the difference between mere thinking and reasoning
-mere thinking: our thoughts simply come to us one after another
-reasoning: we actively link thoughts together in such a way that we believe one thought provides support for another thought, aka inference*
the relationship between inference and argument
When an inference is expressed in statements, a sentence that is used to make a claim that is capable of being true or false, its called an argument: a set of statements that claims that one or more premises support the conclusion, argument: the structure
arguments vs. claims, statements, or views
claim: just the conclusion statement, statement: a claim that can either be true or false, view: opinion?, argument: makes a claim, but has prior premises to bring support to that claim/made up of statements, argument makes use of inferences expressed in
components of an argument
premise(s) and conclusion, every argument claims its premises support its conclusion, Declarative sentences; clear, unambiguous, literal language; shows their structure
deductive vs. inductive arguments
-deductive: an argument whose premises, if true, guarantee the truth of the conclusion
-inductive:an argument who's premises, if true, make it reasonable to conclude that the conclusion is true, but do not provide an absolute guarantee
strength, validity, soundness, and cogency of arguments
-strength: an argument is said to have logical strength when its premises, if true, actually provide support for its conclusion, only for inductive
-validity: A deductive argument is said to be valid if and only if it takes a form that makes it impossible
features of proper argument reconstruction
determining the premises, the conclusion and the precise relationship between them that the author intended to present
interpretive, verification, and reasoning skills
-interpretive skills: a set of capacities that are used to discern the meaning of something, interpreting statements and arguments in a way that makes their meanings as clear as possible
-verification skills: a set of capacities that are used to determine
features of 'standard form'
P1. If Bill runs as an independent, he will split the Republican vote
P2. Bill will run as an independent _______________________________________
C1. He will split the Republican vote (from 1-2)
- if A, then B
-A
-therefore B, just as long as it has both
inference indicators
words that indicate that one thought is intended to support another thought
-ex: therefore, so, hence, thus, since, implies, etc
enthymemes and missing premises
-An argument with a missing premise or conclusion
-finding missing premises:
�Did the author mean to provide conclusive or merely probable support for the conclusion?
�Search for credible premises that:
� is plausible
� the author could reasonably be taki
forms of modus ponens, modus tollens, hypothetical syllogism
-modus ponens: P implies Q; P is asserted to be true, so therefore Q must be true
-modus tollens: denying the consequent: If P, then Q. Not Q. Therefore, not P
-hypothetical syllogism: If P, then Q. If Q, then R. Therefore, if P, then R
steps in evaluating arguments
asking whether the premises are true and if the premises support the conclusion
the concept of truth, as used in this class
� The correspondence of a representation of reality with reality itself
� Here is the basic idea:
� If John thinks snow is white and snow is white, then what John thinks is true.
� If Sally says the earth is roughly spherical and the Earth is roughly sphe
categories of statements:
analytic, complex, contradictory, empirical, observation, simple, synthetic, truth-functional
convergent vs. chained structure
-convergent: Can have many weak premises and the table will still stand
-chained: The argument is only as strong as the weakest link
T vs. V structure in arguments; complex & simple structures
-T argument: an argument with two or more premises, none of which offers significant support for the conclusion by itself, but all the premises do support the conclusion when working together, in combination
-V argument: an argument with two or more premi
proper diagram (tree) for a given argument
-tree diagram is a schematic representation of the structure of an argument using letters P1, P2, P3, MP3, C, etc to represent the premises and conclusion and an arrow to represent therefore
problems with fact/opinion taxonomy
Opinions can be true or false or can be objective, not a clear way of making sense of this distinction, massive amounts of overlap, One way to think about it is that the fact/opinion divide is sometimes presented as mutually exclusive-- as though there ar
principle of charity: strawmanning vs steelmanning
-strawmanning: a fallacious argument that irrelevantly attacks a position that appears similar to, but is actually different from, an opponents position, and concludes that the opponents real position has thereby been refuted
