**Name Calling****Ad Hominem****Responding to Tone****Contradiction****Counterargument****Refutation****Refuting the Central Point**

### Tag Archives: Deduction

## 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.

*: B = Biden will get the Democratic Presidential Nomination*

**Library**S = Sanders will get the Democratic Presidential Nomination

*: B∥S*

**Symbolization**2.) * Natural sentence*: If you take proper precautions, then you can help slow the spread of the novel coronavirus.

*: T = you take proper precautions*

**Library**S = you can help slow the spread of the novel coronavirus

*: T→S*

**Symbolization**3.) * Natural sentence*: Eat your vegetables and your meat before you have dessert.

*: V = eat your vegetables*

**Library**M = eat your meat

D = you have dessert

*: (V&M)→D; (V&M)≡D**

**Symbolization***material bi-conditional/material equivalence, stronger logical symbolization of the statement