Tag Archives: Logic

Concept-Checking: Nonrational vs. Irrational vs. Rational

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…

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An Initial Look into ‘Graham’s Hierarchy of Disagreement’

  1. Name Calling
  2. Ad Hominem
  3. Responding to Tone
  4. Contradiction
  5. Counterargument
  6. Refutation
  7. Refuting the Central Point
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The Principle of Charity (Revisited)

As an adjunct faculty member of Philosophy, one of my soapbox lectures to my students is the importance and application of the Principle of Charity. I mention it in the 1st Day Syllabus, I mention it again about half-way through the semester, and I include it as a short-answer question on the Final Exam.

At its core, the Principle of Charity (PoC) involves thinking well of people; their intentions, their capabilities, and their knowledge level. I take it very seriously because (1) it is the civil, respectful, and necessary thing to do and (2) it actually makes discussions or discourse more efficient by not wasting time on misunderstandings or by committing straw person fallacies. In either case, the PoC has a wide range of important uses and that is why I hammer it into to my students from the get-go. Below, I will explain what it is and give some pertinent examples as well as provide some good resources for further reading.

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Brute Facts: A Primer

There are, generally, two ways to explain a phenomenon: you can either describe what or who “brought it about” or you can describe it at a deeper, more fundamental level. These two approaches have sometimes been referred to as the ‘personal cause’ and the ‘non-personal cause,’ respectively. This bifurcation traces its origins back to Aristotle who originally described four distinct types of causes. But we won’t go into that here (instead, check out my post on Aristotle and the Four Causes). For our purposes, we just need to know that there are different ways of explaining a phenomenon and they are not synonymous.

Relevant video:

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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 More Natural Sentences

1.) Natural sentence: Either I will eat ham or I will eat turkey.
Library: H = I will eat ham, T = I will eat turkey
Symbolization: H v T

2.) Natural sentence: Yesterday, we danced, played, and ate so much!
Library:  D = we danced so much, P = we played so much, A = we ate so much
Symbolization: [D & (P&A)]

3.) Natural sentence: Harrison or John will win Prom King
Library: H = Harrison will win Prom King, J = John will win Prom King
Symbolization: H v J

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Sentential Logic Practice: Assessing Some Proofs

1.) A&B, B > (D&E), derive B > E
(A&B)
B
(D&E)
E
B > E

2.) S > (Q&R), S, derive R
S
(Q&R)
R

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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

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