-steelmanning: the opposite,
ambiguity
having two or more different but possibly quite precise meanings
referential vs grammatical ambiguity
-referential: an ambiguity that arises when a word or phrase could, in the context of a particular sentence, refer to two or more properties or things, (ambiguity of one word)
-grammatical: an ambiguity that arises when the grammatical structure of a sent
two kinds of referential ambiguity: homophony & polysemy
-homophony: words with identical form, but different meanings and the different meanings are unrelated or unconnected
-polysemy: words with identical form but with different meanings, these meanings though are more connected, and more related to one anoth
some sources of ambiguity: use vs. mention, bare plurals
use vs mention: usually, sentences use words, referring to their reference, but sentences may merely mention words, referring to the word itself
-ex: Tom said i was angry vs. Tom said, "I was angry"
-quotation marks are often used to mark the difference
-
how ambiguity is resolved in conversation
By using 'pragmatic' knowledge:
- Background attitudes and beliefs
- Facts about the utterance context
context-sensitivity, and how it's different from ambiguity
-Context-sensitivity: a word's meaning depends on the context in which it is used, has the same meaning but is slightly altered based on context
ex: tall for a 6 year old vs. tall for a bball player
-Ambiguity: a 'phonological/morphological item' has more
vagueness, and how it's different from ambiguity and generality
-Vagueness: a word has 'borderline' cases of a special kind, generates 'sorites' paradoxes
-Ambiguity: a 'phonological/morphological item' has more than one meaning
-Generality: a word applies to a wide range of objects that aren't very similar
-vague: re
generality, and how it's different from ambiguity and vagueness
-Generality: a word applies to a wide range of objects that aren't very similar
-Vagueness: a word has 'borderline' cases of a special kind, generates 'sorites' paradoxes
-Ambiguity: a 'phonological/morphological item' has more than one meaning
-vague: re
concept of borderline cases
-vague: baldness, where do draw the line? at what point are you bald?
implication: how it works and differs from literal meaning
an implication is a conclusion that can be drawn from something else, although it is not explicitly stated
conventional vs. conversational implication
-conventional: one that is part of the meaning of the sentence used, ex: Even Kevin can understand that, Conventional implication is something built into what the words mean (even though it doesn't affect the truth of the claim)-- so "they are poor but ha
rhetorical uses of ambiguity and vagueness to mislead
...
loaded language: associations vs truth-affecting meaning
-loaded language: language with a clear descriptive meaning and a positive or negative evaluative meaning, which is used in an attempt to persuade us to accept the evaluation conveyed by the language
-exploits associations that different words or phrases
analytic vs. synthetic claims
-analytic: true by definition
-synthetic:statement whose truth or falsity is not solely dependent upon the definitions-the meanings-of the words involved
empirical vs. non-empirical claims
-empirical: can in principle be settled by observation/can be checked for truth, empirical claim asserts an empirical fact
-non-empirical: the empirical evidence would not be sufficient to verify or falsify the,
strict 'philosophical' notion of definition
-too strict/rigid of definitions
-not all can fit into this category
-chair: the common name for the movable four-legged seat with a rest for the back...
what fallacies are
Fallacies are general categories of bad argument that are so common they have been given names for easy reference and identification
-an error or weakness in an argument that detracts from its soundness, but is disguised so that it may look like the concl
fallacies deriving from irrelevant, inadequate, or unacceptable premises
� some involve irrelevant premises.
- these premises are sometimes called 'non sequiturs' - even if true, provide no support at all for conclusion
� some involve inadequate premises
- if true, these premises provide some support for
conclusion, but not en
fallacies typically due to irrelevant premises
red herring
virtue/guilt by association
appeal to the person (ad hominem)
appeal to ignorance, tradition, novelty
red herring
the deliberate raising of an irrelevant issue during an argument, used to distract hearers and shift the topic to one about which the speaker is on firmer ground
virtue/guilt by association
accepting or rejecting a claim because it has been held by problematic individuals
-Examples: You know who else believed that the sky is blue? Hitler!
