Caveat lector - This is a primer on the basic terms and concepts used in Philosophy. It is introductory but not comprehensive. It is dense and superficial and thus is not a substitute for lectures or participating in class discussions. For more details, explore associated hyperlinks and your course text or talk to your instructor.
People will say and try to get you to believe all sorts of claims. Some people make apparently credible claims while others make clearly outlandish claims. And sometimes the same person makes both sorts of claims: "I smoked it I but I did not inhale." Even if we trust that the source of a claim is sincere, we cannot easily discern whether we have sufficient reason to accept the claim. Which claims should we accept as true and which should we reject as unsupported or just plain false? How do you deal with what people tell you? Do you suspend doubt (and take what they say on faith) or do you suspend belief until you can sort through the evidence for yourself?
When one speaks or writes a coherent sentence, one makes a claim about something, perhaps themselves or others, one's circumstances, or some other aspect of the world. When anyone sincerely claims that something is the case, they are actually asserting that it is true. If the U.S. president says "Iraqistan has WMDs," then what he is claiming is that it is true that Iraqistan has WMDs. We may state this in another way: the president claims that it is false that Iraqistan has no WMDs. Sometimes we want to understand and evaluate what others claim to be the case, and when we do, philosophical thinking can help. Philosophical analysis provides us with precise concepts, logical tools and credible methods for determining when what someone asserts is true or at least reasonable to accept tentatively.
[For more about LOGIC click here.]
1. Sentences express claims or PROPOSITIONS, but not all sentences express propositions since some sentences are meaningless, nonsensical or merely request information . By convention, the terms 'claim,' 'sentence', 'statement', and 'utterance' are synonyms for whatever (possibly) asserts a proposition. "Colorless green ideas sleep furiously,"—makes no sense. A proposition asserts that something is (or is not) the case; a proposition is true if and only if what it asserts actually is. That is, if a proposition asserts of some entity that it has a certain characteristic or property when in fact it does, then that proposition is true.
2. All propositions are either true or false, but sentences are only derivatively so. To say that a sentence (a purely linguistic entity) is true is to say that the proposition it expresses is true. Thus, truth is a property of propositions. Statements assert and questions ask. COMMANDS—"Just do it!"—and QUESTIONS—"Are your ears painted on?"—do not expess any propositions; so they are neither true nor false. "Get it?" asserts nothing, "Got it!" alleges much.
3. Whatever is true cannot be false. Whatever is false cannot be true. Don't confuse truth and falsity with necessary truth and necessary falsity—these are claims about what is or is not logically possible. A proposition is necessarily true if it not possible for it to be false, given how the world is or could have been. So to say a claim is necessarily true is to say something much stronger than you probably intend. For instance, "It is necessary that I take this class in this semester in order to graduate," means there is no way you can graduate without taking this class now, which is just plain false if you think about it—you could take the course in another semester before you graduate or requirements could change, etc. Thus, I recommend not using the terms 'necessary' or 'necessarily' in any philosophical discussion until you are aware of its implications. More on this later.
A proposition is impossible if it cannot be true. A proposition is contingent if it is neither necessary nor impossible—that is, if it could be true and could be false. A proposition that is not necessarily true is possibly not true. This is all very deep and beyond the scope of an introductory course, so here are some examples of what you need to understand about this point.
- 'All bachelors are married' is necessarily false, since it could not be true (by definition, bachelors are unmarried).
- 'All bachelors are not married' is necessarily true since it could not be false.
- 'Some bachelors are married' is contradictory, since it could not be true.
- 'Kramer is a bachelor and is not a bachelor' is a contradiction since it could not be true. Kramer at any moment isone or the other. Of course, bachelors can become non-bachelors by getting married...
- 'All bachelors are unhappy' is contingent, since it could be either true or false; whether it is actually true or false depends upon the way the world is.
- 'Some bachelors are miserable' is possibly not true, since it is possible that no bachelors are miserable.
