Definitions Flashcards
what is logic?
is the the formal study of valid reason; “formal” because it is intrested in the forms of inferences
Reasoning (inference)
is the move from premises to conclusion
Forms
are empty (without context) and repeatable (adaptable to any context)
Structures are…
content-context sensitive
Argument
is an inference addressed to an audience aimed to convince that the drawn conclusion is true= dialogic form
Difference between reasoning (inference) and argument
is that the inference is simply the mind process that draws conclusions from premises, meanwhile the argument is the expressed form of an inference (inference: just in the mind; argument: expressed inference)
Critical thinking
is the informal logic, informal analysis of the inferences in contents– it is context and content sensitive. The inferences are studied in the concrete contexts and with reference to the contents
Justification
Justifying
is the relation between premises and conclusions– it is used in the expressed form of an inference, meaning just in the arguments
Giving reasons to believe
Reasons
is expressed by declarative sentences; they are thesis or proposistions– as such they can be true or false, strong or weak, relevant or irrelevant in relation to the conclusion
Proof
is an argument wherefor there are no counter-reasons
The proofs are true only relatevely the language in which they are expressed
Validity
it means formally adequate
Two types of validity:
- syntactic: it means based on language, that follows the grammatical rules of the language; syntactically valid
- semantically: it means that an argument is true in every possible world in which the inferences are true, thus also the conclusion
Soundness
Formal validity (both syntactically and semantically) + premises are true in OUR world
Irrelevant reasons
have no relation to the conclusion
Weak reasons
may have some relation, but there can be counter-reasons
Proving
giving strong justifications – there is no counter-reason, no counter-example
Good argument
- has validity in inferences= formally adequate
- premises and conclusions are true
- is sound= is formally adequate and the premises are true in our world (convincing)
A sound argument rationally forces us to accept its conclusions (it’s convincing)
Dialectics
theory and practice of intellectual confrontations
Pragmatics
analysis of the effects of speaking
Reconstructing arguments
- look at possible premises, conclusions and indicators
- isolate the T-conclusion
- remove redundancies and rethoric artificies
- make allusions explicit
- add implicit premises or conclusions
- in case of complex arguments, make a list of sentences (=PARAPHRASIS)
- then represent the justification relations by a diagram (justification expressed by arrows)
Data + Warrant–Claim
Data= preliminary givens (unrestricted contents)
ex. Amal was born in Italy
To move from Data to Claim we need a Warrant
Warrant= other givens
ex. because her parents are italian
Data + Warrant + Backing– Claim
Backing= other data, most frequently generalizations expressing rules/ conventions, common sense principles
Data + Warrant + Backing– Claim + Qualifier
Q= adverbial expressions diminishing or increasing the epistemic (credibility) of the C
They are qualifier, which modifies the claim such as “probably”, “presumably”, “very likely”
Data + Warrant + Backing + Rebuttal– Claim + Qualifier
Rebuttal= counter-reason which blocks the move from D to C
ex. unless she had changed her citizenship
Data + Warrant + Backing + Rebuttal Exclusion – Claim + Qualifier
Rebuttal exclusion (RE)= D-premise importing rebuttal exclusion. Anticipates and rejects the counter-reason (rebuttal). To reject the Rebuttal one has therefore to import some other data
ex. since she did not change her citizenship
Difference between Sentential and Predicate Logic
- Sentential L: inferences based on the connections of sentences
- Predicate L: inferences based on the connections of predicates
Sentences
= declarative premises and conclusions in arguments
Can be true or false
Are truth apt (it is true/false that…)
The alethic feature (truth-related) is only formal: it does not regard the effective possibility of knowing whether the sentence is true or false
Sentential operators
- if..then
- or
- and
- not
- if and only if
They form compound (complex) sentences (the others are simple (atomic) sentences
TRUTH-FUNCIONATILITY - Negation: Neg.p is true only if p is false
- Conjunction: p and q is true iff both p and q are true
- Disjunction: p or q is true iff p or q is true; at least one must be true (they can be both true)
- Conditional: if p then q is true iff it is not the case that the first is true and the second is false
- Bi-conditional: iff p then q is true iff p and q are both the same truth value: both false or both true
Predicative inferences
are revealed by quantifiers (some, all, any, nobody)
Non-quantified sentences
are made out of:
- objects (singular terms)= anything that can have properties
- properties (predicates)= way of being or acting of an object. Are unsaturated empty entities
objects + properties= sentences= state of affairs
Truth (five criteria to establish truth)
it is context and contents sensitive
truth does not exclude falsity; untruth does not imply falsity
- Validity
- Alethic= truth is a contextual value
- Strength= the intended informativeness of sentences (amount of probable truth)
- Relevance= effective connection between premises and conclusions
- Fecundity= there is no vicious circularity– the conclusions adds something new
Fallacies
= violation of one of the five criteria
- Formal= violation of validity: inferences seem to be valid
- Alethic= violation of truth: premises seem to be true
- Of strength= inductive fallacies: something is lacking, the amount of information is disguised or misrepresented, the inference is elusive
- Of relevance= violation of pertinence: there seems to be a relevant connection between premises and conclusions
- Of fecundity= circular reasoning: the conclusions seem to add something new but only repreats the premises
All of these are violation of truth
How is it called a wrong exemplification
Fallacy of accident
How is it called a wrong generalization
Converted accident
Main fallacies in sentential logic (SL)
- AD= affirming an inclusive disjunction
- AC= affirming the consequent
- DA= denying the antecedent
Main fallacies in PL
- wrong “Some”elimination= exemplification
- wrong “All”introduction= generalization
Fallacies of irrelevance
- ad hominem: premises refer to some property of the proponent and not to the thesis under discussion
- ad verecundiam: a thesis is given as true because it comes from some authoritative source
- ad populum: it appeals to popular opinion and overrates common sense
- ad baculum: retaliation, threat
- ad misercordiam: arises pity, gains sympathy
- ad ignorantiam: drawing a conclusion from the negation of the other thesis
Fallacies of circularity
the conclusion is implicitely included in the premises
- begging the question: the argument postulates what is to be proved
- double bind: the conclusion is justifies by the premises. the premises are justifies by the conclusion
- presupposition: arguments based on implicit, arguable assumptions
Alethic fallacies
Untruth can be concealed by a variety of means
- verbal: manipulations and deceits due to ambiguity– more than one word for one thing, more than one thing for one word
- conceptual: the general difficulty of ascribing certain predicates-properties to names-objects
Vagueness and its fallacies
is a property of things that do not have definit
e borders– imprecise limits of concepts
Most predicates are vague or/and prospectival
Vague predicates create vague sentences and therefore vague truths.
Fallacies with vagueness:
- concepts are expressed in a vague way
- taking advantage of definitional vagueness
Alethic fallacies= covered deceptions– two mains
- Lying= saying some believed falsity with the intention to deceive
- Misleading= saying some believed truth with the intention to deceive
Other alethic fallacies
- double bind+ generalization:
- victim blaming
- Strawman: presenting a wrong version of the opposite thesis so that it is easier to discredit it
- Extrapolation: isolating a thesis in a complex discourse
Real arguments
are inductive, meaning incomplete deductions that possess two main features:
- their correct form is obtained by weakening the premises and or the conclusion
- they add new premises to D that may change the conclusion
inductive arguments can be strong or weak (the deductive form instead is valid or invalid
Strength of sentences
= the amount of information that a thesis P is inteded to convey. It has nothing to do with:
- the truth (the exclusion of other atlernatives)
- argumentative plausibility (absence of counter-examples
The strength:
- is a gradualized value
- the negations of strong assertions are weak (most probably also true)
- extremely general assertions are inductively weak and argumentatevely strong
- very strong assertions are most frequently false (and more easily falsified)
inductive fallacies
are semi-formal fallacies that imply:
- excess of categoricalness (presenting smth as universal-objective what is actually partial-subjective)
- inadequate or elusive information
There are:
- wrong generalizations
- fallacy of accident: what is empirically observed is categorically true and necessary
- converted accident: generalizations created on particular cases or even just one
- wrong sample
- wrong examples: against generalizing theses, we search counter-examples
- false analogy: is a weak comparison between things that only accidentally share a property. Weak analogies are used to justify generalization (strong comparisons are given by sharing distinctive and intrinsic properties)
- suppressed evidence: by adding new premises the conclusion may change
