Ethical Realism

September 4, 2012

More Philosophy Definitions Part 2

Filed under: philosophy — JW Gray @ 11:05 am
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I have continued working on the Comprehensible Philosophy Dictionary (a work in progress). There will be many corrections coming soon in addition to many new definitions. You can let me know if any of these definitions can be improved or if I am still missing an important philosophy term. I decided to define a lot more terms used in logic, and many more can still be added. The new definitions I am planning on adding are the following:

A-type proposition – A proposition with the form “all a are b.” For example, “all cats are animals.”

addition – A rule of inference that states that we can use “a” as a premise to validly conclude “a or b.” For example, “Dogs are mammals. Therefore, Dogs are mammals or lizards.”

affirmative categorical proposition – A categorical proposition that has the form “all a are b” or “some a are b.” For example, “all dogs are mammals.”

affirmative premise – A categorical proposition used as a premise that has form “all a are b” or “some a are b.” For example, “some mammals are dogs.”

affirming the disjunct – A fallacy committed by an argument that requires us to mistakenly assume two propositions to be mutually exclusive and reject one proposition just because the other is true. The argument form of an argument that commits this fallacy is “Either a or b. a. Therefore, not-b.” For example, consider the following argument—“Either Dogs are mammals or animals. Dogs are mammals. Therefore, dogs are not animals.”

agent causation – A type of causation that’s neither determined nor random produced from people. Agent causation occurs from an action caused by a person that’s not caused by other events or states of affairs. For example, it’s not caused by the reasoning of the agent. See “prime mover” and “libertarian free will” for more information.

alternate possibilities – Events that could happen in the future or could have happened in the past instead of what actually happened. Alternate possibilities are often mentioned to refer to the ability to do otherwise. For example, some people think free will and moral responsibility require alternate possibilities. Let’s assume that’s the case. If Elizabeth is morally responsible for killing George, then she had an alternate possibility of not killing George. If she was forced to kill George, then she isn’t morally responsible for doing it. Alternate possibilities are often thought to be incompatible with determinism.

appeal to probability – A fallacy committed by an argument that concludes that something will happen just because it might happen. For example, “It’s possible to make a profit by gambling. Therefore, I will eventually make a profit if I keep playing the slot machines.”

appeal to consequences – A type of fallacy committed by arguments that conclude that something is true or false based on the effects the belief will have. For example, “We know it’s true that every poor person can become rich because poor people who believe they can become rich are more likely to become rich.”

appeal to force – A fallacious form of persuasion that is committed when coercion is used to get people to pretend to agree with a conclusion, or in order to suppress opposing viewpoints. The appeal to force can be subtly used in an academic setting when certain views are taboo and could harm a person’s future employment opportunities. However, sometimes people also fear being punished for expressing their “heretical views.” For example, John Adams passed the Sedition Act, which imposed fines and jail penalties to anyone who spoke out against the government. Additionally, there was a time when various heresies (taboo religious beliefs) were punishable by death.

Aristotelian ethics – An ethical system primarily concerned with virtue. Aristotle believes that (a) people have a proper function as political rational animals to help each other and use their ability to reason; (b) happiness is the greatest good worth achieving (c) virtues are generally between two extremes; and (d) virtuous people have character traits that cause them to enjoy doing what’s virtuous and do what’s good thoughtlessly. For example, courage is virtuous because it is neither cowardly nor foolhardy, and courageous people will be willing to risk their life whenever they should do so without a second thought.

Argument from fallacy – See “argumentum ad logicam.”

argument indicator – A term used to help people identify that an argument is being presented. Argument indicators are premise indicators or conclusion indicators. For example, ‘because’ is an argument indicator used to state a premise. See “argument” for more information.

argumentum ad baculum – Latin for “argument from the stick.” See “appeal to force.”

argumentum ad consequentiam – See “appeal to consequences.”

argumentum ad logicam– A type of fallacy committed by an argument that claims that a conclusion of an argument is false or unjustified just because the argument given in support of the conclusion is fallacious. A conclusion can be true and justified, even if people give fallacious arguments for it. For example, Tom could argue that “the Earth exists because Tina is evil.” This argument is clearly fallacious, but the conclusion (that the Earth exists) is both true and justified.