- 'All bachelors seek a mate' is not necessarily true, since it is possible that someone is a bachelor and not seeking a mate.
- 'Bachelorhood, like virginity, cannot be regained' is possibly false, since some married men divorce or become widowers.
[For Aristotle's proof that the most indisputable of all beliefs is that contradictory statements are not at the same time true click here.]
4. Propositions predicate (or say) of some entity that it has at least one specific property. Identify subjects, predicates, properties and propositions (if any) in the following sentences.
- "Snow is white."
- "Earth rotates on its axis at approximately 1000 miles per hour."
- "Bill Clinton lied while under oath on 17 January 1998."
- "Colorless green ideas sleep furiously."
- "Is George Bush impervious to facts?"
- "Do you understand the difference between a lie and a false statement?"
- "Were you lying when you said you could not recall your whereabouts on the date in question or are you lying now when you say you can recall your whereabouts on that date?
(The last three sentences do not express propositions: Can you say why?)
5. How do we decide what to believe? LISTEN carefully to whomever has the best ARGUMENT, CHECK alleged facts, and TEST its assumptions and principles. EVALUATE the evidence and accept the conclusion of the argument if she provides compelling reasons, reject it if she does not. Where evidence matters, avoid hearsay, unsubstantiated opinion, and any unsupported speculation. Evidence presented without circumstantial or other evidentiary support is unreliable, so it is incredible. HEARSAY is any statement made out of court and not under oath which is offered as proof that what is stated by another is true. As a general rule, we disregard any evidence not based on a witnesses personal experience but on another's alleged statement. Such claims cannot be tested because they are made second-hand. There are exceptions to this hearsay-rule, e.g., when such statements are made under rare circumstances that assure reliability.
6. Distinguish ATTITUDES (beliefs, doubts, hopes) about a proposition from the TRUTH of that proposition. Some claims are true whether one believes them or not.
Believing that a proposition is true is not the same as believing a proposition which happens to be (actually) true:
Believing that ingesting megadoses of vitamin C prevents colds is independent and separate from whether, in fact, ingesting megadoses of vitamin C actually prevents colds.
7. Beliefs are RELATIONS between persons (believers, nonbelievers, or disbelievers) and propositions (the meanings of linguistic expressions). For example: "Joe Sixpack believes Stallone is a better actor than DeNiro," describes an attitude Joe Sixpack has about the claim that Stallone is a better actor than DeNiro. That is, Joe believes it is an accurate description which means Joe believes it is true.
Caveat: The origin of a belief never tells us whether a belief is true, however, it does indicate whether it is reasonable to consider. Reliable sources sometimes make false statements. Unreliable sources may be sincere but untrustworthy. Hypocrites and liars sometimes speak truths, but we don't know when to believe what they say. Thus, evidence for a belief must be distinguished from the cause of a belief. Observation and argumentation support beliefs by providing evidence for accepting that certain beliefs are true. Reflecting, wishing, hoping, and fearing, cause a belief to be accepted by producing a motive in the believer for having that belief. Reasons for (or against) a belief must not be confused with one's motive for accepting (or rejecting) it. Reasons JUSTIFY belief; desires MOTIVATE belief. Analytic philosophers care mostly about justifications (rational reasons) and very little about motivations (irrational reasons). The cause of a belief is not evidence for its being true. Further, the intensity of a belief or the certainty with which a belief is held cannot be counted on to reflect the strength of its supporting evidence any more than its sources can be trusted to reveal its justification or truth. Consider:
"Medieval peasants were fools for believing that the sun revolved around the earth."
—Were they fools or were they merely mistaken? How would things have looked if the sun had been circling the earth?
8. A set of beliefs or claims is logically CONSISTENT if and only if it possible for all of the members of the set to be true at the same time. A set of claims is logically INCONSISTENT if and only if it is not possible for all of them to be true at the same time. When a set of claims is inconsistent one cannot consistently assert (claim, believe, accept) all of the claims. Avoiding inconsistencies enables one to avoid false beliefs. To say a set of claims is consistent is to say that all CAN be true at the same time, that is, the set contains no contradictory claims. NOTE: A set of claims in which all are false is also consistent, since all of them could have been true at the same time. Works of fantasy are lie this. The point is that you can't mix true and false claims in a story and then say it is really true.
