50 terms

11PHIL 2018 - Logic and Reasoning

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Argument
A set of claims consisting of one or more premises and a conclusion
Claim
A statement or proposition that is either true or false
Premise
One or more of the claims in an argument that provides reason(s) or support for the conclusion
Unstated premise (aka 'implicit' or 'suppressed' premise)
A premise that is clearly a part of an argument but is not explicitly stated.

For example:
Don't worry, Fido doesn't bark. Because after all, no dingos bark.

UP1. Fido is a dingo
P1. No dingos bark
________________________________________
C. Therefore, Fido doesn't bark
Conclusion
That claim in an argument for which the premises are intended to provide support
Standard form
A clear way we can represent an argument so that we may evaluate that argument more easily
Two essential criteria for (or 'virtues' of) a good argument
1. The premises should all be true
2. The conclusion should follow from the premises (i.e., it should have what philosophers call 'good form')
Chain argument
An argument in which the conclusion of one argument becomes a premise of the next argument
Example/counterexample
An example is used to demonstrate the truth of some claim or reinforce the plausibility of some argument or position. A counterexample is a special kind of example, used to challenge the truth of some claim or undermine the plausibility of some argument or position.
Objection
In argumentation, an objection is a reason arguing against the truth of a premise, the form of an argument, or the conclusion the argument is intended to establish.
Implication
A conclusion that can be drawn from something although it is not explicitly stated; a likely consequence of something.
Conclusion Indicators
Words and phrases which serve to indicate what the conclusion is in a piece of reasoning in ordinary language. For example:
- therefore / thus / so / it follows that
- hence / consequently / it can be concluded that
- suggests / proves / demonstrates that / shows that / which establishes that
- entails / implies / one can infer that
Premise Indicators
Words and phrases which serve to indicate what the premise is (or premises are) in a piece of reasoning in ordinary language. For example:
- because / since
- firstly, secondly, ...
- for / as / after all
- assuming that / in view of the fact that
- follows from / as shown by / as - indicated by / is established by
- may be inferred / deduced / derived from
- the reason for this is...
Valid Deductive argument
In an argument of this kind, if I accept the premises as true, I simply must accept the conclusion. It is not possible for the premises to be true and the conclusion false
Validity
A property of a deductive argument whereby if we accept the premises as true, then the conclusion must also be true
A sound argument
A deductively valid argument with all true premises
Entailment
The very strong relationship between the premises and the conclusion of a valid deductive argument. The premises entail the conclusion. Sometimes, the term is used to express the relationship between just one statement and another. For example, 'Jill has a sister' entails 'Jill has a sibling,' but 'Jill has a sibling' does not entail 'Jill has a sister.'
Conditional Statement (+ Antecedent and Consequent)
Sentences of the form 'If A then B'. For example: 'If it rains, then the picnic will be cancelled' is a conditional statement. The statement in the A position is called the antecedent of the conditional. The statement in the B position is called the consequent of the conditional.

If it rains (A), then the picnic will be cancelled (B). Does it follow that it will in fact rain? No. Is the speaker committed to the claim that the picnic will be cancelled? No, the commitment is only to an increase on the condition that it rains. The truth of a conditional does not require the truth of its parts.

(Note that A and/or B can be compound sentences. In the following example, A is a compound sentence, whilst B is not: 'If the sails are being repaired and the oars have been stolen, then we will not be taking the boat out on the harbour.' )
Counterfactual Statement
A type of conditional statement in which the antecedent (aka 'conditional clause') is false, e.g., "If I had arrived on time . . ."

If I had arrived on time, then I would not have missed dinner (sadly, though, the antecedent is false and I, therefore, did not arrive on time and did miss dinner).

If I had arrived on time, I would have had the chance to meet your sister.

If I had arrived on time, I would not have been fired from my job.