You know, Gandhi believed that abstaining from sex gives you spiritual power. So we should believe that
appeal to the person (ad hominem)
rejecting a claim by criticizing the person who makes it rather than the claim itself
� Personal attack
� Accusation of hypocrisy
� Circumstances (origin of person's view, person's job)
appeal to ignorance, tradition, novelty
-arguing that a lack of evidence against a claim establishes that claim
� appeal to tradition�arguing that a claim must be true just because it's part of a tradition -The appeal to novelty is a fallacy in which one prematurely claims that an idea or propo
fallacies typically due to inadequate premises
genetic fallacy
appeal to authority, popularity
hasty generalization
genetic fallacy
arguing that a claim is true or false solely
because of its origin
appeal to authority, popularity
� appeal to authority - arguing that a view must be true because some 'authority' says so
� appeal to popularity�arguing that a claim must be true merely because a substantial number of people believe it
hasty generalization
drawing a conclusion about a whole group
based on an inadequate sample of the group
fallacies due to unacceptable premises
inconsistency
equivocation
begging the question
false dichotomy
slippery slope
decision point (be able to distinguish from slippery slope)
inconsistency
the fallacy committed by an argument when it contains, implicitly or explicitly, a contradiction, usually between two premises
equivocation
the fallacy committed by an argument when a premise has two interpretations, one acceptable and one unacceptable, and when it is the unacceptable interpretation that is used by the conclusion
begging the question
-the attempt to establish the conclusion of an argument by using that conclusion (or something very similar) as a premise
-Example: God exists. We know that this because the Bible says so, and we should believe what the Bible says because God wrote it.
false dichotomy
asserting that there are only two alternatives to consider when there are actually more than two
-Example: Look, either you support the war or you are a traitor to your country. You don't support the war. So you're a traitor
slippery slope
assuming that taking a particular step will inevitably lead to a further, undesirable step (or steps), long chain events will occur
-ex: We absolutely must not lose the war in Vietnam. If South Vietnam falls to the communists, then Thailand will fall to t
decision point (be able to distinguish from slippery slope)
arguing that because a line or distinction cannot be drawn at any point in a process, there are no differences or gradations in that process
-ex: As Joe loses his hair, there is no point at which we can definitely say that Joe became bald precisely here.
what it takes for a deductive argument to be invalid
So, to show that a deductive argument is invalid, all you have to do is show that it is possible for the premises to be true and the conclusion false
different types of deductive validity: empirical, analytic
-empirical: Valid- but we can't tell it's valid just by understanding the words: we have to do science
-ex: 1. There is some water here
Therefore: There is some H2O here
-analytic: Guaranteed to be true due to the meaning of the word
-ex: Pat is a bachelo
the idea of argument form, and usefully generalizable features guaranteeing validity
-Guaranteed to be true due to the meaning of if... then
-Guaranteed to be true due to the meanings of or and not
-If a premise says anything like 'BLAH and NYAH', then you can conclude BLAH, and you can also conclude NYAH, particular term can make the arg
arguments that are valid in virtue of logical sentential operators
operators: 'not', 'and', 'or', and 'if... then', anything you can use to connect sentences, differs bc truth-functional: the truth of the sentence is determined by the truth of the components
the language of propositional logic & how it illuminates this notion of validity
We are interested when the form of an argument guarantees its validity, language of propositional logic is what allows us to determine whether an argument is valid or not, lets us check bc we are analyzing the form
-So the language of propositional logic
functions, truth-functions, truth-functional operators
-truth-functional connectives like 'and' and 'or' connect two sentences and form a new one whose truth is simply a function of the truth of the smaller sentences
-Truth functions take truth values as inputs and output truth values
-What makes a function t
why some kinds of validity can't be shown with propositional logic
All cows are mammals.
All mammals are animals.
Therefore, all cows are animals.
If we try to show the form in propositional logic:
A
B
Therefore, C
assessing acceptability, adequacy, relevance
-acceptability: consider each premise on its own, relevance: consider how each individual premise relates to the rest of the argument, adequacy: consider how all the premises together relate to the conclusion
ways to show that a deductive argument is invalid
� expose it as an instance of a fallacy of irrelevance or inadequacy
� show that there is some way that the premises could be true but the conclusion false
ways to show that an argument has a false premise
� provide an argument against the premise
� if the premise is a general claim, you might be able to find an example that disproves it, ie. a counterexample
ways to cast doubt on the truth of a premise
So you can argue that a premise is not known without showing it's false
� you only need a good reason to doubt the argument's soundness
� And you can show that something has gone wrong with the argument even if you don't know exactly what has gone wrong
t
identification of implication, loaded language, false confidence, selectivity
...
burden of proof
But to respond to an argument, you don't have to prove that one of these two things has gone wrong.