Suppose someone asserts all of the following claims.
1. Anyone who takes Astrology seriously is a fool.
2. Kim is my sister, and no sister of mine has a fool for a husband.
3. Jake is Kim's husband and he reads the horoscope column in the newspaper every morning.
4. Anyone who reads the horoscope column every day takes astrology seriously.
All of these claims cannot be true, therefore this set of claims is inconsistent. One can believe all of these claims however it is not possible that all of them are true simultaneously. So if one believes each of these claims is true then one has an inconsistent set of beliefs, since together they entail a contradiction: Can you state it?
"To believe something is to believe that it is true. Therefore, a reasonable person believes each of his beliefs to be true; yet experience has taught him to expect that some of his beliefs, he knows not which, will turn out to be false. A reasonable person believes, in short, that each of his beliefs is true and that some of them are false."
What do you believe? What follows from these beliefs? That is, what else is true as a result, if in fact these beliefs are true?
Conditional propositions assert that something is the case on the condition that something else is the case.
"If Anna is in Sacramento, then she is in California."
"All plants undergo photosynthesis."
[For more kinds of propositions see the chart at the bottom of this page.]
An argument is GOOD if and only if (1) all of its premises are true, and (2) the conclusion follows from the premises.
Depending upon how well the conclusion follows from or is supported by its premises, an argument is deductive or non-deductive.
The only way to demonstrate that an argument is invalid in form is to produce a COUNTER-EXAMPLE. A counter-example is any instance of the argument in question that has true premises and a false conclusion. Doing so demonstrates that the conclusion does not follow from the premises stated.
A deductive argument is one which:
IF all of the premises are true, then its conclusion must be true also. Its structure actually guarantees the truth of its conclusion. So, the form of an argument makes it deductive.
Arguments are good when their conclusions follow from their assumptions, and they are even better when those assumptions are true.
(a) An argument is VALID if and only if: It is not possible for all the premises to be true and for the conclusion to be false. I.e., IF all of its premises are true, then the conclusion MUST be true. If it would be inconsistent both to assert the premises and to deny the conclusion of the argument, then the argument is VALID.
(b) An argument is INVALID when it is not valid. If it is consistent both to assert the premises and to deny the conclusion of the argument, then the argument is INVALID.
[For more about the concept of logical VALIDITY click here.]
Although a valid argument whose premises are true MUST have a true conclusion, a valid argument whose premises are false CAN have a true conclusion. Thus, validity alone guarantees neither true premises nor true conclusions. Recall that an argument is good if and only if its conclusion is true because its premises are true. Few deductive arguments are good arguments; ultimately we seek SOUND arguments.
A deductive argument is SOUND if and only if it is: (1) VALID and has (2) TRUE PREMISES.
Is the following argument valid? Is it sound? WHY?
1. All spiders have ten legs.
2. All ten-legged creatures have wings.
3. Therefore, all spiders have wings.
This argument is VALID but not SOUND. (1) and (2) together imply (3) even if all of the claims are false. One way to think of this: If the premises WERE all true, then the conclusion would have to be TRUE also, given the valid form. Do you see why?
"P deductively implies Q" means 'It is impossible for P to be true and Q to be false.' Only the logical relation between premises and conclusions distinguishes deductive from non-deductive reasoning.