association – A rule of replacement that takes two forms: (a) “a and/or (b and/or c)” means the same thing as “(a and/or b) and/or c.” (b) “a and (b and c)” means the same thing as “(a and b) and c.” (“a,” “b,” and “c” stand for any three propositions.) The parentheses are used to group certain statements together. For example, “dogs are mammals, or they’re fish or reptiles” means the same thing as “dogs are mammals or fish, or they’re reptiles.” The rule of association says that we can replace either of these statements of our argument with the other precisely because they mean the same thing.

association fallacy – A type of fallacy committed by an argument with an unwarranted assumption that two things share a negative quality just because of some irrelevant association. For example, we could argue that eating food is immoral just because Stalin ate food. Also see the “halo effect” and “ad hominem” for more information.

bad company fallacy – See “association fallacy.”

bad reasons fallacy – See “argumentum ad logicam.”

base rate fallacy – A fallacy committed by an argument that makes a statistical error based on information about a state of affairs. For example, we might assume that a test used to detect a disease that’s 99% accurate will correctly detect that more people have a disease than it will falsely claim have the disease. However, if only 0.1% of the population has the disease, then it will falsely detect around ten times as many people as having the disease than actually have it. See “false positive” for more information.

base rate information – Information about a state of affairs that is used for diagnosis or statistical analysis. For example, we might find out that 70% of all people with a cough and runny nose have a cold. A doctor is likely to suspect a patient with a cough and runny nose has a cold in consideration of how common colds are. “Base rate information” can be contrasted with “generic information” concerning the frequency of a state of affairs, such as how common a certain disease is.

biased sample – (1) A sample that is not representative of the group it is meant to represent for the purposes of a study. For example, a poll taken in an area known to mainly vote for republican politicians that proves that the republican presidential candidate is popular with the population at large. It might be the case that the republican candidate is not popular when all other voters are accounted for, and the sample is so biased that we can’t use it to have any idea about whether or not the republican candidate is truly popular with the population at large. Also see “selective evidence” and “hasty generalization” for more information. (2) A fallacy committed by an argument based on a biased sample. For example, to conclude that a republican presidential candidate is popular with the population at large based on a poll taken in a pro-republican area.

bifurcation fallacy – See “false dilemma.”

black or white fallacy – See “false dilemma.”

booby trap – (1) A logical booby trap is a peculiarity of language that makes it likely for people to become confused or to jump to the wrong conclusion. For example, an ambiguous word or statement could make it likely for people to equivocate words in a fallacious way. Some people think all forms of debate are attempts at manipulative persuasion, but there are rational and respectful forms of debate. See “equivocation” for more information. (2) In ordinary language, a booby trap is a hidden mechanism used to cause harm once it is triggered by a certain action or movement. For example, Indiana Jones lifted an artifact from a platform that caused the room to collapse.

borderline case – A state of affairs that can be properly described by a vague term, but it is difficult to say how the vague term can be properly applied. For example, it might not be clear whether or not it’s unhealthy to eat a small bag of potato chips is unhealthy. Even so, we know that eating one potato chip is not unhealthy, and eating a thousand potato chips is unhealthy. See “vague” for more information.

character ethics – See “virtue ethics.”

commutation – A rule of replacement that states that “a and b” and “b and a” both mean the same thing. (“a” and “b” stand for any two propositions.) For example, we know that “all dogs are animals and all cats are animals” means the same thing as “all cats are animals and all dogs are animals.” If we use one of these statements in an argument, then we can replace it with the other statement.

commutation of conditionals – A fallacy committed by arguments that have the logical form “if a, then b; therefore if b, then a.” (“a” and “b” stand for any two propositions.) For example, “If all snakes are reptiles, then all snakes are animals. Therefore, if all snakes are animals, then all snakes are reptiles.”

commutative – To be able to switch symbols without a loss of meaning. “a and b” has the same meaning as “b and a.” For example, “dogs are animals and lizards are reptiles” has the same meaning as “lizards are reptiles and dogs are animals.”

compound proposition – A proposition that can be broken into two or more propositions. For example, “Socrates is a man and he is mortal” can be broken into the following two sentences: (a) Socrates is a man. (b) Socrates is mortal. “Compound propositions” can be contrasted to “non-compound propositions.”

compound sentence – See “compound proposition.”

composition – (1) In logic, ‘composition’ refers to the “fallacy of composition.” (2) When a creditor agrees to accept a partial payment for a debt. (3) The arrangement of elements found in a work of art. (4) Producing a literary work, such as a text or speech.

