Word for knowing what to do and not doing it

If you are thinking of a psychological term that's experienced recent popularity, it could be executive dysfunction. In the psychological literature this condition is quite complex, but in common discourse between individuals (particularly those suffering from depression or other debilitating mental health issues), this is the term used for exactly what you've described.

It depends on the context, but "timid" could describe that situation. It means "lacking in courage or confidence". For example, if one knows they should speak out against something but hold back anyway they might be described as timid.

But that same word may not make sense for a situation like a teenager staying out past their curfew. They know they are supposed to be home by 8, but they stay out later anyway. That would be considered "rebellious" not "timid", so it really can depend on the reason for not doing something that they know they should.

In dialectical behaviour therapy, I learned about willfulness. It can apply in that it affects one's willingness to do what one knows one ought to do. Another word: Procrastinating. Also: Uninvested. Apathetic too may apply. "Conflicted." "Frozen" "Undecided" "Scattered" "Distracted"

From a biblical perspective, the word you might be looking for--though not likely a word Plato might have used--is sin. Yes, the word is sin.

James, the half-brother of Jesus of Nazareth, used the word in his letter to the Diaspora:

Therefore, to one who knows the right thing to do and does not do it, to him it is sin (James 4:17 NASB).

In 1973, Dr. Karl Meninger released a book entitled "Whatever Became of Sin?" Here is how a bookseller describes the book:

Dr. Menninger, educated, intelligent and highly respected gives a good insight into social interaction. Society no longer recognizes sin as sin, hence the condition we are in. Written in the early 70's, one would think it was written last year.

The word you are looking for may be lethargy.

Lethargy means lack of interest or enthusiasm to do anything. It may be a mental condition

see the link

https://www.yourdictionary.com/lethargy

If I am not mistaken, the word you are searching for is akrasia. See this related question or Wikipedia

Factors that lead me to believe this are

1. It is of Greek origin
2. It describes a state of mind or human condition as you asked
3. It is related to Plato

To be honest I can not really add anything meaningful further than Wkipedia, maybe the headline definition helps as a motivation to read the article:

Akrasia [...] is described as a lack of self-control or the state of acting against one's better judgment.

I sincerely hope this is the word you are searching for, as I just performed a significant search effort after being in the same situation as you and being bugged out several weeks by not being able to remember the word :D

Q.

Word for knowing what to do and not doing it

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A. procrastinating

procrastinate; verb [ I ] Ref C.E.D.

to keep delaying something that must be done, often because it is unpleasant or boring:

Example

I know I've got to deal with the problem at some point - I'm just procrastinating.