(Diagram the STANDARD FORM of each to see the special truth-preserving character of each pattern of reasoning.)
modus ponens (method of affirming)
1. If this is a plant, then it undergoes photosynthesis.
2. It is a plant.
3. Therefore, this undergoes photosynthesis.
modus tollens (method of denying)
1. If Spike is a racist, then he discriminates on the basis of race.
2. Spike does not discriminate on the basis of race.
3. Thus, Spike is not a racist.
disjunctive syllogism (an either-or argument)
1. Either God created humans or humans evolved from non-living matter by cosmic accident.
2. Humans did not evolve.
3. Therefore, humans were created by God.
hypothetical syllogism (a conditional argument)
1. If we successfully develop nuclear fusion power, then power will become cheap and plentiful.
2. If power becomes cheap and plentiful, then the economy will flourish.
3. Therefore, if we successfully develop nuclear fusion power, then the economy will flourish.
1. Truth is a property of propositions. Propositions are either true or false; arguments are neither true nor false. In logic, and philosophy in general, TERMS such as 'argument', 'truth', 'valid', 'invalid', 'sound' and 'unsound' have strict and precise definitions intended to clarify conceptual and logical analysis. In formal reasoning or writing, take care not to confuse the logical senses of these terms with the loose and popular senses such terms have in ordinary language unless you intend to be vague or misunderstood.
2. An argument is a connected series of propositions intended to establish the truth of a specific conclusion. Only deductive arguments are valid or invalid, sound or unsound; propositions are never sound and they are neither valid nor invalid. Sound arguments are always valid but not all valid arguments are sound. Every argument is a PROOF or demonstration of the truth or reasonableness of its conclusion, but this only describes its intent, since any proof is only as credible as its assumptions.
3. Good arguments frequently fail to persuade non-believers or disbelievers; bad arguments are often very persuasive. People believe claims for good or bad reasons. Persuasive arguments may be irrational, weak, based upon false presumptions or mistaken background beliefs; persuasiveness is a poor indicator of the truth of an argument's conclusion. Whether an argument succeeds in convincing you that its conclusion is true is a judgment call you alone must make. People can believe claims for good or bad reasons. Decide for yourself what you will believe.
"All humans are mortal. Hillary is a human. Therefore, Hillary is mortal."
Deductively valid arguments provide an absolute guarantee that the conclusion is true (when premises true, one cannot derive a false conclusion) but this is also a limitation, since one can assert nothing more than what is already given in the premises.
Strength: If a deductive argument is sound, then we are compelled to accept its conclusion.
Weakness: The conclusion of a sound deductive argument states only what is contained in the premises. Such arguments are only truth-preserving, not truth-generating.
"Everyone infected with HIV has contracted AIDS. Marcel is HIV positive, so he will contract AIDS."
An inductive argument is neither valid nor invalid, however, its premises are intended to provide sufficient evidence, but less than conclusive support, for the conclusion. How good an inductive argument is depends upon how probable its premises are, and whether those premises weakly or strongly support the conclusion.
Strength: Inductive arguments give us new information and permit us to make retrodictions (claims about the distant or unobserved past) and predictions.
Weakness: We cannot prove the conclusions of inductive arguments; we can only disprove them. Also, generalizing from observed cases to unobserved cases may produce mistaken inferences.
Inductive arguments are strong or weak according to (1) the sample size from which data is drawn; and (2) how much or how well the sample represents the population about which the inductive conclusion generalizes.
A. Induction by enumeration
PRESUMES that "If all observed X are also Y, then (probably) all X are Y."
"All ravens we have ever observed are black, so (we may conclude) that all ravens are black."
Conclusions of enumerative inductions are stronger when they cover a larger, more representative sample of a population. BUT COUNTER-EXAMPLES ARE DEVASTATING. One non-black raven defeats this conclusion.
B. Induction by analogy
PRESUMES that "If X and Y are relevantly similar in most respects, then (probably) X and Y are similar in another respect."
1. Person A has properties p, q, r, and s.
2. Person B has properties p, q, and r.
3. Therefore, (probably) person B has property s also.
[p: has a backpack; q: has a class schedule; r: has this text; s: is a student]
BUT similarities may be superficial, coincidental or irrelevant to the issue at hand. Conclusions of arguments based on similar cases are more improbable because their weaker conclusions tell us very little. Such inferences only permit us to say how things are similar, in certain respects.
