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Starting with my own (not Buddhist) analysis perhaps there are two types of "traditional/typical idea of a western self":
By "social" I include everything that would be impossible if one were (perhaps by some miracle of Science Fiction) alone in the world:
I'll gloss over these, they aren't the main focus of this answer.
A lot of the suttas are by the Buddha and intended for monks who have "gone forth" and renounced these kinds of attachments and possessions and types of identity (also including "caste").
I think that Buddhism doesn't deny that such exist -- and I think it advises lay-people on how to fulfil some of their social obligations skilfully and wisely (e.g. Sigalovada Sutta (DN 31)) -- but that's not specifically "doctrine about self" (I'd consider it rather doctrine about "morality" etc.), and not the main focus of the suttas.
Still if you are interested in what advice can be found in the suttas specifically for lay-people, that's collected in this book titled The Buddha's Teachings on Prosperity: At Home, At Work, in the World.
Even so I think it's safe to say that, according to Buddhism, these things are all sankharas. They are (therefore) impermanent, not permanently satisfying, and their loss is an occasion for grief if one is unwisely attached to or clinging to them -- which is why (traditionally Meeting the Divine Messengers) the Buddha was inspired to "go forth" from his life as a lay-person.
By "personal" I mean to include what you may be aware of when you're alone in a forest -- as in fact a Bhikkhu might be or might have been.
Briefly, Buddhist doctrine categorises those as the "five aggregates".
Perhaps I'm wrong but I think the "form" includes the body (though there is another word for body, i.e. kāya) -- so you might say, "I have a body", or "I am a body", or "I die when the body dies", and so on.
Similarly for the other aggregates -- famously in the West, cogito ergo sum ("I think, therefore I am"), which I guess is a kind of identifying self with thought. There are also perceptions ("I see you"), feelings ("I am having a good time" or "I am sad").
The aggregates are also the "clinging aggregates" which are named at the end of the First Noble Truth (in SN 56.11).
After the Dhammacakkappavattana Sutta (SN 56.11) I think the next two suttas were the Fire Sermon and the Anatta-lakkhana Sutta, which introduces anatta which is the subject of (at least) nearly 200 topics/questions on this site.
In conclusion a good summary might be what MN 2 says about A thicket of wrong views.
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Both ways of thinking, being or not being, are hindrances, causing suffering, and so the suggestion of ways of thinking focuses on to see clear whether something is worthy to take on as ones own, good householder. Be or not, isn't a question. Perceptions have causes, coming into being, decay, has an origin, isn't without cause.
Most usefull for understanding and not falling into extremes: Selves & Not-self
And yes, there are temporary perceptions of self, having cause in not knowing, seeing, so foolish to say there is no such as Self, which is the practice of the Jains.
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In Buddhism we talk of two kinds of truths: the conventional truth (or relative, worldly) and the ultimate truth (or absolute).
In the conventional truth we can say that there is a self. For example, we can say things like “take refuge in myself” or “one should restrain oneself”. In the Dhammapada there is a full chapter of verses of the Buddha speaking in terms of this conventional self (chapter 12). In the conventional truth we can also speak of a “temporary self” as you said.
On the other hand, in the ultimate truth we cannot say that there is a self, as something that is separated, independent and permanent. In the same Dhammapada the Buddha says that all phenomena is non-self (verse 279).
The body is always changing, subject to growth and decay. It’s moving all the time, cells are working and renewing, blood is flowing, air is coming in and out. It’s never the same unchanged body. The body is also interconnected with everything else. The food with eat, the water we drink, the air we breath, they come from outside and become part of the body, and then they are expelled and go back to the outside. The shape of our body comes from all our ancestors and also from the environment we lived all our life. The body is made of all these things, interconnected with everything. Looking more deeply we see that the body is made of skin, organs, bones, muscles, etc. The skin is made of cells, hairs, blood, etc. The cells are made of this and that, and so on. We come to see that, in fact, in the body there is nothing that can be called “body”. We can say that the body is not a body. The body is just an idea in the mind. All these things can be said also for feelings, perceptions, mental formations and consciousness. They can be said for all phenomena. Everything is non self, non separated, not permanent.
The self is just an idea in the mind and we try to remove that idea, without need to replace it with a new idea. Non self is not a theory, it’s a practice of removing the wrong perception of a separate self entity. To meditate on non self it’s a practice for liberation and for freeing us from suffering and affliction.