Justified True Belief

(●) Affirming the consequent treats the "then" half of an "if, then" sentence coming true as proof of the "if" half. + If it rained last night, the street is wet. There are four ways to argue from a sentence like that, and the two that fail look very like the two that work. (1) The shape of the move is a conditional run backwards. - That sentence is a conditional. Logicians call its "if" half the antecedent and its "then" half the consequent. It promises one thing, that rain guarantees a wet street, and says nothing about what a wet street guarantees. - "It rained, so the street is wet" is modus ponens, Latin for "the way that affirms": affirm the antecedent and the consequent follows. "The street is dry, so it did not rain" is modus tollens, "the way that denies": deny the consequent and the antecedent goes too. Both hold: rain cannot fall without wetting the street. - The other two only look like them. "The street is wet, so it rained" is affirming the consequent, and "It did not rain, so the street is dry" is denying the antecedent. One sprinkler breaks both: it wets a street without a drop of rain. - The reasons an argument offers are its premises, and what they support is its conclusion. In both bad forms the premises can be true while the conclusion is false, which is what invalid means. Copi and Hurley, the standard textbooks, file them among the formal fallacies: the fault is in the pattern, so anything poured in comes out broken. (2) It tempts because a wet street really is evidence of rain. - Walk out to a wet street and rain is the first thing you think of, and rightly so. A consequent that turns up makes its antecedent more likely, just not certain, and the fallacy is the slide from "more likely" to "so it happened". - A doctor lives on that line. "If it is strep, the throat will be red" makes a red throat worth a swab rather than a diagnosis. - Ordinary speech hides the gap. "If the porch light is on, someone is home" is meant both ways round, an "if and only if", and we hear "if" that way so often that a one-way sentence gets run backwards unnoticed. (3) Aristotle named it, and its twin belongs to the same family. - Aristotle caught the move in the Sophistical Refutations around 350 BC, called it the fallacy of the consequent, and used this very example: wet ground taken for rain. The Stoics catalogued the two valid forms a century later, and the Latin names are medieval. - Denying the antecedent is the twin, and it fails the same way. "He never went to college, so he cannot be well read." Affirming the consequent swaps a conditional's halves, giving its converse (if wet, then rain); denying the antecedent negates both, giving its inverse (if no rain, then no wet). Finding the sprinkler cures both. Therefore, affirming the consequent is a promise read backwards: a conditional guaranteed one direction, and the argument helps itself to both.

(●) Simple example: "If it rained last night, the street will be wet. The street is wet. So it rained last night." + Your neighbour says it over the fence at seven in the morning, and nine mornings in ten he is right. (1) What is claimed and what is offered. - The claim is that it rained. The support is a true conditional and a true observation: rain wets streets, and this street is wet. (2) Why the support does no work. - The sprinkler on the corner house runs at five every morning, and "if rain, then wet" never ruled it out. - Try the swap. "If the sprinkler ran, the street is wet. The street is wet. So the sprinkler ran." Same shape, and a different culprit. A form that names two culprits from one wet street has settled on neither. - What would settle it is the car roof or the lawn: something rain wets that a sprinkler cannot reach. (3) What the reply was really doing. - It was doing something reasonable and calling it something stronger. The word "so" turned a fair suspicion into a verdict, and on the tenth morning the verdict is wrong.

(●) A critic says: "If there were good arguments for God, believing in him would be rational. There aren't any. So believing in him is irrational." + A coworker who has read a little philosophy says it kindly over lunch. It is the twin, denying the antecedent, and the challenge inside it is real even though the argument wrapped around it is not. (1) What is being argued. - The claim is that Christian belief is irrational. The support is a conditional and the denial of its antecedent: good arguments would make belief rational, and there are none. - The published ancestor is W. K. Clifford's "The Ethics of Belief" (1877), which laid down that "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." - Alvin Plantinga calls the demand that belief in God earn its keep by evidence the evidentialist objection, and in "Reason and Belief in God" (1983) he takes Clifford and Antony Flew as its standard bearers. Flew's version is the presumption of atheism: the burden of proof sits with the believer. (2) Where the fallacy sits. - The conditional says arguments would be enough for rational belief. It never says they are required. Deny the antecedent and nothing follows about the consequent: the street may be wet from the sprinkler, and belief may be rational from some source other than argument. - That other source has a name. Plantinga argues that belief in God can be properly basic: held rationally without being inferred from anything, the way you believe you had breakfast on the strength of memory rather than proof. If belief works that way, "no good arguments" leaves it standing. - Try the mirror. "If there were good arguments against God, unbelief would be rational. There are none. So unbelief is irrational." The coworker will feel at once that his atheism does not hang on that conditional. (3) The sound version. - The evidentialist challenge survives as a challenge rather than a deduction. Belief ought to answer to evidence, and a believer who has never asked whether hers does is careless in the way Clifford warned against. - Plantinga grants the sharpest part himself. A properly basic belief can still be defeated, knocked out by a good argument against it, and the problem of evil is a serious candidate. - The valid form of his argument is modus tollens: "If belief in God were rational, it would survive the best objections. It does not. So it is not rational." The fight then moves to that second premise, where it belongs. (4) How to answer it. - "Your first sentence says arguments would be enough. Are they the only way a belief can be rational? You hold plenty you never argued for. Let's ask whether belief in God is one of those, and then take up the objections you think it can't survive." See also: Philosophical Theology: Meta-Apologetics: Reformed Philosophical Theology: Meta-Apologetics: Evidentialist Philosophy / Epistemology: Warrant

