole can't' won't carry us. What we can argue is that a thought is about something, and nothing physics measures is about anything. Let's argue that." See also: Natural Theology: Free-Thinking Argument

(●) A charge that misses: "Every man who exists has a mother, so by your logic the human race must have a mother. The cosmological argument is composition, plain and simple." + Bertrand Russell put the mother line to Frederick Copleston in a BBC studio in 1948, never naming the fallacy himself, and it has been the standard form of the charge ever since. (1) What the charge claims. - On Russell's reading, the cosmological argument says that every thing in the universe is contingent (it could have failed to exist, and depends on something else) and concludes that the universe is contingent too. That is parts to whole, and mothers show why it fails. (2) Why the charge misses. - Copleston replied that he had never argued from each thing's cause to the whole's cause. His claim was that a series of dependent things, however long, does not explain itself. That can be disputed, but it is not a slip of logic. The exchange has been argued both ways ever since. - The Kalam argument does not use composition at all. Its premise, that whatever begins to exist has a cause, is applied to the universe directly, and the case that the universe began rests on its expansion and on the arguments against an actual infinite, a completed collection with infinitely many members. That is how William Lane Craig and James Sinclair set it out, and the charge aims at a step they never take. - Here is the line. Composition is valid for expansive properties and invalid for the rest, so the test to carry away is one question: does this property spread, or does it only add up? Colour spreads: a wall of red bricks is red. Weight adds up: a van of light boxes is heavy. Having a mother does neither. - Then ask which kind "contingent" is. The disagreement between Russell and Copleston is about the world, not about reasoning. (3) What the charge would need to be true. - It would need "contingent" to be like "has a mother" rather than like "weighs something". Russell's own ground for refusing a necessary being was his view that "necessary" belongs only to analytic propositions, a claim about language. And it would need the only road to a contingent universe to run through a headcount of its parts. - The charge lands on one thing, and it should be granted. Christians really do say "everything in the universe has a cause, so the universe has a cause", and said like that it is composition, unless the speaker can say why causation transfers. The Kalam's premise is worded to close that gap. (4) How to answer it. - "Russell was right that mothers don't add up. The question is whether dependence does. Put a hundred borrowed dollars in a jar and you still don't have a dollar nobody borrowed. Tell me why the universe is different, and we'll be having the real argument." See also: Natural Theology: The Kalam Argument Natural Theology: Leibniz' Contingency Argument