� The burden of proof is on the person putting forward the argument.
counterarguments
� try to show directly that the conclusion is false (counterargument)
-a method for arguing back by constructing a different argument attempting to show that the conclusion under criticism is false or problematic
counterexamples
a particular exception to a generalization used to show that the generalization relied upon in the argument is not universally true
general form of parallel reasoning (& method of absurd examples)
-try to show that other arguments of the same form are bad
-method of absurd examples: a method for arguing back by construction an argument with a closely parallel structure to the one being criticized, with true premises and with an obviously false or a
cases of parallel reasoning
-maybe it commits a fallacy like decision point. (We know that such arguments go wrong, even if we don't know why)
1. Two grains of sand don't make a heap.
2. For every n, if n grains don't make a heap, then n+1 grains don't make a heap. (Otherwise it wou
statistical arguments as type of inductive (risky) argument
-Argumentative statistics involves inference from observed things to unobserved things
-risky or defeasible arguments:
� These involves reasons or support rather than
proofs or deductions
� They aim to be very strong rather than outright deductively valid
degrees of strength vs. outright deductive validity
But not every argument is deductive: there are
risky or defeasible arguments
� These involves reasons or support rather than
proofs or deductions
� They aim to be very strong rather than outright deductively valid
-degree of strength: they differ in how m
the trade-off between support of premise and strength of argument
-There is a trade-off between how well supported the premise is and how well the premise supports the conclusion for inductive (risky) arguments, inductive: gap between premises and conclusion, cannot guarantee truth of conclusion, way to make gap smaller
descriptive vs. argumentative statistics
-Descriptive statistics involves reporting, depicting, and analyzing data about observations, data set and just trying to characterize median, mean, just trying to use the statistics to describe population, different descriptions can be more or less usefu
strengths & weaknesses of various notions of the central tendency of a data set
-central tendency:
The 'average/mean' is often used as the moral
or distillation of the whole data set.
Competing measures of centrality: ? Mean / truncated mean
? Median
? Mode
? Midrange
-weaknesses: Outliers are data points that are far away from the o
resistance to outlier effects
-When measure of centrality is highly affected by outliers, we say it has low resistance
central tendency vs shape of data, usefulness of standard deviation
-none of these measures of centrality give us much sense of the spread of data
-standard deviation: The mean amount that the values vary from the mean, tThen we can also ask how many SDs outside the mean a data point lies, thus refining the idea of an 'ou
importance of data visualization and opportunity for misleading presentation
to see how wide spread the data is, central tendency might not represent the wide range which can be misleading
ways to report data dishonestly
-cherry-picking data points
-choosing convenient measure or level of generalization
cherry-picking data points
-pick only the data points that support your view and ignore any that go against your view
choosing convenient measure or level of generalization
-Immigrants have a lower overall crime rate than non-immigrants...
True! But wait...
-Illegal immigrants have a higher overall crime rate than non-immigrants...
True! But wait...
-Illegal immigrants, controlling for age and gender, do not have a higher ov
criteria for adequate statistical study
-size of sample (law of large numbers & importance for p-value), p-value gets smaller when size increases
-lack of sample bias (adequate match of variety)
size of sample (law of large numbers & importance for p-value)
-too small of a sample can give you extreme data/outliers that can skew your data
-if the sample size is too small, its easier to get the correlation due to chance, the p value gets smaller when size increases
-p value: shows how likely it was to happen b
lack of sample bias (adequate match of variety)
-A sample is biased when the proportions of every relevant subgroup in the target don't match the proportions of the subgroups in the sample.
� That is, a sample should have the same sort of variety as its target population
achieving variety through random sampling, stratification
-randomness is harder to achieve than you might think
-A Stratified Random Sample
? The population to be sampled is first divided into groups of entities, one for each relevant group. These groups are called strata.
? A simple random sample is taken from
pitfalls for surveys
-voluntary response surveys and selection effects
-biased questions
voluntary response surveys and selection effects
? Composed of those people who voluntarily choose to respond to the call for data. (self-selected)
? This is the sampling method most commonly used in surveys distributed by mail.
? Beware an observational selection effect
� Strongly favors very strong op
biased questions
when a survey asks for information with questions which are worded in a way that tends to encourage a particular response
? 'Push-polling'� intentional use of biased questions
? Sometimes questions can be biased by the context in which they're asked.
post hoc ergo propter hoc
the fallacious argument that because something comes before an event, it must therefore be the cause of that event
E1 occurs before E2
Therefore E1 is a cause of E2
correlations
'associated with', 'linked', 'related', a mutual relationship or connection between two or more things
Negative & positive correlation
-Positive correlation
Binary: x and y come and go together
Scalar: x and y rise and fall together
- Negative correlation
Binary: when one comes, the other goes
Scalar: when one rises, they other falls
Scalar/binary correlation
* Scalar features come in degrees; binary features
don't
-positive binary correlation:
E1 is present when E2 is present and E1 is absent when E2 is absent
-negative binary correlation:
E1 is present when E2 is absent and E1 is absent when E2 is present
-p
why reliable joint occurrence or correlation is inadequate to conclude causation
-Correlations aren't always perfect, it comes in varying degrees
-Even reliable conjoint occurrence does not imply causation! Suppose:
� Whenever A occurs, E occurs later.
