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Necessary Assumption
A statement that must be true for an argument's reasoning to work; if false, the argument falls apart.
What is a necessary assumption in logical reasoning?
An unsaid belief required for the premises to lead to the conclusion.
Logical gap
The gap in reasoning that a necessary assumption fills to support the conclusion.
Negation Test
A technique for identifying necessary assumptions by negating an answer choice and seeing if the argument collapses.
Causal leaps
Assumptions made when an argument concludes one event causes another.
Quantifier shifts
Assumptions that occur when there is a transition between general and specific terms like 'some,' 'most,' or 'all'.
Comparison/analogy assumption
Assuming that two items are similar in relevant aspects if they are treated as relevantly similar in the argument.
Affirming the consequent flaw
A logical fallacy where the presence of a consequent also implies the presence of the antecedent.
Sufficient Assumption
A statement that, if added to the premises, makes the conclusion logically follow.
How does a sufficient assumption differ from a necessary assumption?
A sufficient assumption seals the argument, while a necessary assumption is required for it to hold.
Identifying the conclusion
Key step in discerning if an assumption is necessary or sufficient.
Bridge between premises and conclusion
A function of sufficient assumptions that connects evidence directly to the conclusion.
Causal assumption
An assumption that eliminates alternative explanations for a causal claim.
Conditional statement flaw
A logical error when the argument incorrectly assumes a two-way condition from a one-way premise.
Common wording for necessary assumptions
Includes phrases like 'depends on' or 'assumes'.
Examples of necessary assumptions
Include statements that link premises to conclusions without which reasoning fails.
Strength of assumption
Necessary assumptions are often minimal, while sufficient assumptions are stronger and bridge gaps.
Proof reading sufficient assumptions
Pretend the answer choice is an extra premise and check if the conclusion can still be false.
Revising argument with a sufficient assumption
Re-work the argument as if the assumption is true to ensure the conclusion follows logically.
Common pitfalls with necessary assumptions
Choosing overly strong statements, confusing necessary with sufficient, and incorrect negations.
Common pitfalls with sufficient assumptions
Choosing answers that merely strengthen rather than force the conclusion.
Scope shifts in argument
The need for a sufficient assumption to address shifts from 'some' to 'all' in premises to conclusions.
Example of a necessary assumption
“There were no other changes in those neighborhoods that would have prevented crime from decreasing.”
Example of a sufficient assumption
“A product is truly eco-friendly if and only if it uses biodegradable packaging.”
Logical reasoning skill enhancement
Identifying necessary and sufficient assumptions helps strengthen critical thinking and logical argumentation.
Typical necessary assumption question stems
“Which of the following is an assumption on which the argument depends?”
Typical sufficient assumption question stems
“Which assumption justifies the argument?”