Some most all reasoning
52 flashcards covering Some most all reasoning for the LSAT Logical Reasoning section.
Quantifiers like "some," "most," and "all" are key tools in logical reasoning that describe the extent to which a statement applies to a group. For instance, "all birds have feathers" means every single one does, while "some birds can fly" indicates only a portion. These terms help us make precise inferences and evaluate arguments by clarifying relationships between categories, which is essential for building strong logical skills.
On the LSAT Logical Reasoning section, questions often test these quantifiers in argument analysis, flaw detection, and inference problems. You'll encounter scenarios where statements involve partial overlaps or universal claims, with common traps like overgeneralizing "some" to mean "all" or ignoring exceptions in "most" statements. Focus on carefully parsing the language and diagrams to avoid faulty assumptions, as these elements frequently appear in strengthen/weaken or assumption questions.
Always double-check the scope of each quantifier before drawing conclusions.
Terms (52)
- 01
All (quantifier)
In logic, 'all' means every member of a group satisfies a condition, such as 'All cats are mammals' implying no exceptions.
- 02
Some (quantifier)
In logic, 'some' means at least one member of a group satisfies a condition, but not necessarily all, like 'Some cats are black' which could mean one or more.
- 03
Most (quantifier)
In logic, 'most' means more than half of a group satisfies a condition, such as 'Most students passed the exam' indicating a majority but not all.
- 04
No (quantifier)
In logic, 'no' means none of a group satisfies a condition, like 'No cats are dogs' indicating complete exclusion.
- 05
Universal affirmative
A statement that asserts something is true for every member of a group, typically starting with 'all', such as 'All A are B'.
- 06
Particular affirmative
A statement that asserts something is true for at least one member of a group, often using 'some', like 'Some A are B'.
- 07
Universal negative
A statement that denies something for every member of a group, such as 'No A are B', meaning none overlap.
- 08
Particular negative
A statement that denies something for at least one member of a group, like 'Some A are not B'.
- 09
Conversion of a statement
The process of switching the subject and predicate in a categorical statement, valid only for certain forms like 'No A are B' becomes 'No B are A'.
- 10
Obversion of a statement
Changing a categorical statement by negating the predicate and altering the quality, such as 'All A are B' becomes 'No A are not B'.
- 11
Contraposition of a statement
Switching and negating both subject and predicate in a categorical statement, valid for 'All A are B' as 'All not B are not A'.
- 12
Affirming the antecedent
A valid form of argument where if 'If A then B' is true and A is true, then B must be true.
- 13
Denying the consequent
A valid form of argument where if 'If A then B' is true and B is false, then A must be false.
- 14
Square of opposition
A diagram showing relationships between categorical statements, where contradictories cannot both be true or false, and contraries cannot both be true.
- 15
Contradictories
Two statements that cannot both be true and cannot both be false, like 'All A are B' and 'Some A are not B'.
- 16
Contraries
Two statements that cannot both be true but can both be false, such as 'All A are B' and 'No A are B'.
- 17
Subcontraries
Two statements that cannot both be false but can both be true, like 'Some A are B' and 'Some A are not B'.
- 18
Subalterns
A universal statement and its corresponding particular statement, where if the universal is true, the particular is true, like 'All A are B' implies 'Some A are B'.
- 19
Existential import
The assumption that a class mentioned in a statement exists, which affects the truth of particular statements like 'Some A are B' implying A exists.
- 20
Undistributed middle
A fallacy in syllogisms where the middle term is not distributed in at least one premise, making the conclusion invalid, as in 'All A are C' from 'All A are B' and 'All B are C'.
- 21
Illicit distribution
An error in syllogisms where a term is distributed in the conclusion but not in the premises, like distributing the subject in the conclusion without proper premise support.
- 22
Negation of quantifiers
The rule for negating quantified statements, such as negating 'All A are B' to 'Some A are not B', or 'Some A are B' to 'No A are B'.
- 23
Double negation
In logic, two negations cancel out, so negating a negated statement returns it to its original form, which can clarify complex arguments.
