Buddhists sometimes say that there is "no person" (anattā). What does that mean? If there is no soul and no inner "self", what then is reborn or experiences the results of kamma?

The principle of non-self, anatta (anattā), does not claim that you do not exist. It claims that neither in the body nor in the mind is there a permanent owner - someone who directs the body, thoughts, emotions, feelings, consciousness and sensations, and does not change in the process.

Arguments appear in many suttas of the canon - for example, these two from SN 22.59:

• if the “self” were equivalent to our body, we could dispose of it completely: “let my body be thus”; it does not work that way;
• the body is impermanent, and what is subject to change inevitably leads to suffering (painfulness is not required here; the sense is closer to the absence of reliability, of a stable support). So it cannot be equated with an eternal and unchanging inner essence, taken as “this is mine, this I am, this is my self”.

The same logic is then applied to feelings (more precisely, their tone, vedanā), perception (saññā), volitional formations (saṅkhārā) and consciousness (viññāṇa). The Buddha breaks down what we call ourselves into these five aggregates (khandhā).

The question “is there a self or not” itself the Buddha leaves unanswered. For example, he stays silent at the direct question in the conversation with the wanderer Vacchagotta in one of the suttas. Answering “there is” would side with the teaching of an eternal essence; answering “there is not” would leave the questioner worrying that he existed and has now been destroyed (SN 44.10). In other words, anatta, non-self, is not so much the doctrine “I do not exist” as a way of looking at the whole of our experience.

But what, then, is the object of the law of kamma?

• In MN 109 a monk has exactly this thought: if form, feeling and the rest are not-self, then what “self” will be affected by deeds done by not-self? The Buddha replies that this is how a person trying to outwit the teaching might think, and returns the conversation to what can be checked: is form impermanent, is the impermanent reliable, is it reasonable to take such a thing as yourself.
• In SN 12.12, asked “who consumes the nutriment of consciousness?”, the Buddha says he does not claim that “someone consumes”; the right question is what consciousness serves as nutriment for, and the answer: for the future renewal of existence.

MN 38 opens up the theme of rebirth well. The monk Sāti decided that what is reborn is “the same consciousness, wandering from life to life”. That is entirely wrong, the Buddha corrects. Consciousness arises in dependence on conditions and is named after them, the way a fire is named after its fuel - a wood fire, a grass fire. In dependent origination, becoming (bhava) serves as the condition for birth (jāti). The conviction that the one who does the deed and the one who experiences its fruit in the next life are the same person leads to eternalism; the thought that they are different - to annihilationism. In place of both extremes stands dependent origination (SN 12.17).

Where to read: MN 109, MN 38, MN 22.