Truth Tables and Logical Fallacies Explained

Posted on Jan 25, 2025 in Philosophy and ethics

Truth Tables

We use two distinct methods to do this:

  1. Using statements in tables.
  2. Using the truth of the laws of logical inference (transformation rules).

How to Make a Truth Table

The goal of building a truth table is to perform the calculation that allows us to know if the logical formula is:

  • A tautology (all true)
  • An indeterminacy (alternating V and F)
  • A contradiction (all false)

The steps are:

  1. Determine the number of atomic variables.
  2. Calculate the number of rows in the table using the formula 2n (where n is the number of variables).
  3. Establish the dominant logic symbol of the logical formula to determine the outcome of our table (the column gives you the result).
  4. Finally, calculate for each of the connectives to reach the main or dominant one.

Informal Logic

Informal logic, also known as the logic of good reasons, studies the conditions to be met by arguments to be correct. Arguments convince our partners of something to show them what we say is correct, but often we make mistakes in our reasoning.

To the arguments that look correct but are not, we call fallacies. When expressed intentionally, fallacies are called sophisms. When expressed without intention, they are called paralogisms.

Formal Fallacies

Affirming the Consequent

It resembles the Modus Ponens (MP) or affirmation of the antecedent:

  • If you smell pollen, then allergy comes.
  • I’m allergic.
  • So I smelled pollen.

Denial of the Antecedent

It is similar to Modus Tollens (MT) or denial of the consequent:

  • If I smell pollen, then the allergy comes.
  • I do not smell pollen.
  • Therefore, I do not have the allergy.

Disjunctive Syllogism Fallacy

It is similar to Syllogismus Disjunctivus (SD). If one term is denied, the other is true:

  • You like music or you like reading.
  • You like music.
  • Then you do not like reading.

Informal Fallacies

Ambiguity

They use words with different meanings or ambiguously. Among them we can distinguish:

  • Equivocation: Only man is rational. No woman is a man. Therefore, no woman is rational.

  • Excluded Middle or False Dichotomy: You are with me or against me.

  • Complex Questions: Have you stopped bothering your cousin? (Assuming that you bother your cousin).

Material Fallacies

There are two groups:

Data Insufficiency

Where the premises do not provide enough support for the conclusion to be drawn from them, and yet, we try to convince you otherwise. These may include:

Lack of Evidence

  • The exception proves the rule (false evidence).

  • I bet twice on the same number and won (poor generalization).

  • There must be life beyond death, otherwise this life is meaningless (appeal to adverse consequences).

Lack of Causes

  • We prayed to the Virgin and then it rained. Therefore, praying to the Virgin is the cause of rain (false cause or post hoc ergo propter hoc).

  • When the bell rings in Villaluenga, students leave for recess in a courtyard of a Toledo high school (accidental correlation).

It differs from previous events in that they need not succeed in time in a corresponding manner.