- Name Calling
- Ad Hominem
- Responding to Tone
- Contradiction
- Counterargument
- Refutation
- Refuting the Central Point
Tag Archives: Induction
An Initial Look into ‘Graham’s Hierarchy of Disagreement’
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.
Sentential Logic Practice: Symbolizing Natural Sentences
1.) Natural sentence: Either Joe Biden or Bernie Sanders will get the Democratic Presidential Nomination.
Library: B = Biden will get the Democratic Presidential Nomination
S = Sanders will get the Democratic Presidential Nomination
Symbolization: B∥S
2.) Natural sentence: If you take proper precautions, then you can help slow the spread of the novel coronavirus.
Library: T = you take proper precautions
S = you can help slow the spread of the novel coronavirus
Symbolization: T→S
3.) Natural sentence: Eat your vegetables and your meat before you have dessert.
Library: V = eat your vegetables
M = eat your meat
D = you have dessert
Symbolization: (V&M)→D; (V&M)≡D*
*material bi-conditional/material equivalence, stronger logical symbolization of the statement