conclusion indicator – A term used to help people identify that an conclusion is being stated. For example, “therefore” or “thus.” See “conclusion” for more information.

conditional proof – A strategy used in natural deduction used to prove an argument form is logically valid that has an if/then proposition as a conclusion. We know the argument form is valid if we can assume the premises are true and the first part of the conclusion is true in order to deduce the second part of the conclusion. For example, consider the argument “If A, then B. If B, then C. Therefore, if A, then C.” We can use the following conditional proof to know this argument is valid:

  1. We can assume the first part of the conclusion (“A”) and prove the second part of the conclusion (“C”).
  2. We know “if A, then B” is true and “A” is true, so we know “B” is true. (See “modus ponens.”)
  3. We know “if B, then C” is true and “B” is true, so we know “C” is true. (See “modus ponens.”)
  4. We have now deduced that the second part of the conclusion is true, so the argument form is logically valid.

conjunction – A rule of inference that states that we can use “a” and “b” as premises to validly conclude “a and b.” (“a” and “b” stand for any two propositions.) For example, “Socrates is a man, and Socrates is mortal. Therefore, Socrates is a man and he is mortal.”

constructive dilemma – A rule of inference that states that we can use the premises “a and/or b,” “if a, then c,” and “if b, then d” to validly conclude “c and/or d.” (“a”, “b,” and “c” stand for any three propositions.) For example, “Either all dogs are mammals and/or all dogs are lizards. If all dogs are mammals, then all dogs are animals. If all dogs are lizards, then all dogs are reptiles. Therefore, all dogs are animals and/or reptiles.”

contradiction – In categorical logic, contradiction is a process of negating a categorical statement and expressing it as a different categorical form. For example, “all men are mortal” can be contradicted as “some men are not mortal.”

contradictory – In categorical logic, a contradictory is the negation of a categorical statement expressed in a different categorical form. For example, “no men are immortal” is the contradictory of “some men are immortal.”

contraposition – (1) To switch the terms of a categorical statement and negate them both. There are two valid types of categorical contraposition: (a) “All a are b” means the same thing as “all non-b are non-a.” (b) “Some a are not b” means the same thing as “some non-b are not non-a.” For example, the following argument is valid—“Some snakes are not mammals. Therefore, some non-mammals are not non-snakes.” (2) To infer a contrapositive from a categorical proposition. See “contrapositive” for more information. (3) In modern logic, it is also known as “transposition.”

contrapositive – A categorical proposition is the contrapositive of another categorical proposition when the terms are negated and switched. For example, the contrapositive of “all mammals are animals” is “All non-animals are non-mammals.” It is valid to infer the contrapositive of two different types of categorical propositions because they both mean the same thing: (a) “All a are b” means the same thing as “all non-b are non-a.” (b) “Some a are not b” means the same thing as “some non-b are not non-a.” For example, “some people are not doctors” means the same thing as “some non-doctors are not non-people.”

contrary propositions – Propositions that are mutually exclusive. For example, “Socrates is a man” and “Socrates is a dog” are contrary propositions.

converse – A categorical proposition or if/then statement with the two parts switched. The converse of “all a are b” is “all b are a.” (“a” and “b” are any two terms.) The converse of “if c, then d” is “if d, then c.” (“c” and “d” are any two propositions.) For example, the converse of “if all fish are animals, then all fish are organisms” is “if all fish are organisms, then all fish are animals.” It is valid to infer the converse of any categorical statement with the form “no a are b” or “some a are b.” See “conversion” for more information.

conversion – To switch the terms of a categorical statement. There are two valid types of conversion: (a) “No a are b” means the same thing as “no b are a.” (b) “Some a are b” means the same thing as “some b are a.” For example, the following is a valid argument—“No birds are dogs. Therefore, no dogs are birds.”

definiendum – The term that is defined by a definition. Consider the definition of “argument” as “one or more premises that supports a conclusion.” In this case the definiendum is “argument.” “Definiendum” can be contrasted with “definiens.”

definiens – The definition of a term. Consider the definition of “premise” as “a proposition used to give us reason to believe a conclusion.” In this case the definiens is “a proposition used to give us reason to believe a conclusion.” “Definiens” can be contrasted to “definiendum.”