If I had arrived on time, I would have completed the exam.
Modus ponens
The deductively valid form:
P1. If A then B
P2. A
_________________________
C: Therefore, B
Modus tollens
The deductively valid form:
P1. If A then B
P2. Not B
_________________________
Therefore, not A
Affirming the consequent
The deductively invalid argument form:
P1. If A then B
P2. B
_________________________
C: Therefore, A

P1. If London is in Scotland (A) then London is in Britain
P2. London is in Britain (B)
_________________________
C: Therefore, London is in Scotland (A)

True premises yield a false conclusion. It is an unreliable way to reason. The form is invalid.
Denying the antecedent
The deductively invalid argument form:
P1. If A then B
P2. Not A
_________________________
C: Therefore, not B

P1. If Melbourne is in NSW (A) then it is in Australia (B)
P2. It is not the case that Melbourne is in NSW (Not A)
_________________________
C: Therefore, it is not the case that Melbourne is in Australia (Not B)
Inductive strength
The degree to which the premises of an inductive argument support the conclusion. An argument to the conclusion that Australia will not become a republic in the very near future based on a survey of a large number of Australians chosen in order to satisfy many sophisticated criteria for representativeness would be inductively strong. An argument to the conclusion that the next student I meet while on yard duty will be enrolled in Year 11 Philosophy on the basis that that the last two have been would be inductively weak.
Inductive argument (aka 'ampliative argument')
In an argument of this kind, if I accept the premises as true, then the conclusion seems probable, but not inescapable
Argument to the best explanation
An inductive argument that seeks to explain some fact or phenomena using the best available explanation.

P1. Event E has occurred
P2. The best explanation for E is X
______________________________________
C. Therefore, X
A cogent argument
An inductively strong argument with all true premises
Inductive generalisations
A type of inductive inductive argument that relies upon projecting a sample of a population onto the whole population.

The general form is:
P1. X% of observed A's have been B's
________________________
C. X% of all A's are B's.

"All the lollies I have eaten from the bag so far have been jelly beans. Therefore, all the lollies in the bag are jelly beans."
Analogy
A comparison between two objects, or systems of objects, that highlights respects in which they are thought to be similar
Argument from analogy
A type of inductive argument that takes note of the fact that two or more things are similar in some respects and concludes that they are probably also similar in some further respect.

An argument from analogy typically takes the following form:
P1. X and Y share properties a, b, c
P2. X also has property d
_______________________________
C. Therefore, Y also has property d
Is/ought fallacy
This fallacy occurs when the assumption is made that because something *is* a certain way that it *ought* to be that way. For example, in nature, it is the case that the strong often take from the weak. If one was to commit this fallacy, they would conclude that it oughtis fallacy occurs when the assumption is made that because something *is* a certain way that it *ought* to be that way. For example, in nature, it *is* the case that the strong often take from the weak. If one was to commit this fallacy, they would conclude that it ought to be the case that the strong take from the weak.
Equivocation
Using an ambiguous term in more than one sense, thus making an argument misleading.

For example:
P1. Noisy children are a real headache
P2. Two aspirin will make a headache go away
___________________________________________
C: Therefore, two aspirin will make noisy children go away
Begging the question
A form of circular reasoning in which the conclusion is derived from premises that assume the truth of the conclusion

A type of reasoning in which the conclusion is supported by the premises and the premises are supported by the conclusion. This creates a circle in the reasoning, where no useful information is being shared.

Example #1
Joe: What are electrolytes?
Terry: They're what they use to make Gatorade!
Joe: But why do they use them to make Gatorade?
Mary: [raises hand after a pause] Because Gatorade's got electrolytes.

Example #2
The Bible is the Word of God because God tells us it is... in the Bible.
Slippery slope
A type of argument in which a party asserts that a relatively small first step leads to a chain of related events culminating in some significant (usually negative) effect
Logical contradiction
Putting forward or defending some statement and simultaneously putting forward the denial of that same statement. In other words, the conjunction of a statement P with its own denial not-P. Contradictions are necessarily false. 'Today is Monday and today is not Monday' is a contradiction. But so is 'Anna is taller than Bertie, and Bertie is taller than Sue, and Sue is taller than Anna.'
Logical consistency
When a statement (or set of statements) involves no logical contradiction.
The law of non-contradiction
A fundamental law of logic that a statement and its denial cannot both be true simultaneously.

