Chapter 1 Flashcards
Deductive reasoning
Spelling out whatever conclusion follows logically from your premises, without reference to any external information
Deductive proof
Demonstrating that a particular conclusion logically follows from certain premises, and that this conclusion must be true if these premises are true
Truth-preserving
when used correctly, deductive reasoning is guaranteed to preserve the truth of its premises is its conclusion.
Unwarranted
A conclusion that is not supported by the argument
Necessary condition
Must be met if something is to be true, but cannot by itself guarantee the truth of that thing
Sufficient condition
One that, if met, does guarantee the truth of something
Logic
The study of the principles distinguishing correct from incorrect reasoning
Affirming the antecedent
A valid form of argument in which, because one thing is said always to follow from another, the truth of the first guarantees the second is also true
Premise 1: Premise 2: Conclusion:
If A, then B. A. Therefore, B.
Formal fallacy
An invalid form of argument representing an error in logic, meaning that arguments in this form cannot be relied on to arrive at valid conclusions
Affirming the consequent
An invalid argument which mistakenly assumes that, when one thing always follows from another, the truth of the second also guarantees the first
Premise 1: Premise 2: Conclusion:
If A, then B. B. Therefore, A.
Denying the consequent
A valid form of argument in which, because one thing is said always to follow from another, the fact that the second isn’t true also guarantees the first isn’t true
Premise 1: Premise 2: Conclusion:
If A, then B. Not B. Therefore, not A.
Denying the antecedent
An invalid argument which mistakenly assumes that, when one thing always follows from another, the fact that the first isn’t true also guarantees the second isn’t true
Premise 1: Premise 2: Conclusion:
If A, then B. Not A. Therefore, not B.
Sound Argument
A deductive argument that is both valid and has true premises, meaning its conclusion must also be true
Unsound Argument
An argument that does not meet the standard of soundness, either because it is invalid or because one or more of its premises is untrue, or both
Inductive reasoning
A form of reasoning in which premises strongly support
a conclusion, but where we can never be absolutely certain that it is true
Ampliative reasoning
Another way of describing inductive reasoning – intended to show that such reasoning works by ‘amplifying’ premises into a broader conclusion
Ranking inductive arguments
Determining which arguments are more or less convincing relative to one another
Inductive strength or inductive force
A measure of how likely we believe an inductive argument is to be true
Cogent
An inductive argument that has a good structure, but whose conclusion we should not necessarily accept as true (similarly to a valid deductive argument)
Inductively forceful
An inductive argument that has both a good structure and true premises, and whose conclusion we thus have good reason to accept as true (similarly to a sound deductive argument, although without its certainty)
Implicit qualification
When a general statement is not literally intended, some implicit qualification needs to be assumed, indicating the frequency with which it applies
Rational expectation
Whatever it would be most reasonable to expect in a particular situation; this can be quite different to what somebody personally expects
Sample
The particular cases you are using to stand for the entire category about which you wish to make an inductive generalization
N = 1
A sample size of one indicates an anecdote rather than a serious investigation; any inductive argument based on a single instance is likely to be very weak
Representative samples
Closely resemble the larger group about which claims are being made, while unrepresentative samples fail to do so
Randomized sample
One selected at random from across a field of study, with no particular element misleadingly over- represented
Sampling bias
Biases introduced by imperfect methods of selecting a sample
Observational error
Errors due to the accuracy of your measuring system, usually reported as ±X, where X is the potential difference between measured and actual values
Margin of error
An expression of the degree to which results based on a sample are likely to differ from those of the overall population
The problem of induction
No matter how likely we believe something to be, an inductive argument can never actually prove it to
be true
Falsification
The contradiction of something previously accepted as true or obvious
Counter-example
An example whose discovery makes
it necessary to rethink a particular position, because it directly contradicts a generalization previously believed to be true
Black swan event
An event that defies both previous experience and expectations based on that experience, making it almost impossible to predict
Fallacy
A flawed general type of argument that establishes a faulty connection between premises and conclusion, thus failing to give us a good reason to accept the conclusion
Fallacious argument
An argument whose conclusion does
not follow from its premises, because its reasoning rests on an identifiable fallacy
Appeal to popularity
a fallacious form of argument based on the assumption that whatever most people think must be true.