DeMorgan’s laws – A rule of replacement that takes two forms: (a) “It’s not the case that both a-and-b” means the same thing as “not-a and/or not-b.” (b) “It’s not the case that a and/or b” means the same thing as “not-a and not-b.” (“a” and “b” stand for any two propositions.) For example, “it’s not the case that dogs are either cats or lizards” means the same thing as “no dogs are cats, and no dogs are lizards.”

denying a conjunct – A logical fallacy committed by arguments with the following form—“It’s not the case that both a-and-b. Not-a. Therefore, b.” This argument form is logically invalid. For example, “Socrates isn’t both a dog and a person. Socrates isn’t a dog. Therefore, Socrates isn’t a person.”

distribution – A rule of replacement that takes two forms: (a) “a and (b and/or c)” means the same thing as “(a and/or b) and (a and/or c).” (b) “a and/or (b and c)” means the same thing as “(a and b) and/or (a and c).” (“a”, “b,” and “c” stand for any three propositions.) For example, “all lizards are reptiles, and all lizards are either animals or living organisms” means the same thing as “either all lizards are reptiles or animals, and either all lizards are reptiles or living organisms.”

division – (1) See “fallacy of division.” (2) A mathematical operation based on a ratio or fraction. For example “4 ÷ 2 = 2.” (3) To split objects into smaller parts.

doctrine of the maturity of chances – (1) The false assumption that the past results of a random game will influence the future results of the game. For example, a person who loses at black jack five times in a row might think that she is more likely to win if she plays another game. (2) See the “gambler’s fallacy.”

double negation – (1) A rule of replacement that states that “a” and “not-not-a” both mean the same thing.(“a” stands for any proposition.) For example, “Socrates is a man” means the same thing as “it’s not the case that Socrates isn’t a man.” (2) A “double negative.” When it’s said that something isn’t the case twice. For example, “it’s not the case that Mike didn’t turn the TV on means the same thing as “Mike turned the TV on.”

E-type proposition – A proposition with the form “no a are are b.” For example, “no cats are reptiles.”

enthymeme – (1) A categorical syllogism with an unstated premise. For example, “all acts of abortion are immoral because all fetuses are persons.” In this case the missing premise could be “all acts of killing people are immoral.” (2) Any argument with an unstated premise or conclusion. For example, “all fetuses are people and all acts of killing people are immoral” has the unstated conclusion “all acts of abortion are immoral.”

epistemic modality – The distinction between what is believed and what is known. Moreover, epistemic modality can involve the degree of confidence a belief warrants. For example, we know that more than three people exist and we are highly confident that this belief is true. We communicate epistemic modality through terms and phrases, such as “probably true,” “rational to believe,” “certain that,” “doubt that,” etc.

epistemic randomness – When something happens that is not reliably predictable. For example, when we roll a six-sided die, we don’t know what number will come up. We say that dice are good for attaining random results for this reason.

equivalence – A rule of replacement that takes two forms: (a) “a if and only if b” means the same thing as “if a, then b; and if b, then a.” (b) “a if and only if b” means the same thing as “a and b” and/or “not-a and not-b.” (“a” and “b” stand for any two propositions.) For example, “Socrates is a rational animal if and only if Socrates is a person” means the same thing as “Socrates is a rational animal and a person, or Socrates is not a rational animal and not a person.”

etymological fallacy – A fallacy committed by an argument when a word is equivocated with another word it’s historically derived from. For example, “logic” is derived from “logos,” which literally meant “word.” It would be fallacious to argue that “logic” is the study of words just because it is historically based on “logos.”

exclusive premises – A fallacy committed by categorical syllogisms that have two negative premises. There are no logically valid categorical syllogisms with two negative premises. For example, “No dogs are fish. Some fish are not lizards. Therefore, no dogs are lizards.”

existential quantifier – A term or symbol used to say that something exists. For example, “some” or “not all” are existential quantifiers in ordinary language. “Some horses are mammals” means that at least one horse exists and “not all horses are male” means that there is at least one horse that is not a male. The existential quantifier in symbolic logic is “∃.” See “quantifier” for more information.

exportation – A rule of replacement that states that “if a and/or b, then c” means the same thing as “if a, then it’s the case that if b, then c.” (“a”, “b,” and “c” stand for any three propositions.) For example, “if Socrates is either a mammal or an animal, then Socrates is a living organism” means the same thing as “if Socrates is a mammal, then it’s the case that if Socrates is an animal, then Socrates is a living organism.”

