Though this is a relatively rare distinction to be made, it is nonetheless an important one. Nonrationality is NOT the same thing as irrationality. These two terms are different and must be recognized as such. While we are at it, we should discuss what ‘rationality’ actually is…
Continue readingCategory Archives: Epistemology
An Initial Look into ‘Graham’s Hierarchy of Disagreement’
- Name Calling
- Ad Hominem
- Responding to Tone
- Contradiction
- Counterargument
- Refutation
- Refuting the Central Point
Sentential Logic: Rules of Inference for Deriving Proofs
EXCELLENT RESOURCE AVAILABLE HERE: https://courses.umass.edu/phil110-gmh/text/c05.pdf
Ampersand-In (&I): If one has available lines, A and B, then one is entitled to write down their conjunction, in one order A&B, or the other order B&A.
Ampersand-Out (&O): If one has available a line of the form A&B, then one is entitled to write down either conjunct A or conjunct B.
Wedge-In (∨I): If one has available a line A, then one is entitled to write down the disjunction of A with any formula B, in one order AvB, or the other order BvA.
Wedge-Out (∨O): If one has available a line of the form A∨B, and if one additionally has available a line which is the negation of the first disjunct, ~A, then one is entitled to write down the second disjunct, B. Likewise, if one has available a line of the form A∨B, and if one additionally has available a line which is the negation of the second disjunct, ~B, then one is entitled to write down the first disjunct, A.
Double-Arrow-In (↔I): If one has available a line that is a conditional A→B, and one additionally has available a line that is the converse B→A, then one is entitled to write down either the biconditional A↔B or the biconditional B↔A.
Double-Arrow-Out (↔O): If one has available a line of the form A↔B, then one is entitled to write down both the conditional A→B and its converse B→A.
Arrow-Out (→O): If one has available a line of the form A→B, and if one additionally has available a line which is the antecedent A, then one is entitled to write down the consequent B. Likewise, if one has available a line of the form A→B, and if one additionally has available a line which is the negation of the consequent, ~B, then one is entitled to write down the negation of the antecedent, ~A.
Double Negation (DN): If one has available a line A, then one is entitled to write down the double-negation ~~A. Similarly, if one has available a line of the form ~~A, then one is entitled to write down the formula A.