Appeal to probability

It's possible that they cause good luck; as luck would have it though, it's damn unlikely. (Source)

Cogito ergo sum
Logic and rhetoric

Key articles

* Logical fallacy
* Syllogism
* Argument

General logic

* Apex fallacy
* Argument from silence
* Scope fallacy
* Counterfactual fallacy
* Truth table
* Falacia de atribución

Bad logic

* Overgeneralization
* Slothful induction
* Gore's Law
* Escape to the future
* Scope fallacy
* Logical fallacy

v \- t \- e

An appeal to probability, also known as appeal to possibility, is the logical fallacy of assuming that something will happen simply because it is possible that it will happen.

Alternate forms include the appeal to probability, where the occurrence of an event is assumed even though no evidence is provided for the event, but instead fallacious reasoning is used in order to overstate the probability of the event.

The fallacy is an informal fallacy.

## Contents

* 1 Form
* 2 Explanation
* 3 Examples
* 3.1 Appeal to possibility
* 4 Exceptions
* 4.1 Science
* 4.2 Certain or impossible things
* 4.3 Large risks
* 5 External links
* 6 See also
* 7 References

## Form[edit]

The argument, when expressed, usually takes the form:

P: X is possible.

C: X is certain.

However, the argument relies on the form:

P1: X is possible

P2: (Unstated) Anything which is possible, is certain.

C: X is certain.

The fallaciousness of this line of logic should be apparent from the second, unstated premise (P2), which is logically inconsistent.

## Explanation[edit]

The appeal is based on a faulty premise -- that possibility is the same as certainty, or that uncertainty is the same as impossibility. This premise is not supported and logically inconsistent.

Consider a lottery with 1,000,000 players and 1 winner. If you bought one ticket, it is possible (at 0.0001%, the chance is nonzero) that you might win the lottery; however, it does not follow that you will win the lottery. Let's say the lottery pays out $5,000,000 (a tempting sum) and costs $10 (a trifle). Is it worth it? If we accept the appeal to possibility, then of course! According to the appeal to possibility, we ignore the improbability of winning and just assume that we will win. Thus we should play because we want the $5'000'000. Yet this is not borne out by the evidence. Your realistic expectations of gain are laid out in the table below:

| Probability:  | Worth:  | Value:

|
|
|

Winning the lottery:  | 0.0001%  | +$5,000,000  | 0.000001 x +$5,000,000 =  +$5
Buying a ticket:  | 100%  | -$10  | 1 x -$10 = -$10
Total:  | -$5

Buying a ticket, on average, loses you $5.

The law of large numbers supports this -- as the number of games you play diverges to infinity, you would on average win only 0.0001% of the time almost surely.

Note also that, by construction of the lottery, there will be exactly one winner. Therefore, the statement "it is very unlikely that a randomly chosen player wins the lottery" is true, while the statement "it is impossible that any player wins the lottery" is false.

## Examples[edit]

An example of the appeal is Murphy's Law -- if something can go wrong, it will. (This is more an example of unending pessimism rather than a logical argument, so it doesn't quite count).

Other examples:

* There are so many religions so one of them has to be correct.[1]

* There can be many worldviews -- and all of them wrong!

* I will never reach this goal because it is possible that I cannot reach this goal.[2]
* I'm certain to win the lottery if I just keep buying tickets.[3]

Simply, you may never win the lottery. And as noted above, it costs more money to purchase the ticket than you can expect to get back, so it's not even worth trying.
* There are so many stars in the Universe that it is certain, that not only is there intelligent life out there (see the Drake equation), but that it has visited the Earth.[2]
* There are many hackers on the internet, therefore, you will be hacked.[2]
* I’m going to play professional basketball when I grow up. I don't need to worry about my grades much since I'll be making millions after I am drafted into the NBA. I know there are only a couple hundred professional slots, and millions of aspiring young players, but since I have as much a chance as any other young player, I will succeed.[3]

### Appeal to possibility[edit]

From Logically Fallacious:[4]

> Dave: Did you know that Jesus was gay?
>  Tim: And why do you say that?
>  Dave: You have to admit, it is possible!
>  Tim: So is the fact that you are a moron.

## Exceptions[edit]

### Science[edit]

The first and major exceptions are that of science. Science bases all of its evidence on probability -- by showing that alternate hypotheses are extremely unlikely, science shows that its favored hypothesis is extremely likely. Science is exempt from the appeal to probability for exactly that reason -- science never asserts that something is certain, merely extremely likely. The difference between a "fact" (something certain) and a "scientific fact" (something extremely likely) should make this apparent.

### Certain or impossible things[edit]

The second major set of exceptions is when something truly is either certain or impossible. If something has a 100% chance (a certainty) of being true then necessarily it will happen. The opposite is true for something that has a 0% chance (an impossibility) of being true. These cases are usually only found in formal logic and mathematical proofs, where a set of axioms are assumed to be 100% true, for the purpose of argument. So, in truth, these results are "certain" or "impossible" only within the bounds of the axioms that support them.

