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Using Modal Logic to Address Anxiety

This blog shows how to use modal logic with logic-based therapy to beat anxiety.

Key points

  • The imagination is a powerful faculty for creating possible worlds.
  • By imagining undesirable possible worlds, people often make themselves anxious.
  • This anxiety arises from a contradiction between such imagined possibilities and perfectionistic declarations that no such possibilities exist.
  • Modal logic can be used to interpret and draw inferences from such statements as they occur in people’s emotional reasoning.

Do you suffer from anxiety in your everyday life? This blog shows how a form of logic known as alethic modal logic can be used with logic-based therapy (LBT) to construct the emotional reasoning that generates your anxiety.

Emotional reasoning is the inferential, irrational thinking often involved in emotions such as anxiety, depression, guilt, grief, and anger, among other negative emotions. To illustrate, I use an example of test anxiety. What I say here about test anxiety, however, can be applied to other possible real-world scenarios about which you may be experiencing anxiety.

Logic-based therapy (LBT) is a form of philosophical counseling that I developed starting in the mid-1980s under the guidance of rational-emotive behavior therapy (REBT) founder Albert Ellis. REBT is the first form of cognitive-behavior therapy (CBT), and LBT is largely based on it.

Logic is the study of reasoning. Alethic modal logic studies reasoning by using modalities of truth such as possibility, impossibility, and necessity. Because the premises and conclusions of the chains of emotional reasoning involved in anxiety rely on the latter kinds of modalities, a modal analysis of anxiety appears to fit well with the use of modal logic.* While modal logic uses symbols to represent such operators as necessity (a square ◻) and possibility (a diamond ♢) in the expression of modal statements, I avoid the use of symbolism here, given the informal nature of this presentation.

Constructing Possible Worlds in the Imagination

Following Saul Kripke, I understand modal statements (ones using necessity and possibility) in terms of possible worlds. Hence, to say that a statement is necessary (for example, it is necessary that all triangles have three sides) is to say that it is true in all possible worlds, meaning that there are no contexts or situations in which the statement would not be true. On the other hand, to say that a statement is possible (for example, it is possible that the next President of the United States will be a Russian spy) is to say that there is at least one possible world in which it is true. The latter, of course, does not mean that this possibility is actualized; it means only that there is a comprehensive and consistent set of statements that describes a world in which this statement is true.

The human imagination is a powerful faculty for creating possible worlds. Indeed, it is due to our ability to imagine very unsettling, even if remotely possible, worlds that we often manage to make ourselves anxious. Keep in mind, too, that the same brain processes that are activated during thinking about actual worlds are activated when imagining possible worlds.

For example, imagine that it is the night before your final exam, and you are envisioning failing the exam. When you imagine such a world, you feel a sense of dread, for it is a world that you think must not exist. But you have imagined it, which means that it is a possible world. But such a possible world, you think, would be a horrible world. What is more, it is possible that the actual world will match this horrible world at a future time!

Now, there is a contradiction between the necessity of there not being such a world and the possibility of such a world, and it is this contradiction that sets the stage for your discomfort or anxiety. This is because something that you think must not happen may happen. You do not know if the actual world will match this possible world that you think must not be because the future has not yet played out.

Identifying Your Emotional Reasoning

In modal terms, the emotional reasoning behind your anxiety about the possibility of failing your exam would proceed like this:

  1. It is necessary that (necessarily) there not be a possible world (situation) in which I fail my final exam [demanding perfection].
  2. Therefore, it is necessarily true that if there is such a possible world, then it will be a horrible world [world damning].
  3. But there is such a possible world (the one I imagined).
  4. Therefore, it is necessarily true that such a possible world will be a horrible world.
  5. But it is possible that the actual world will be identical to this horrible possible world at a future time.
  6. Therefore, I can’t stop thinking about it [volitional can’t-stipation].

Notice how the above emotional reasoning, which generates your “test anxiety,” proceeds in terms of modal terms of possibility and necessity construed in terms of possible worlds. Thus, Premise 1 imposes an order on the world. It is held as a cosmic truth, that is, something that is true in all possible worlds, namely that there must not be any possible situations that would include your failing your exam. By imposing and demanding this order, you attempt to cosmically prescribe reality.

Thus, Premise 1 is not merely saying that it is necessarily true that there are no possible worlds in which I fail my exam. Rather, it is saying that it is necessary that it be necessary that there are no possible worlds in which I fail my exam. (This entails that necessarily, there are no such possible worlds since, in modal logic, "It is necessary that it is necessary that p" entails "It is necessary that p.") This is tantamount to demanding or decreeing, as a sort of cosmic law, that such possibilities not exist!

