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If I commit to X, am I always committing to not ~X?

In classical propositional logic, double negation always the same as not negating at all. I'm curious if this principle applies to commitments. In general it seems to be true. If I commit that my homework will be done, I commit that my homework will not be undone.

Non-classical logic does not always admit this rule. I'm curious if there are philosophers who have explored the concept of commitment using logic where a commitment to ensure X is not necessarily a commitment to ensure the compliment of X does not come to pass (or a related phrasing). Clearly logics such as intuitionistic logic have been explored, but have philosophers explored applying them to the concept of commitments?

Cort Ammon
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  • If the object of commitment is a proposition (eg that your homework will be done), then (classical or intuitionistic or whatever) propositional logic applies directly. – E... Jul 27 '19 at 14:36
  • Perhaps this question might be a first attempt at understanding Commitment? https://philosophy.stackexchange.com/questions/40068/what-is-the-difference-between-responsibility-and-commitment – Paul Ross Jul 27 '19 at 14:43
  • Commitment is a modal construct, a form of should. Negation does not work the same with most modal concepts. The most obvious example is temporal: If I will do not X, that doesn't necessarily mean I will not do X. Maybe I will do both X and not X, at different times or under different circumstances. The modality injects a dimension into the logic that keeps X from being a fully-formed proposition. – hide_in_plain_sight May 05 '20 at 01:58

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If I commit to X, am I always committing to not ~X?

..where a commitment to ensure X is not necessarily a commitment to ensure the compliment of X does not come to pass...

Call X a group of results. Assume you have commited to make Group X a reality. Your commitment about what actions are permissible depends on the content and scope of not-X.

First, call not-X the group of results that would, if realized, specifically prevent the existence of Group X. Your first commitment (create X) requires your commitment to avoid creating Group not-X.

However, a change in definition makes a difference. Call not-X the group of all results which are not part of X, whether or not a result within Group not-X could have any possible effect on Group X. Now your commitment is more open. You would remain free to pursue actions which were irrelevant to the creation or prevention of Group X.

I can offer this answer to clarify this issue, but I cannot name a specific philosopher who addressed it. I recommend that you focus on those who worked in deontic logic. "Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts." (Wikipedia).

Mark Andrews
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