false conversion – See “illicit conversion.”

fallacy fallacy – (1) See “argumentum ad logicam.” (2) A type of fallacy committed by an argument that falsely claims another argument commits a certain fallacy. For example, Lisa could argue that “Sam is an idiot for thinking that only two people exist. We have met many more people than that.” Sam could then respond, “You have committed the ad hominem fallacy. My belief should not be dismissed, even if I am an idiot.” In this case Lisa’s argument does not require us to believe that Sam is an idiot. It is an insult, but it can be separated from her actual argument.

fallacy of composition – A fallacy committed by an argument that falsely assumes that a whole will have the same property as a part. For example, “molecules are invisible to the naked eye. We are made of molecules. Therefore, we are invisible to the naked eye.” The “fallacy of composition” is often contrasted with the “fallacy of division.”

fallacy of the consequent – See “affirming the consequent.”

fallacy of division – A fallacy committed by an argument that falsely assumes that a property that a whole has will also be a property of the parts. For example, “We can see humans with the naked eye. Humans are made of molecules. Therefore, we can see molecules with the naked eye.”

false positive – A positive result that gives misleading information. For example, to test positive for having a disease when you don’t have a disease. Let’s assume that 1 of 1000 people have Disease A. If a test is used to detect Disease A and it’s 99% accurate, then it will probably detect that the one person has the disease, but it will also probably have around ten false-positive results—it will probably state that ten people have Disease A that don’t actually have it.

false precision – See “overprecision.”

formal language – Languages that are devoid of semantics, such as the languages used for formal logic. See “formal logic” and “formal system” for more information. “Formal language” can be contrasted with “natural language.”

gambler’s fallacy – Fallacious reasoning based on the assumption that the past results of a random game will influence the future results of the game. For example, if you toss a coin and get heads twice in a row and conclude that you are more likely to get tails if you keep playing. Gamblers who lose a lot of money often have this assumption when they make the mistake in thinking that they will more likely start winning if they keep playing the same game.

golden mean – Aristotle’s concept of virtues as being somewhere between two extremes. For example, moderation is the character trait of wanting the right amount of each thing, and it’s between the extremes of gluttony and an extreme lack of concern for attaining pleasure.

golden rule – A moral rule that states that we ought to treat other people how we want to be treated. For example, we generally shouldn’t punch other people just because they make us angry insofar as we wouldn’t want them to do it either.

grandfather’s axe – A thought experiment of axe with all the parts that have been replaced. The question is whether or not it’s the same axe.

guilt by association – See “association fallacy.”

hidden assumption – An assumption of an argument that is not explicitly stated, but is implied or required for the argument to be rationally persuasive. For example, consider the argument “the death penalty is immoral because it kills people.” This argument requires a hidden assumption—perhaps that “it’s always immoral to kill people.”

hot hand fallacy – An argument commits this fallacy when it requires the false assumption that good or bad luck will last a while. For example, a gambler who wins several games of poker in a row is likely to think she’s on a “winning streak” and is more likely than usual to keep winning as a result.

hypothetical syllogism – A rule of inference that states that we can use “if a, then b” and “if b, then c” to validly conclude “if a, then c.” (“a” and “b” stand for any two propositions.) For example, “if all dogs are mammals, then all dogs are animals. If all dogs are animals, then all dogs are living organisms. Therefore, if all dogs are mammals, then all dogs are living organisms.”

I-type proposition – A proposition with the form “some a are b.” For example, “some cats are female.”

illicit affirmative – The fallacy committed by categorical syllogisms that have positive premises and a negative conclusion. All categorical syllogisms with this form are logically invalid. For example, “Some dogs are mammals. All mammals are animals. Therefore, some dogs are not animals.”

illicit contraposition – In categorical logic, illicit contraposition refers to a fallacy committed by an invalid argument that switches the terms of a categorical statement and negates them both. There are two types of illicit contraposition: (a) No a are b. Therefore, no non-b are non-a. (b) Some a are b. Therefore, some non-b are non-a. For example, “Some horses are non-unicorns. Therefore, some unicorns are non-horses.”

illicit conversion – Invalid forms of conversion—invalid ways to switch the terms of a categorical statement. There are two types of illicit conversion: (a) All a are b. Therefore, all b are a. (b) Some a are not b. Therefore, some b are not a. For example, the following is an invalid argument—“Some mammals are not dogs. Therefore, some dogs are not mammals.”