Premise 2, in turn, you deduce from Premise 1. The suppressed (assumed) premise in this deduction is that if it is necessary that there not be any possibility of your failing the exam, then such a possible world in which you do fail the exam would defy (contradict) a cosmic law. It would be tantamount to the loss of cosmic order, chaos. This would underscore the "horror" or "awfulness" of such a world. On a bad scale of 0 to 10, where 10 is the absolute worst possibility (a concept that itself is incoherent since there is no absolute worst possibility), it would be a 10.

Premise 3 is a reality check, where you realize that there is truly nothing impossible about your failing the exam. Indeed, it can conceivably happen since there is no internal contradiction in its happening, just your conceived demand that such possibilities be wiped clean from the cosmos.

Premise 4 is clearly a valid deduction from premises 2 and 3. Necessarily (it's true in all possible worlds that), if there is a possible world in which you fail the exam, then this world will be a horrible world. But there is such a world, namely the one you consistently imagined. Therefore, this world must be a horrible world.

Premise 5 then expresses awareness that future possibilities are unknown so that the dreaded possible world can, in fact, turn out to be the future that actually plays out.

The Conclusion, in point 6, is then deduced from Premise 5 and assumes that, under the conditions set by 5, it is impossible to exercise willpower over ruminating about such a “horrible” outcome.

A Modal Definition of Anxiety

In this analysis, anxiety thus emerges as a disturbing, ruminative perception of the possibility of a dreaded possible world matching the actual world, arising from a contradiction between the imagined possibility and a perfectionistic, universal demand that no such possibility exists.

This is the power of the imagination to frame possible worlds, construct modal statements about such imagined possibilities, and declare their impossibility. Then, deducing, from such cosmic decrees, the awfulness of the imagined worlds, we deny ourselves the capacity to navigate them.

However, it is not true in all possible worlds that you do not fail your exam. Such a statement is far-flung from statements like “All triangles have three sides” or “All bachelors are unmarried,” which are, arguably, necessarily true, that is, true in all possible worlds. Likewise, the “horror” of failing is overrated in comparison to much worse possible worlds (for example, one in which one suffers from a fatal disease). Similarly, the ability to navigate undesirable possibilities through the exercise of willpower is not impossible, so the use of modal terms such as “can’t” are misplaced.

The Emotional Reasoning Fallacies

There are, therefore, three fallacies engendered in Premises 1, 2, and 6, respectively referred to in LBT as demanding perfection, world damnation, and volitional can’t-stipation. First, you deduce world damnation from demanding perfection, and then can’t-stipation from world damnation. Notice, however, that if you gave up the demand for perfection (that there be no possibility of your failing your exam), then you would have no basis for damning the world were you to fail the exam. In turn, you would then have no basis to can’t-stipate yourself (tell you can’t control yourself) if you no longer damned the possible world in which you fail the exam.

Guiding Virtues to Counteract the Fallacies

The process of LBT offers guiding virtues to counteract these three fallacies:

  1. Metaphysical Security, which means feeling comfortable about the imperfections in the universe, including the possibility of failing at things.
  2. Cosmic Respect, which means that you accept the universe as such unconditionally, even if you do not like some of its possibilities.
  3. Tolerance or Patience, which means that you do not underestimate the power of your will by telling yourself you can’t endure or tolerate things.

Accordingly, if you experience anxiety, such as test anxiety, you can overcome your tendency to try to demand into existence a necessary truth, which leaves no possibility of failing. You can do this by working to be more metaphysically secure. This is itself possible by philosophically reframing the way you perceive failure in an empowering way that resonates with you. For example, you can see it as a learning experience since learning is possible only through trial and error.

Similarly, instead of damning the world, you can build cosmic respect by reframing the bad possibilities, for example, seeing them as that which makes the universe even better. If there wasn't the possibility of failure, then what would success even mean, and what worth would it have?

Similarly, instead of can't-stipating yourself, you can, for example, take advice from the Stoics and distinguish what truly is in your control from what is not, the former including the way you think and feel, the latter including the actions of others.


Clearly, you are in the driver's seat when it comes to imagining possible worlds and turning them into potential nightmares by demanding that they not exist and then ruminating about the possibility that they will actualize. LBT, with the use of modal logic, can help you to identify the modal premises and conclusions of your irrational emotional reasoning chains and their fallacies, and then, using the guiding virtues, along with an empowering philosophical interpretation, you can work toward overcoming your anxiety.


*The idea that modal logic could be a useful tool for LBT is due to University of Bucharest researcher Lidia Istrate, who presented a paper, “Could Modal Logic and LBT be a match?” at the 4th International Conference on Philosophical Counseling and Practice on February 12, 2022.

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