C. Statistical induction
PRESUMES that "If the sample accurately reperesents the population from which it is drawn, then (probably) whatever is a property of the sample is also a property of the population."
"On standard intelligence tests, asians consistently outscore whites and whites outscore blacks. Thus, whites have higher IQs than blacks and asians have higher IQs than both whites and blacks."
Here one concludes that the percentage of a sample having a certain property is the same percentage as the population from which that sample was drawn.
BUT the sample must accurately represent the population from which it is drawn.
Sample-size and sample-representativeness determine how strong (or weak) an inductive argument is. Personal experiences as evidence for general claims fail to be sufficiently large or representative and are dismissed as anecdotal or non-evidentiary.
D. Causal induction
PRESUMES that "If there is a strong correlation between X and Y, where X and Y do NOT accidentally coincide and X and Y do NOT have a common cause and Y does NOT cause X, (probably) X causes Y."
"Many smokers are afflicted by chronic bronchitis, asthma, emphysema, heart disease, mouth and lung cancer. Heavy smokers suffer these problems even more so than do light smokers. Further, non-smokers living with smokers suffer these problems more than non-smokers who do not. Obviously smoking causes these problems."
Strong correlations of events lead us to believe (often erroneously) that one event causes another or that they have a common cause. BUT correlation never implies a causal link. Correlations can be accidental (merely coincidence). Non-accidental correlations can be the result of a common cause or the result of one event actually causing the other.
Deductive Arguments are summarizing or simplifying inferences while inductive arguments are generalizing or amplifying inferences.
generalization = any claim that asserts a universal or statistical or stereotypical proposition which summarizes beyond the scope of supporting observations and assumptions
prediction = any claim that asserts a proposition about the future
retrodiction = any claim that asserts a proposition about the past
hypothesis = (1) any assertion that allegedly describes or explains some state of affairs; or, (2) sense [1] AND is testable (i.e., it is possible to show it is false, IF it is). Hypotheses in science are assertions requiring justification. A person considers or accepts an hypothesis because, if it were true, then it would describe or explain phenomena. Causal hypotheses specify causes of correlations between events.
theory = (1) any argument or explanation which has a conclusion that describes how things are, or have been, or will be, OR has a conclusion which asserts what ought to be the case; or, (2) sense [1] AND is supported by testable assertions.
science = (1) A fallible, self-correcting PROCESS which aims to produce knowledge about the world. SCIENTISTS employ primarily empirical (experience-based) and analytical (logic-based) methods of inquiry to TEST HYPOTHESES and construct theories that describe, explain and predict phenomena; or, (2) The PRODUCT of that process expressed in data, observations, hypotheses, theories, explanations (much of which is based on verifiable or falsifiable assertions).
- A knowledge-seeking process is scientific only if it proposes and tests theories that describe or explain phenomena.
**Is science the most reliable means for forming true and useful beliefs?
Non-deductive inference permits you to conclude something more than what is assumed or observed, without a strong guarantee, but you risk accepting a false (even if plausible) conclusion:
deduction: use modus tollens to disprove hypotheses
Science, medicine, history, all use primarily non-deductive inferences:
induction: use statistical generalizations to produce accurate descriptions and make reliable predictions
abduction: inferring that the best explanation from those available is (very likely) true
When we have evidence E and are considering several hypotheses, say H1 and H2, we should infer H1 rather than H2 exactly IF H1 is a better explanation (of observations) than H2.
In this way the methods of scientific reasoning are more like modus tollens, not modus ponens.
- Evidence/observations discriminate between some alternative hypotheses but not others; this is a limitation.
"Heart attack victims suffer chest pains."
- Testable hypotheses make predictions we would not expect to come true if they (a given hypothesis) actually were false.
"If he had a heart attack, he will display an erratic EKG."
- Acceptable theories do not make false predictions.
"Heart attack victims usually display erratic EKGs."
(a) Apply the Surprise Principle: An observation O strongly supports H1 over H2 when
(1) IF H1 were true, you would expect O; AND (2) IF H2 were true, you would expect not-O.