illicit process – A fallacy committed by categorical syllogisms that have a term distributed in the conclusion without being distributed in a premise. All categorical syllogisms that commit this fallacy are logically invalid. For example, “All lizards are reptiles. Some reptiles are lizards. Therefore, all reptiles are lizards.” See “distribution,” “illicit major” and “illicit minor” for more information.

illicit negative – The fallacy committed by categorical syllogisms that have one or two negative premises and a positive conclusion. All categorical syllogisms with that form are logically invalid. For example, “No fish are mammals. Some mammals are dogs. Therefore, some fish are dogs.”

illicit transposition – See “improper transposition.”

implication – A rule of replacement that states that “if a, then b” and “not-a and/or b” both mean the same thing. (“a” and “b” stand for any two propositions.) For example, “if dogs are lizards, then dogs are reptiles” means the same thing as “dogs are not lizards, and/or dogs are reptiles.”

improper transposition – A logically invalid argument with the form “If a, then b. Therefore, if not-a, then not-b.” For example, “If all lizards are mammals, then all lizards are animals. Therefore, if not all lizards are mammals, then not all lizards are animals.” See “transposition” for more information.

interchange – In categorical logic, interchange is to switch the first and second term of a categorical statement. For example, the interchange of “all men are mortal things” is “all mortal things are men.” See “conversion” for more information.

indirect proof – A strategy used in natural deduction used to prove an argument form is logically valid consisting of assuming the premises of an argument are true, but the conclusion is false. If this assumption leads to a contradiction, then the argument form has been proven to be logically valid. For example, consider the argument form “If A, then B. A. Therefore, B.” (“A,” “B,” and “C” are specific propositions.) An indirect proof of this argument is the following:

  1. Assume the premises are true and the conclusion is false (not-B is true).
  2. We know that “if A, then B” is true, and B is false, so A must be false. (See “modus tollens.”)
  3. Now we know that A is true and false.
  4. But that’s a contradiction, so the original argument form is logically valid.

intentional objects – The object that our thoughts or experiences refer to. For example, seeing another person involves an intentional object outside of our mind—another person. Some intentional objects are thought to be abstract entities, such as numbers or logical concepts.

inversion – To infer an if/then proposition from another if/then proposition. See “inverse” for more information.

inverse – An if/then proposition that is inferred from another if/then proposition. It is valid to conclude that one if/then proposition can be inferred from another whenever they both mean the same thing. It is valid to conclude from any proposition with the form “if a, then b” that “if not-b, then not-a.” For example, we can infer that “if it is false that all dogs are animals, then it is false that all dogs are mammals” from the fact that “if all dogs are mammals, then all dogs are animals.” See “transposition” for more information.

jargon – Technical terminology as used by specialists or experts. Jargon is not defined in terms of common usage—how people generally use a term in everyday life. Instead, they are defined in ways that are convenient for specialists. For example, logicians, philosophers, and other specialists define “valid argument” in terms of an argument form that can’t possibly have true premises and a false conclusion at the same time, but people use the term “valid argument” as a synonym for “good argument.” See “stipulative definition” for more information. “Jargon” can be contrasted with “ordinary language.”

logical equivalence – Two sentences that mean the same thing. For example, “no dogs are lizards” is logically equivalent to “no lizards are dogs.”

missing conclusion – A conclusion of an argument that is not explicitly stated, but is implied. For example, consider the argument “the death penalty kills people and it’s immoral to kill people.” This argument implies the unstated conclusion—that the death penalty is immoral.

monadic predicate – A predicate that only applies to one thing. For example, “x is mortal” could be stated as “Mx.” (“M” stands for “is mortal,” and “x” stands for anything.)

monadic predicate logic – A system of predicate logic that can express monadic predicates, but can’t express polyadic predicates. See “monadic predicate” and “predicate logic” for more information.

