Modal Fallacy (1)

 A modal fallacy occurs when there is a logical error involving the use of modal terms such as "necessarily" (□) and "possibly" (◇). Modal logic deals with necessity and possibility, and mistakes in reasoning about these modalities often lead to modal fallacies. Here are some common types of modal fallacies and their descriptions:

1. Confusion between Necessity and Possibility

This type of fallacy involves mistakenly inferring that because something is possible, it is necessarily possible, or because something is necessary, it is necessarily so in all contexts.

Example:

• Fallacious reasoning: "It is possible for John to become president. Therefore, it is necessarily possible for John to become president."
• Correct reasoning: "It is possible for John to become president" only implies that there is at least one scenario in which John can become president, not that this possibility is necessary in all contexts.

2. Confusion between De Dicto and De Re Modalities

This involves confusing statements about the necessity or possibility of propositions (de dicto) with statements about the necessity or possibility of the properties of things (de re).

Example:

• De Dicto (about a statement): "It is necessary that 2+2=4."
• De Re (about a thing): "The number 4 necessarily follows from 2+2."

A fallacy occurs if one incorrectly infers properties about the subject from the properties of the statement.

3. The Fallacy of Modal Scope

This fallacy involves incorrect assumptions about the scope of modal operators, such as assuming that what is true in some possible world is true in all possible worlds.

Example:

• Fallacious reasoning: "If it is possible that I will win the lottery, then it must be that I will win the lottery in some possible world."
• Correct reasoning: "It is possible that I will win the lottery" means there is some possible world where I win, but it does not imply that this possibility holds across all possible worlds.

4. Necessary vs. Contingent Truths

This fallacy occurs when one mistakenly assumes that if something is true, it must be necessarily true, confusing contingent truths (true in some possible worlds) with necessary truths (true in all possible worlds).

Example:

• Fallacious reasoning: "Water boils at 100°C at sea level. Therefore, it is necessarily true that water boils at 100°C at sea level."
• Correct reasoning: "Water boiling at 100°C at sea level is a contingent truth; it is true given certain conditions, but it is not necessarily true in all possible worlds."

Examples in Modal Logic

To illustrate with modal logic notation:

1. Possibility to Necessity Fallacy:

   • Fallacious: ◇P → □P
   • Correct: ◇P does not imply □P.

2. Necessity to Possibility Fallacy:

   • Fallacious: □P → ◇P
   • Correct: While □P implies ◇P (if something is necessary, then it is also possible), reversing this incorrectly (i.e., ◇P → □P) is a fallacy.

Summary

Modal fallacies often arise from misunderstanding the principles of modal logic and the difference between necessary and contingent truths, de dicto and de re modalities, and the scope of modal operators. Understanding these distinctions helps avoid such logical errors.

For further reading, consider delving into:

• "An Introduction to Modal Logic" by G.E. Hughes and M.J. Cresswell
• "Naming and Necessity" by Saul Kripke
• "Modal Logic for Philosophers" by James W. Garson