(●) A Christian says: "If the Bible is God's word, it will be historically accurate. It is accurate. So it is God's word." + A popular apologist says it from a stage and the room nods, because every clause is one the room believes. The trouble sits where it sat with the neighbour's wet street, at the word "so". (1) What is being argued. - The claim is that the Bible is God's word. The support is a conditional and the affirmation of its consequent: inspiration would make the Bible accurate, and the Bible is accurate. - The evidence for that accuracy is real: Luke's titles for local officials that inscriptions keep confirming, the Pool of Bethesda dug up with the five colonnades John describes, the ossuary (bone box) of Caiaphas. The case for the Gospels as history stands on its own. (2) Where the fallacy sits. - Inspiration guarantees accuracy. Accuracy does not guarantee inspiration. Thucydides is accurate, and nobody thinks God dictated the Peloponnesian War. A book can be accurate because its authors were careful and close to the events, which is what the apologist has just shown about the Gospels. That is the sprinkler. - The same slip lives in a favourite resurrection line: "If Jesus rose, the disciples would be transformed. They were. So he rose." As a deduction it affirms the consequent, because grief and shared conviction can transform people too. - As confirmation it is fine, and that is how the minimal facts argument uses it. Habermas and Licona build from the handful of facts nearly every scholar grants, and present the case as an inference to the best explanation, the detective's kind of reasoning. (3) The sound version. - Accuracy is confirmation. A book right wherever it can be checked is likelier to be right where it cannot. And accuracy is more to be expected of a book that is God's word than of one that is not, so the checkable facts raise the probability of inspiration without settling it. The honest sentence is "the accuracy is what you would expect if it is God's word", and then stop. - The argument the apologist should have made runs through Jesus. The Gospels are reliable history, checked the ordinary way. Reliable history records that Jesus rose, which vindicates his authority. And Jesus treated the Scriptures as God's word, answering each temptation in the wilderness with "It is written" (Matthew 4:4). Every step runs forward, from "if" to "then", by modus ponens. (4) How to answer it, when a fellow Christian says it. - "Accuracy is a good sign, and I'd keep it. But an accurate book isn't the same as an inspired one, and a sharp skeptic will say so. Let's argue it the long way, through Jesus. It's stronger, and it's honest." See also: Christian Evidences: The Gospels: Real History CE / Resurrection: Minimal Facts Argument (Habermas) Philosophical Theology: Sola Scriptura

(●) A charge that misses: "Design arguments are just affirming the consequent. If God, then order. There is order. Therefore God." + It turns up in lecture halls and in comment threads, and answering it means telling two kinds of argument for God apart. (1) What the charge claims. - Design arguments, the charge says, are the wet street in a robe. A finely tuned universe has other possible causes, so "therefore God" does not follow. (2) Why the charge misses. - It would land if the argument claimed certainty, and the serious versions do not. The fine-tuning argument is abductive, an inference to the best explanation: of the live explanations, the one that makes the evidence least surprising wins. Peter Lipton's Inference to the Best Explanation (2004) sets out the form's standards, and no logic text files it among the fallacies. - Robin Collins's 2009 essay, the standard statement of the fine-tuning argument, never says "therefore God". A life-permitting universe is far more expected on theism than on a single godless universe, so fine-tuning confirms theism over that rival. Collins calls this the likelihood principle: evidence counts in favour of whichever hypothesis makes it more expected. That is the wet street handled correctly: rain confirmed, not proved. - One version is not abductive at all. Run as "necessity, chance, or design; not necessity, not chance; therefore design", it is a disjunctive syllogism, the valid form that rules out every option but one, and all its weight lands on the premise doing the ruling out. - Hypothesis testing in science has this shape: if the theory is true, the needle will move, and the needle moved. Karl Popper built a philosophy of science on how unequal the two outcomes are. A failed prediction refutes by modus tollens; a successful one only corroborates, his word for passing the tests so far, not for proof. - So the test to carry away is whether an argument claims certainty from the consequent or only support. "Therefore" and "proves" are the tell; "best explains" and "more expected on" are the honest words. (3) What the charge would need to be true. - It would need an argument that says "therefore" and means a proof. Some popular apologetics does, and there the charge lands: "look at the order, therefore God" is exactly the fallacy. - It also lands, in part, on lazy confirmation. A wet street barely confirms rain where the sprinklers run every morning, and the multiverse is the sprinkler a design argument must handle rather than wave away. Support from a consequent is only as strong as the rivals are weak. (4) How to answer it. - "You're right that 'there is order, therefore God' would be a fallacy, and I won't argue it that way. The claim is that fine-tuning is far more expected if there is a designer than if there isn't. Which rival explanation do you think does better?" See also: Natural Theology: Cosmic Fine-Tuning Natural Theology: Paley (The Watchmaker) Philosophy / Logic: Deductive Arguments Philosophy / Logic: Inductive Arguments