I.e., IF H1 were true, O [erratic EKG] would be unsurprising and IF H2 were true, O [erratic EKG] would be surprising.
Successful prediction provides strong (but not conclusive) evidence for an hypothesis only when what you observe is not what you would expect were the hypothesis false.
H1 = heart attack (predict erratic EKG ---> clear EKG would be surprising)
H2 = not-H1 (predict clear EKG ---> erratic EKG would be surprising)
(b) Avoid the "only game in town" fallacy: Occurs when one mistakenly infers that one explanation MUST be correct in the absence of better (more plausible, credible) alternatives.
"My house is haunted since I hear strange noises at night but see no evidence of rats."
"The patient did not have a heart attack since her EKG is normal."
These forms are error-prone because their conclusions do not follow from their premises. Even if their premises are true, these forms are not truth-preserving. If one describes a possible state of affairs in which all of the premises are true but the conclusion is false, then one demonstrates that the conclusion does not follow from the premises, that is, one demonstrates that the argument is invalid but showing that its form fails to guarantee that its conclusion is true. Accomplishing this is called producing a COUNTER-EXAMPLE.
For instance: If I find a rotten apple in the fresh apple barrel at the fruit stand, then I find a
counter-example to the claim that "All apples in the fresh apple barrel are unspoiled."Sketch the form of each argument by symbolizing its propositions and imagining counter-examples.
Fallacy of affirming the consequent:
"When you have a cold, your sinuses become congested, your eyes itch, and you have headaches. You are congested, your eyes itch and you have a headache. So you have a cold."
Fallacy of denying the antecedent:
"If abortion is murder, then it is wrong. But abortion is not murder. So abortion is not wrong."
Fallacy of affirming a disjunct:
"Jesus was the son of God or Jesus was a liar. Since Jesus was the son of God, Jesus was not a liar."
Fallacy of undistributed middle:
"All reptiles lay eggs, and all birds lay eggs. Therefore, all birds are reptiles."
1. If Spike is a racist, then he discriminates on the basis of race. Spike discriminates on the basis of race, therefore he is a racist.
2. If you study, you will pass the test. You do not study, so you will not pass the test.
3. If you don't let him buy a Hummer, then you don't love him. But you let him buy a Hummer, so you love him.
4. Unless she has a fever, she doesn't have the flu. She doesn't have the flu, so she doesn't have a fever.
5. If it is raining my car will get wet. But it is not raining. So my car will not get wet.
6. Every person should avoid keeping loaded guns around the house. People who have the capacity to kill should avoid keeping loaded guns around the house. Every person has the capacity to kill.
7. Liars mislead and deceive; Ollie is a liar because he gave misleading and deceiving testimony.
8. I should not diet, so I should jog. I want to get into shape. If I want to get into shape, either I should jog or I should diet.
9. Mice fed saccharin develop bladder cancer. It follows that humans who consume saccharin also develop bladder cancer, because substances that cause cancer in mice cause cancer in humans.
10. Nobody should be forced to risk their health against their will unless there is some greater benefit. Allowing cigarette smoking in public places provides no greater benefit. Cigarette smoking in public places should not be allowed because doing so forces the nearby non-smoker to risk her health against her will.
11. Capital punishment is an acceptable social policy only if it either deters murder or is justifiable revenge. Since capital punishment does not deter murders and is not justifiable revenge, capital punishment is not an acceptable social policy.
12. Time has neither a beginning nor an end, that is, time is eternal. If time had a beginning, then there would have been a time before time. If time had an end, then there would be a time after time. The idea of there being a time before time or a time after time is absurd since before and after mean before and after in time.
13. If God is all-powerful, then God would be able to abolish evil. If God is all-good, then God would not allow evil to be. Either God is not able to abolish evil, or God allows evil to be. Therefore, either God is not all-powerful, or God is not all-good.