� Whenever E occurs, A occurred earlier.
Still, this is not enough to conclude caus
various types of misleading correlations
� Correlation due to mere chance
� Correlation due to common cause
� Correlation due to side effect (e.g. placebo) � Correlation due to reverse causation �Correlation due to regression to the mean
mere chance
the correlation is present solely because of chance
why a chance hypothesis cannot simply be judged by its likelihood
...
must be compared to likelihood of causal hypotheses
However unlikely these correlations are, the causal hypothesis is even more unlikely
importance of assessing plausibility of proposed causal mechanism (The processes or pathways through which an outcome is brought into being)
Even with a 'statistically significant' correlation, we must ask about a plausible mechanism for causation
� This is how we rule out the lemon-accidents
hypothesis, and the mountain-homicides hypothesis.
� However unlikely these correlations are, the caus
statistical significance and p-value
-When studies find a 'statistically significant' correlation, this still means there is some fixed chance, but p-value is less than or equal to .05, the result from testing or experimenting is not likely to occur randomly or by chance, but is instead like
reverse causation
-The more firemen go to a fire, the greater the damage to the house!
- The more a student is tutored, the worse their grade!
- The more diets you go on, the less likely you are to be normal weight!
swimmer's body illusion
-does training as a swimmer cause that physique, or does having a genetic capacity for that physique lead to excellence in swimming?
- time spend active/standing per day correlated with better health...
common cause
Some third factor C is responsible for both A and B, and as a result they are found together
importance of avoiding explanation freeze
It is hard to overlook the correlation between these two factors, and will settle with this as the solution
- avoid explanation freeze by coming up with a list of possible causes, and eliminate each one by trial and error
what it means for socioeconomic status to be a pervasive confounder
socio-economic status as a pervasive confounder for health, mortality:
- moderate wine intake?-having a glass of red wine everyday is healthy? only bc the wealthy can afford to do this and they have more $ for health care
- swimming vs other sports? (Some
side effect (including placebo)
-In some cases where C correlates with E because C occurs together with some other condition or side effect that actually causes E
-The placebo effect is a good example of causation due to side effect
-For example, studying captive animals might not give
power of placebo effects in various domains
-It refers to the real or felt improvement in a patient's condition that is due to beliefs about the treatment rather than the medical efficacy of the treatment itself
-it is important to investigate side effects to ensure that experimental results are re
regression to the mean
if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement�and if it is extreme on its second measurement, it will tend to have been closer to the average on its first
pervasiveness of regression to the mean leading to illusions of causation
When it looks like something is going wrong, often something is added to intervene and regression to the mean makes it look like the intervention was effective, but in reality it would have gotten better either way bc of regression to the mean
illusions of control & relevance of cognitive biases
-we often treat chance events as if they involve skill and are hence controllable
notion of confounding variable
a variable, other than the independent variable that you're interested in, that may affect the dependent variable
-This can lead to erroneous conclusions about the relationship between the independent and dependent variables
inadequacy of methods for controlling for them (confounding variables)
...
difficulty of defining adequate form for causal argument
-no standard from because some require necessary, sufficient, proximate, etc causes, causality has to do with relations in the world, arguments just pick out parts, lots of different forms possible
causal relevance: contributory vs primary cause
-contributory: not necessary nor can it cause the event by itself, only contributes
-primary: the cause of x, the main overarching cause
causally necessary vs. sufficient conditions
-If A is necessary for B (necessary cause) that means you will never have B if you don't have A. In other words, of one thing is a necessary cause of another, then this cause is required for the event to happen, when X is absent, Y cannot occur
-If A is s
proximate vs. distal causes
-A proximal cause is a cause that is close in time or sequence to the thing it is causing, immediately responsible for the event
-A distal cause is one you can trace back to the beginning: the very first event in a chain of causes, a distal cause is far a