E.g., "Dallas is in Texas" and "Dallas is not in Texas" cannot both be true at the same time.

E.g., "There is a ceiling above me" and "There is not a ceiling above me" cannot both be true at the same time.
The law of excluded middle
A fundamental law of logic that states that for any proposition, either that proposition is true OR its negation is true (i.e., it is impossible that there should be anything between the two parts of a contradiction - the middle is excluded)

E.g., It is either the case that "Dallas is in Texas" or that "Dallas is not in Texas."

E.g., It is either the case that "There is a ceiling above me" or that "There is not a ceiling above me."
Necessary condition
If A is not true without B's being true, then the truth of B is a necessary condition for A.

For example, having the same mother is a necessary condition for being a full biological sister to someone.

A supply of oxygen is a necessary condition for human life.

A necessary condition for getting an A in 11PHIL is that a student completes the SACs. This means that if a student does not complete the SACs, then that student will not get an A, or, equivalently, if a student gets an A, then that student has completed the SACs.
Sufficient condition
If whenever A is true so is B, then A is a sufficient condition for B (it is "enough" for B; it is "sufficient" for B).

For example, a sufficient condition for getting an A in 11PHIL is getting an A on every piece of graded work in the course. This means that if a student gets an A on every piece of graded work in the course, then the student gets an A.

Completing the SACs, however, is not a sufficient condition for getting an A in the course. It is possible to complete all of the SACs and not get an A in the course.

Getting an A on every piece of graded work is not also a necessary condition for getting an A in the course, however, for it is possible to get an A in the course even though one fails to get an A on some piece of graded work.
If and only if (iff)
Used to introduce a condition that is both necessary and sufficient OR used to introduce a set of conditions that are individually necessary and jointly sufficient.
Assumption
Something accepted as true or as certain to happen without reflection, proof, good reason, or an argument.
Intuition
Something one believes they know or consider likely from an instinctive feeling rather than conscious reasoning or evidence
Descriptive definition
The ordinary or everyday meaning of a word
Stipulative definition
The way a word is to be used in a particular context
The principle of charity
The process in which one aims to understand another person's argument fully, accurately and fairly before evaluating it
Infinite regress
A sequence of reasoning or justification which can never come to an end
Paradox
A collection of claims which, taken individually, seem very plausible, but when taken collectively, seem logically unacceptable or absurd. It may or may not involve contradiction.
Physical possibility/impossibility
Physical possibility is that which is compatible with physical laws. For example, it is physically possible for some human beings to run in excess of 44 kilometres per hour, however, it is *physically impossible* for human beings to run at 100 kilometres an hour. Similarly, it is physically *possible* to fly a human being to the moon with the aid of technology, but it is physically impossiblepossibleossibility is that which is compatible with physical laws. For example, it is *physically possible* for some human beings to run in excess of 44 kilometres per hour, however, it is *physically impossible* for human beings to run at 100 kilometres an hour. Similarly, it is physically *possible* to fly a human being to the moon with the aid of technology, but it is physically impossible for a human being to fly to the moon without the aid of technology (due to the physical limits of human beings, the distance to the moon, and so forth).
Logical possibility/impossibility
In order for some proposal to be *logically possible*, it must not be self-contradictory. For example, the proposal "human beings run at 100 kilometres an hour" may not be *physically possible*, but it is logically possible insofar as the proposal does not contradict itself. The statement "the planet is both a perfect sphere aphysically possibleposal to be *logically possible*, it must not be self-contradictory. For example, the proposal "human beings run at 100 kilometres an hour" may not be *physically possible*, but it is logically possible insofar as the proposal does not contradict itself. The statement "the planet is both a perfect sphere and a perfect cube", however, is logically impossible in that it is self-contradictory. Hence, a logically possible proposal does not have to be physically possible, or even likely to happen, but merely logically imaginable.

Note: Any consistently describable word is is considered a logically possible world (aka "possible world"). Hence, there IS a possible world in which pigs fly, but no possible world in which there is a round square.
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