Monte Carlo fallacy – See “gambler’s fallacy.”

natural language – Language as it is spoken. Natural language includes both specialized language used by experts and ordinary language. “Natural language” can be contrasted with “formal systems.”

natural deduction – A method used to prove deductive argument forms to be valid. Natural deduction uses rules of inference and rules of equivalence. For example, consider the argument form “A and (B and C). Therefore, A.” (“A,” “B,” and “C” are three specific propositions.) The rule of implication known as “simplification” says we can take a premise with the form “a and b” to conclude “a.” (“a” and “b” stand for any two propositions.) We can use this rule to take “A and (B and C)” to conclude “A.” Therefore, that argument is logically valid.

negative categorical proposition – A categorical proposition that has the form “not all a are b” or “some a are not b.” For example, “some dogs are not mammals.”

negative conclusion – A categorical proposition used as a conclusion with the form “no a are b” or “some a are not b.” For example, “no dogs are reptiles.”

negative premise – A categorical proposition used as a premise with the form “no a are b” or “some a are not b.” For example, “some animals are not mammals.”

non-compound proposition – A sentence that can’t be broken into two or more propositions. For example, “Socrates is a man.” “Non-compound propositions” can be contrasted to “compound propositions.”

non-compound sentence – See “non-compound proposition.”

O-type proposition – A proposition with the form “some a are not-b.” For example, “some cats are not female.”

obverse – A categorical proposition is the obverse of another categorical proposition when it has a certain different quantification and a negated second term. There are four different forms of obversion: (a) The obverse of “all a are b” is “no a are non-b.” (b) The obverse of “no a are b” is “all a are non-b.” (c) The obverse of “some a are b” is “some a are not non-b.” (d) The obverse of “some a are not b” is “some a are non-b.” It is always valid to infer the obverse of a categorical propositions because the two propositions mean the same thing.

obversion – To infer the obverse of a categorical proposition. See “obverse” for more information.

ontological randomness – When something happens that could not possibly be reliably predicted because it could have happened otherwise. If anything ontologically random happens, then determinism is false—there are events that occur that are not sufficiently caused to happen due to the laws of nature and state of affairs. Ontological randomness can be contrasted with “determined” events and the acts of “free will.” It is generally thought that acts of free will are not random (and perhaps they’re not determined either). Imagine that you time travel to the past without changing anything, and all people make the same decisions, but a different person won the lottery as a result. That would indicate that there are elements of randomness that effects reality.

ordinary language – Language as it is used by people in everyday life. Words in ordinary language are generally defined in terms of “common usage” (i.e. how people tend to use the word). “Ordinary language” can be contrasted with “formal language” and “jargon.”

overprecision – A fallacy committed by an argument that requires precise information for the premises in order to reach the conclusion, and it uses misleadingly precise premises in order to do so. For example, a person was told that a frozen mammoth was five thousand years old five years ago, so she might insist that the frozen mammoth is now “5,005 years old.”

polyadic predicates – A predicate that applies to two or more things. For example, “John is taller than Jen” could be expressed as “Tab.” (In this case “T” stands for “is taller,” “a” stands for “John” and “b” stands for “Jen.”

positive categorical proposition – A categorical proposition with the form “all a are b” or “some a are b.” For example, “some mortals are men.”

positive conclusion – A categorical proposition used as a conclusion with the form “all a are b” or “some a are b.” For example, “some animals are mammals.”

positive premise – A categorical proposition used as a premise with the form “all a are b” or “some a are b.” For example, “all mammals are animals.”

predicate term – See “major term.”

premise indicator – A term used to help people identify that an premise is being stated. For example, “because” or “considering that.” See “premise” for more information.

proof by absurdity – See “indirect proof.”

proposition type – Different logical forms categorical propositions can take. There are four proposition types: A, I, O, and E. Each of these refers to a different logical form: (A) all a are b, (I) some a are b, (O) some a are not b, and (E) no a are b.

propositional connectives – See “logical connectives.”

propositional variables – Symbols used in propositional logic to represent propositions. Capital letters tend to stand for specific propositions. For example, “A” could stand for “Socrates is mortal.” Lower-case letters or Greek letters tend to stand for any possible proposition. For example, “a” could stand for any possible proposition.

public reason – John Rawls’s concept of reason as it should exist to justify laws and public policy. Ideally, everyone should be able to rationally accept the laws and policies no matter what their worldview is, so laws and public policies should be justified in secular ways that don’t require acceptance of controversial beliefs. Public reason does not require controversial religious beliefs or a comprehensive worldview precisely so it can help assure us that every reasonable person would find the laws and public policies to be justified—even if they have differing worldviews.

quantificational logic – See “predicate logic.”

randomness – See “epistemic randomness” or “ontological randomness.”