14. God is all-good. An all good being would want to destroy all evil. God is all-powerful. An all-powerful being can destroy any evil. So, if God exists, there will be no evil. Evil exists. Therefore, God does not exist.
15. If God exists, life has meaning. But God does not exist, so life has no meaning.
16. Life has meaning only if God exists. But God does exist, therefore life has meaning.
Merlino's reasons for not accepting illegitimate excuses
17. If you are able to do whatever it is that you are required to do, then you should do it. For example, you should do homework if you are able to do it. Of course, if you should do something, then you are able to do it. So, if you are able to do homework, then you should do it.
18. If you do not complete your homework assignment by the deadline stated and you have no legitimate excuse for not doing it, then you receive a failing grade for that assignment. Suppose you do not receive a failing grade on your homework. So, either you do your homework or you have a legitimate excuse for not doing it.
19. I stipulate that one has a legitimate excuse for missing an assignment if and only if one demonstrates that one is UNABLE to do it. When you demonstrate that you are unable to do an assignment then you produce irrefutable evidence that you could not do it. Since you do not produce evidence demonstrating that you were unable to complete the homework, then you receive an F for that assignment.
20. If you do not complete your homework assignment by the deadline and you have no legitimate excuse, then you receive a failing grade for that assignment. If you are not able to complete your homework assignment by the deadline, then you have a legitimate excuse. If you are not willing to complete your homework assignment by the deadline, then you do not have a legitimate excuse. You did not complete your homework assignment by the deadline. Either you were unable or unwilling to do your homework. But you were able to do your homework, so you were unwilling to do your homework. Therefore, you have received a failing grade for that assigment.
21. An explanation is not an argument. Describing the cause of an event does not justify it. Without a legitimate excuse for not doing the homework you receive an F. If your excuse is legitimate, then your explanation of your circumstances must be acceptable AND your argument for your being a victim of those circumstances must to be cogent. But all you present to me is an acceptable explanation. You have not presented any argument. Thus, your excuse is illegitimate.
22. Practice makes perfect. Nobody is perfect. Therefore, nobody practices.
Last update: Wednesday, 22 January, 2014 3:47 PM
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simple statement | connective | |
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assertion |
"p is true" | (none) | |
negation |
"p is false" | (none) | |
identity |
"p is q is true" | (none) | |
tautology |
"p or not-p is true" | (none) | |
contradiction |
"p and not-p is true" | (none) | |
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compound |
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disjunction |
"either p is true, or q is true, or both" | p or q | |
conjunction |
"both p and q are true" | p and q | |
implication |
"if p is true, then q is true" | if p then q | |
equivalence |
"p and q are either both true or both false" | p if and only if q | |
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categorical |
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universal affirmative |
A | "all p is q" | implication |
universal negative |
E | "no p is q" | implication |
particular affirmative |
I | "some p is q" | conjunction |
particular negative |
O | "not every p is q" or "some p are not q" | conjunction |
| p | q | p or q | p and q | if p then q | p if and only if q |
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T
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F
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F
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More on logical truth tables here...
Contrary-to-Fact Conditional Fallacies (a la David Lewis)
The Traditional Square of Opposition concerning the relation between contraries an contradictories (Terence Parsons, SEP)
“All right," said Hermione, disconcerted. "Say the Cloak existed ... what about the stone, Mr. Lovegood? The thing you call the Resurrection Stone?"
"What of it?"
"Well, how can thatbe real?"
"Prove that it is not," said Xenophilus.
Hermione looked outraged.
But that’s—I’m sorry, but that’s completely ridiculous! How can I possibly prove it doesn’t exist? Do you expect me to get hold of—of all the pebbles in the world and test them? I mean, you could claim that anything’s real if the only basis for believing in it is that nobody’s proved it doesn’t exist!"
"Yes, you could. I am glad to see that you are opening your mind a little"
- Hermione and Xenophilus Lovegood talking about a mythical object called the Resurrection Stone, in the 7th book, Harry Potter and the Deathly Hallows (2007, p411).