Appeal to irrelevant authority
A fallacious form of argument based on the perceived opinion of an authority without any expertise in a relevant area
Unwarranted hidden assumption
The faulty, unstated element of reasoning that a fallacy relies on, and that we aim to spell out in order to identify what is at fault
Comparable example
A method for testing potentially fallacious arguments, and illustrating their flaws, by applying exactly the same reasoning in a different context
Informal fallacy
If you need to consider both the content of an argument and its relationship with external infor- mation, this is an
Formal fallacy
If the error is purely related to the structure of an argument, you are dealing with
Fallacy of relevance
An argument relying on premises that are insufficiently relevant to its conclusion for us to accept this conclusion
Argument by appeal
The fallacy of appealing to external factors such as authority or popularity to justify a conclusion, rather than using rigorous reasoning
Ad hominem
The fallacy of attacking the person making
an argument rather than what they actually say
Fallacy of ambiguity
Shifting the meaning of terms during reasoning, or exploiting uncertainty in order to support an unjustified conclusion
Equivocation
Using a word in two quite different senses while pretending that they are the same in order to create the appearance of reasoning
Amphiboly
Using a phrase or sentence that can be interpreted as meaning more than one thing, without clarifying which
The fallacy of composition
Mistakenly arguing that whatever is true of the individual parts must also be true of the whole
The fallacy of division
Mistakenly arguing that whatever is true of the whole must also be true of its individual parts
Material fallacies
Fallacies that either covertly assume the truth of a conclusion or avoid the real issues at stake
Begging the question
putting the conclusion to be proven into your premises,
thus producing something convincing-sounding that proves nothing
Circular reasoning
an argument whose premise supports its conclusion, and whose conclusion supports its premise, making it a closed loop
Post hoc ergo propter hoc
the fallacy of assuming that, when one thing happens after another, the first thing must be the cause of the second thing
Correlation is not causation
the fallacy of assuming that, if two phenomena or sets of data closely follow one another, one must be caused by the other
Inverting cause and effect
The fallacy of confusing the direction of causation between two related phenomena, and thus mistakenly labelling an effect as a cause
False dilemma
Fallaciously claiming that, in a complex situation, it is only possible for one of two things to be true
Loaded/complex question
Asking a question about one thing that also includes an unstated assumption about another, in an attempt to force someone to accept this assumption
Faulty analogy
Claiming two things are similar, even though they are not, in order to make an unreasonable conclusion look reasonable
Faulty generalization
Using a small amount of evidence to justify a much larger observation that isn’t actually warranted
Slippery slope
Arguing on the basis that, if one small thing is allowed to happen, an inevitable and increasingly serious chain of further events will be set in motion
The undistributed middle
A formal fallacy which mistakenly confuses something that applies to all members of a category with something that applies only to members of that category
Base rate neglect
Ignoring the underlying frequency of one element in
an analysis, and
thus potentially reaching an incorrect conclusion about the likelihood of a certain result
False negative
A negative test result produced in error, when whatever is being tested for is in fact present (e.g. a pregnancy test saying you are not pregnant when you actually are)
False positive
A positive test result produced in error,
when whatever is being tested for is in fact absent
(e.g. a pregnancy test saying you are pregnant when you actually are not)
True positive
a positive test result that correctly corresponds to the presence of whatever you’re testing for
Bayes’s theorem
a method for calculating the probability of an event based on our knowledge of previous events
Base rate
the initial, underlying likelihood that something we are investigating is the case (e.g. the base rate of disease X in this population is one case per 2,000 people per year)