### Large risks[edit]

The third major set of exceptions are risks which, if they ever came true, would pose such a large threat that they should be avoided at all costs (or at least, have their probability reduced as far as possible) -- even if there's only a chance that they occur.

Essentially, one must use game theory again: even a very small probability of a very bad event is sufficient to make it very important.

One example is a concussion: repeatedly ramming your head into a wall isn't certain to give you a concussion, but it's not worth the risk (the benefits don't outweigh the harms). Another is nuclear war: because it could possibly (though this is unlikely) kill everyone on the planet, it has been argued that no other goal takes higher priority than reducing the risk of nuclear warfare. Unfortunately, our politicians have not taken the same attitude to anthropogenic climate change and other environmental degradation, even though it is far more likely to cause the collapse of modern civilization than nuclear war ever was.

One counterexample is that of a small meteor strike: simply put, the real (nonzero) possibility that a small meteor will strike your house while you sleep does not warrant your concern, because [1] there is nothing you can do to stop said impact and [2] the impact of such an event would be relatively small.[3]

## External links[edit]

* Appeal to Probability, Toolkit for Thinking
* Appeal to Probability Fallacy a Day
* Appeal to probability, Dweebed
* Logical Fallacy of the Week, Appeal to Probability, Rich Kozlovich (anti-environmentalist blogger)

## See also[edit]

* Improbable things happen

## References[edit]

1. ↑ http://hubpages.com/politics/Logical-Fallacies-Most-Commonly-Used-in-Arguments
2. ↑ 2.0 2.1 2.2 http://fallacybingo.kinja.com/1st-formal-fallacy-appeal-to-probability-possibility-1653040193
3. ↑ 3.0 3.1 3.2 https://logfall.wordpress.com/appeal-to-probability/
4. ↑ https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/41/Appeal_to_Possibility

