Standard treatments of cognitive-behavior therapy (CBT) rely primarily on truth-functional logic to help clients overcome their irrational thinking. Thus, the client learns to avoid overgeneralizations (“My partner is always complaining”) and false hypotheses (“My boss did not say hello to me today so he is intending to fire me”) by paying careful attention to the empirical evidence (“My partner complains more than I prefer but not always”); and alternative explanations (“Maybe my boss was preoccupied with something when he ignored me this morning”).
While the value of the latter is inestimable, this empirical approach does not address locutions that are not truth-functional, that is, neither true nor false. Consider “I must never fail,” “Others should always treat me fairly,” and “I am a bad person.” These locutions are often performed in the context of people’s emotional reasoning, where they support emotions such as depression, anxiety, anger, and guilt. The meaning or purpose of such locutions is primarily a function of illocutionary force rather than propositional content. I call this new logic illocutionary force logic, or force logic for brevity. A version of force logic, v. F2, is presented here.
The illocutionary force of a locution is its potential to perform a certain type of speech act when spoken. For example, the locution “I must never fail” has the potential to make a demand on oneself when spoken to oneself. Hence, viewing the latter performance as a report of a subjective state (“I don’t want to fail”) would confuse truth-functional logic with force logic. This is because this performance would ordinarily not be intended by the actor to self-report their subjective desire, but rather to make a demand on oneself.
Operationally, the use of “must” signifies that
(a) The actor is making a demand, and
(b) This demand ranges over a modal “necessity” operator.
In modal logic (the logic of necessity and possibility), the operator in (b) is commonly symbolized as “□” to mean “true in all possible worlds.” For the demand in (a), F2 uses the lightning bolt “Ϟ” to symbolize an illocutionary force operator followed by “s-dd” to specify self-referential demanding (Cohen, 2026):
Ϟ s-dd [(□ I do not fail)]
Hence, in the very act of performing the above locution, I am demanding that it be true in every possible set of circumstances (“true in all possible worlds”) that I do not fail.
Applying Force Logic to Emotional Reasoning
Force logic maps onto truth-functional and modal components of emotional reasoning. For example, consider:
- I must never fail.
- I failed my exam.
- So, I am a total failure.
F2 uses the symbol “Ϟ rt” to symbolize the act of reporting. So, Premise 2 can be represented as “Ϟ rt (I failed my exam).” It effectively reports that I failed my exam in the world I presently inhabit. F2 also uses “Ϟ s-dn” to signify the act of self-damning. Hence, when symbolized in F2, the client’s emotional reasoning looks like this:
- Ϟ dd [□ (I do not fail)]
- Ϟ rt (I failed my exam)
- ∴ Ϟ s-dn [□ (I am a failure)]
In the above symbolized inference, premise 1 makes a demand (Ϟ dd) and does not itself make a truth-functional report (Ϟ rt). The universal state of affairs it demands (□) could be said to be unrealistic or not likely to be achieved based on knowledge gleaned from human experience.
Focusing on the improbability of what is demanded would miss the point that premise 1 is making a demand, not a report or a prediction that could be tested. Demands, themselves, are neither true nor false. So, a therapist who told a client that premise 1—that “I must never fail”—was false would be misleading the client.
Premise 2 does, however, make a report that is truth-functional and is therefore subject to disconfirmation. “No, actually, the teacher curved the grades, and you got one of the highest grades in the class!”
Due to the necessity operator (□) in 3 (signifying being a “total” failure, that is, being a failure “in all possible worlds”), this conclusion can also be empirically challenged, for example, by asking the client if they were successful at anything else.
In some cases, a client may mean that they are a failure just because they failed their exam, without regard to any other previous or future successes or failures. Then the conclusion would be formulated without the necessity operator:
(3*) Ϟ s-dn (I am a failure)
As such, 3* would not make any truth-functional report, except that I failed the exam in question.
Accordingly, force logic can be integrated into truth-functional and modal logic to help to clarify the specific speech acts performed in cognitive emotions like anxiety and depression; what they commit us to, the logical relationships they bear to one another, and what experience can—and cannot—establish with respect to them, thus avoiding potential for considerable confusion.