- 24
Exclusive or
A logical operator meaning one or the other but not both, unlike inclusive or, and it can appear in arguments requiring mutual exclusivity.
- 25
Inclusive or
A logical operator meaning one, the other, or both, which is the default in most logical statements unless specified otherwise.
- 26
Valid syllogism
A deductive argument with two premises and a conclusion where, if the premises are true, the conclusion must be true, following logical rules.
- 27
Invalid syllogism
An argument that appears to be a syllogism but breaks logical rules, leading to a conclusion that does not necessarily follow from the premises.
- 28
Flaw: Confusing all and some
A common error in arguments where 'all' is mistakenly treated as 'some' or vice versa, weakening the logic by overgeneralizing or undergeneralizing.
- 29
Flaw: Affirming the consequent
An invalid argument form where from 'If A then B' and 'B is true', one concludes 'A is true', which does not logically follow.
- 30
Flaw: Denying the antecedent
An invalid argument where from 'If A then B' and 'A is false', one concludes 'B is false', ignoring other possibilities.
- 31
Strategy for quantifier questions
When evaluating arguments with quantifiers, diagram the statements to visualize relationships and check for logical consistency before assessing the question.
- 32
Diagramming 'All A are B'
Represent 'All A are B' as a subset, where the entire A circle is inside the B circle, helping to see implications in logical puzzles.
- 33
Diagramming 'Some A are B'
Represent 'Some A are B' as an overlap between A and B circles, indicating at least one shared element without full inclusion.
- 34
Diagramming 'No A are B'
Represent 'No A are B' as separate circles with no overlap, showing complete exclusion between the groups.
- 35
Diagramming 'Some A are not B'
Represent 'Some A are not B' as part of A outside of B, indicating at least one A that does not belong to B.
- 36
Strengthening with quantifiers
To strengthen an argument involving quantifiers, provide evidence that shifts a 'some' claim toward 'all' or confirms the majority in 'most' statements.
- 37
Weakening with quantifiers
To weaken an argument, introduce counterexamples that contradict the quantifier, like showing exceptions to an 'all' statement.
- 38
Assumption in quantifier arguments
Arguments often assume that quantifiers are accurately applied, so identifying unstated assumptions can reveal flaws in reasoning.
- 39
Quantifier in necessary conditions
Quantifiers can modify necessary conditions, like 'All A require B', meaning B is necessary for every A, which must hold without exceptions.
- 40
Quantifier in sufficient conditions
Quantifiers can apply to sufficient conditions, such as 'Some A guarantee B', indicating that for at least one A, B follows.
- 41
Common trap: Overgeneralization
Assuming a 'some' example represents 'all', which is a flaw that can invalidate conclusions in arguments.
- 42
Common trap: Undergeneralization
Treating an 'all' claim as only 'some', leading to weaker conclusions than the evidence supports.
- 43
Existential fallacy
Assuming that a universal statement implies existence, like thinking 'All unicorns have horns' means unicorns exist.
- 44
Categorical syllogism
A deductive argument with two premises and a conclusion, each being a categorical statement with quantifiers.
- 45
Distributed terms
In a categorical statement, a term is distributed if it refers to all members of its class, as in 'All A are B' where A is distributed.
- 46
Undistributed terms
In a statement, a term that does not refer to all members, like the predicate in 'All A are B' where B is undistributed.
- 47
Venn diagram for logic
A visual tool using overlapping circles to represent relationships between sets, useful for analyzing quantifier statements on the LSAT.
- 48
Immediate inference
Drawing a conclusion directly from a single statement, such as converting or obverting it, which must follow logical rules.
- 49
Mediate inference
Drawing a conclusion from two or more statements, as in syllogisms, requiring valid connections between quantifiers.
- 50
Quantifier ambiguity
When a quantifier like 'some' is vague in context, leading to misinterpretation, such as whether it means 'at least one' or 'a few'.
- 51
Flaw: Hasty generalization
Making a broad quantifier claim based on insufficient evidence, like concluding 'all' from a single 'some' instance.
- 52
Flaw: Sweeping generalization
Applying a general rule to a specific case without justification, often misusing 'all' in arguments.