v \- t \- e

Articles about logical fallacies

Informal fallacies: |  Appeal to tradition • Appeal to novelty • Appeal to nature • Argument from morality • Argumentum ad martyrdom • Big words • Certum est quia impossibile est • Morton's fork • Friend argument • Exception that proves the rule • Extended analogy • Hindsight bias • Race card • Moralistic fallacy • Release the data • Gish Gallop • Terrorism-baiting • Uncertainty tactic • Greece-baiting • Ham Hightail • Red-baiting • Gore's Law • Nazi analogies • Mistaking the map for the territory • Red herring • Quidquid latine dictum sit, altum videtur • Presentism • Sunk cost • Two wrongs make a right • Flying carpet fallacy • My enemy's enemy • Appeal to ancient wisdom • Danth's Law • Argumentum ad lunam • Balance fallacy • Golden hammer • Loaded question • Escape to the future • Word magic • Spider-Man fallacy • Sanctioning the devil • Appeal to mystery • Informal fallacy • Common sense • Post-designation • Hyperbole • Relativist fallacy • Due diligence • Straw man • Good old days • Infinite regress • Circular reasoning • Media was wrong before • Is–ought problem • Ad iram • Just asking questions • Pink-baiting • Appeal to faith • Appeal to fear • Appeal to bias • Appeal to confidence • Appeal to consequences • Appeal to emotion • Appeal to flattery • Appeal to gravity • Appeal to hate • Argument from omniscience • Argument from silence • Argumentum ad baculum • Argumentum ad fastidium • Association fallacy • Broken window fallacy • Category mistake • Confounding factor • Counterfactual fallacy • Courtier's Reply • Damning with faint praise • Definitional fallacies • Equivocation • Fallacy of accent • Fallacy of accident • Fallacy of amphiboly • Gambler's fallacy • Imprecision fallacy • Moving the goalposts • Nirvana fallacy • Overprecision • Pathos gambit • Pragmatic fallacy • Quote mining • Argumentum ad sarcina inserta • Science doesn't know everything • Slothful induction • Spotlight fallacy • Style over substance • Toupee fallacy • Genuine but insignificant cause • Argument from incredulity • Appeal to age • Argumentum ad nauseam • Phantom distinction • Appeal to common sense • Argumentum ad hysteria • Omnipotence paradox • Argument from etymology • Appeal to trauma • Countless counterfeits fallacy •
| Ad hoc: |  No True Scotsman • Moving the goalposts • Escape hatch • Handwave • Special pleading • Slothful induction • Nirvana fallacy • God of the gaps • PIDOOMA • Ad hoc • Tone argument •
| Arguments from ignorance: |  Science doesn't know everything • Argument from incredulity • Argument from silence • Toupee fallacy • Appeal to censorship • Science was wrong before • Holmesian fallacy • Argument from omniscience • Willful ignorance • Argument from ignorance •
| Causation fallacies: |  Post hoc, ergo propter hoc • Correlation does not imply causation • Wrong direction • Counterfactual fallacy • Regression fallacy • Gambler's fallacy • Denying the antecedent • Genuine but insignificant cause •
| Circular reasoning: |  Infinite regress • Argument by assertion • Argumentum ad dictionarium • Appeal to faith • Circular reasoning • Self-refuting idea •
| Emotional appeals: |  Appeal to fear • Appeal to emotion • Appeal to confidence • Deepity • Argumentum ad baculum • Appeal to shame • Appeal to flattery • Tone argument • Appeal to money • Argumentum ad fastidium • Appeal to gravity • Appeal to consequences • Loaded language • Style over substance • Appeal to pity • Appeal to hate • Pathos gambit • Shaming • Degenerate • Abomination •
| Fallacies of ambiguity: |  Fallacy of accent • Equivocation • Fallacy of amphiboly • Quote mining • Fallacy of ambiguity • Moral equivalence • Scope fallacy • Suppressed correlative • Not as bad as • Etymology • Continuum fallacy • Wronger than wrong • Definitional fallacies • Code word • Phantom distinction •
Formal fallacies: |  Confusion of the inverse • Denying the antecedent • Non sequitur • Affirmative conclusion from a negative premise • Not even wrong • Chewbacca Defense • Affirming a disjunct • Illicit process • Four-term fallacy • Negative conclusion from affirmative premises • Fallacy fallacy • Substituting explanation for premise • Enthymeme • Syllogism • Formal fallacy • Existential assumption • Masked man fallacy • Self-refuting idea • Argument by gibberish • One single proof • Affirming the consequent • False dilemma • Conjunction fallacy •
Fallacious arguments: |  Bumblebee argument • Fatwa envy • Gotcha argument • Hoyle's fallacy • Intuition pump • Logic and Creation • Not Circular Reasoning • Peanut butter argument • Great Beethoven fallacy • Fallacy of unique founding conditions • Evil is the absence of God • Argument from first cause • How do you know? Were you there? • Argument from design • Argument from beauty • Appeal to nature • Solferino fallacy • Religious scientists • Nothing to hide • Argument from fine tuning • Creep shaming • "I used to be an atheist" • Atheism as a religion • Argumentum ad populum • Argument from morality • Anti-environmentalism • Appeal to bias • Apophasis • Argumentum ad nauseam • Appeal to censorship • Argumentum ad sarcina inserta • Blaming the victim • Bait-and-switch • Danth's Law • Chewbacca Defense • Canard • DARVO • Demonization • Escape hatch • Friend argument • Everyone is racist • Gish Gallop • Greece-baiting • Gore's Law • Ham Hightail • Just asking questions • Leading question • Loaded language • Linking to authority • Loaded question • Lying by omission • Motte and bailey • Nazi analogies • Moving the goalposts • One single proof • Pink-baiting • One-way hash argument • Pathos gambit • Quote mining • Poisoning the well • Quidquid latine dictum sit, altum videtur • Race card • Red-baiting • Red herring • Release the data • Science was wrong before • Shill gambit • Straw man • Silent Majority • Uncertainty tactic • Style over substance • Terrorism-baiting • Weasel word • What's the harm (logical fallacy) • Whataboutism • Bullshit • Logical fallacy • Banana argument • Scapegoat • How come there are still monkeys? • Anti-racist is a code word for anti-white • Ontological argument • Omnipotence paradox • Presuppositionalism • Just a joke • Countless counterfeits fallacy •
Conditional fallacies: |  Slippery slope • What's the harm (logical fallacy) • Special pleading • Conditional fallacy • On the spot fallacy • Appeal to the minority • Argumentum ad populum • Galileo gambit • Professor of nothing •
| Genetic fallacies: |  Genetic fallacy •
|  | Appeals to authority: |  Ipse dixit • Appeal to confidence • Argumentum ad populum • Argument from authority • Linking to authority • Silent Majority • Invincible authority • Appeal to celebrity • Ultracrepidarianism • Appeal to the minority • Galileo gambit • Appeal to identity • Weasel word • Professor of nothing • Euthyphro dilemma • Divine command theory •
|  | Ad hominem: |  Ad iram • Argumentum ad cellarium • Bulverism • Poisoning the well • Blaming the victim • Tu quoque • Whataboutism • Nutpicking • Jonanism • Demonization • Shill gambit • Appeal to bias • Fallacy of opposition • Association fallacy • Damning with faint praise • Pathos gambit • Appeal to identity • Argumentum ad hominem • Nazi analogies • Not an argument • Nothing to hide • Scapegoat • 地下室论证 •
| Imprecision fallacies: |  Apex fallacy • Overprecision • Cherry picking • Overgeneralization • Texas sharpshooter fallacy • False analogy • Appeal to fiction • Spotlight fallacy • Pragmatic fallacy • Selection bias • Anecdotal evidence • Category mistake • Nutpicking • Imprecision fallacy • Confounding factor • Fallacy of accident • Neyman's bias •
Valid logical methods: |  Rapoport's Rules • Negative evidence • Reductio ad absurdum •
Fallacy collections: |  SeekFind • Nizkor Project • Fallacy Files • Your Logical Fallacy Is • Logically Fallacious •