reasonable pluralism – Disagreement among people who have reasonable yet incompatible beliefs. A plausible example is of a person who believes that intelligent life exists on another planet and another person who doesn’t think life exists on another planet. John Rawls coined this phrase because he believed that society should fully embrace cultural diversity involving various worldviews and religious beliefs insofar as such religious beliefs and worldviews can be reasonably believed—the evidence we have for many of our beliefs is inconclusive, but it can be reasonable to have the beliefs until they are falsified (or some other standards of reason are violated).

reduction – To conclude or speculate that the parts of something are identical to the whole. For example, water is H2O, and diamonds are carbon molecules with a certain configuration.

relational predicate logic – A system of predicate logic that can express both monadic and polyadic predicates.

rules of replacement – Rules that tell us when two propositions mean the same thing. We can replace a proposition in an argument with any equivalent proposition. For example, we know that “all dogs are animals and all cats are animals” means the same thing as “all cats are animals and all dogs are animals” because of the rule known as commutation—“a and b” and “b and a” both mean the same thing. (“a” and “b” stand for any two propositions.)

schema – See “scheme of abbreviation.”

scheme of abbreviation – A guide used to explain what various symbols refer to for a set of symbolic logical propositions, which can be used to translate a proposition of symbolic logic into natural language. For example, consider the logical proposition, “A ∧ B.” A scheme of abbreviation for this proposition is “A: The President of the USA is a man; B: The President of the USA is a woman.” “∧” is used to mean “and/or.” We can then use this scheme of abbreviation to state the following proposition in natural language—“The President of the USA is a man or a woman.”

set – (a) A group of things that all share some characteristic. For example, the set of cats includes every single cat that exists. (b) In Egyptian mythology, Set is the god of deserts, storms, and foreigners. Set has the head of an animal similar to a jackal, and he is known as “Sēth” in Ancient Greek.

Ship of Theseus – A ship used as part of a thought experiment. Imagine a ship is slowly restored and all the parts are eventually replaced. This encourages us to ask the question—Is it the same ship?

simplification – A rule of inference that states that we can use “a and b” as premises to validly conclude “a.” (“a” and “b” stand for any two propositions.) For example, “Socrates is a man and Socrates is mortal; therefore, Socrates is a man.”

social construction – The ability of collective attitudes and actions to create something. For example, our collective attitudes and actions create money, language, and the Presidency of the USA. These things would stop existing if we no longer believed in them.

social reality – Reality that exists because of the collective attitudes and actions of many people. For example, money, language, and the Presidency of the USA only exist because of the attitudes and actions of people. These things would stop existing if our attitudes and actions were changed in certain ways. See “institutional fact” for more information.

spurious accuracy – See “overprecision.”

state of affairs – A situation or state of reality. For example, the state of affairs of dropping an object while standing on the Earth will lead to a state of affairs consisting of the object falling to the ground.

subject term – See “minor term.”

symbolic logic – A formal logical system devoid of content. Symbols are used to replace content and logical connectives. For example, “if all men are mortal, then Socrates is mortal” could be written as “A → B.” In this case “A” stands for “all men are mortal, “B” stands for “Socrates is mortal” and “→” stands for “implies.” See “formal logic” and “logical connectives” for more information.

tautology – A rule of replacement that has two forms: (a) “a” and “a and a” both mean the same thing. (b) “a” and “a and/or a” both mean the same thing. (“a” stands for any propositions) For example, “Socrates is a man” means the same thing as “Socrates is either a man or a man.”

temporal modality – What makes a proposition true or false based on whether it is being applied to the past, present, or future. For example, dinosaurs existed in the past, but they do not presently exist.

transposition – A rule of replacement that states that “if a, then b” means the same thing as “if not-b, then not-a.” (“a” and “b” stand for any two propositions.) For example, “if Socrates is a dog, then Socrates is a mammal” means the same thing as “if Socrates is not a mammal, then Socrates is not a dog.”

Trigger’s Broom – A broom used in a thought experiment in which all the parts of the broom have been replaced. This encourages us to ask the question, “Is it still the same broom?”

truth preservation – The property of reasoning that can’t have true premises and false conclusions. See “valid” for more information.

universal quantifier – A term or symbol used to say something about an entire class. For example, “all” and “every” are universal quantifiers used in ordinary language. “All horses are mammals” means that if a horse exist, then it is a mammal.” This statement does not say that any horses actually exist. The universal quantifier in symbolic logic is “∀.” See “quantifier” for more information.

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