What a nice question. Defining these things in the abstract is not without difficulty. I'm not sure that we can define 'feeling' in any other ways than by synonym (e.g. experience, knowledge, consciousness-of-something, etc) and invitation to internally reflect on what these words mean, although once grasped I think the concept is one of the easiest ones to understand. 'Activity' is easier to define as it is much more public. I suppose we might say activity is, in the most general terms, any change initiated by a conscious object. Will that do?

I'm interested in the relationship between activity and feeling. As a panpsychist I've come to the view that things do what they do because of how they feel, and they feel what they feel because of what they do. That seems true of me, at least. I eat because I feel hungry. I feel pain because I stuck my foot in a hole.

Being, or identity, is perhaps linked to repeated pattern of behaviour. I'm a human being because the matter of my body persists in behaving in a way that preserves a persistent form and function over time. I'm a footballer because I play football every day. Once I stop doing these things, my being changes.

What i think is that "feeling" is response of our body to a thought. So feeling can initiate some activity and activity can provoke feelings.
If you think about something long enough, it will increase related feelings. These heightened feelings will result in increase in thought's intensity. And this is some kind of loop which is leading cause of suicides.
And suicide is an activity!!

"feeling" is response of our body to a thought. — ahmad bilal

True. Thought does trigger feelings. Thinking of a lover who is dead can cause an array of feelings, some pleasant, some not at all pleasant. Feelings, emotions, are also responses to sensations. If you are walking along and you spot a poisonous snake in your path, you might have feelings (fear is quite common) before you can register anything else. If you see your best friend or lover, you may experience happiness before you think of anything.

As is the case with thinking and feeling, we are always engaged in an activity--existing is an activity. Sleep is an activity. To exist is to think and to do--something.

But then there is purposeful activity that is performed only occasionally. Most people are fairly purposeful about sex, cooking, eating, playing games, washing dishes, cleaning the kitchen floor, painting a wall, bathing, reading, etc. Quote often we choose an activity to get a particular emotion. We might go to a bar to experience whatever excitement happens there, or camaraderie, various stages of inebriation (drunkenness), or to find sex. Sex is exciting, pleasant (usually--if not do something else for a while), pleasurable, and later relaxing. We might go for a bike ride to feel exhilarated, or to feel confidence that we are healthy enough to ride for quite a while (whatever that is).

Sometimes we engage in activities to escape emotion--like going to the bar to escape boredom; going for a bike ride to escape ennui. We might go for a walk to reduce anxiety.

Anyway, activity, thought and emotion are a merry-go-round.

Great answers from everyone, thanks. At a logical level feelings and activities can't be identical. Of course this very much depends on how we define the two. When I say they can't be identical, I am assuming that we are thinking of an activity as some type of physical movement in "public". Feelings are internal and don't seem to necessarily entail physical "public" activity, although the converse seems to be true.

I do understand that feelings entail internal brain activity, yet I'm using "activity" to mean external, observable physical activity — jancanc

Feelings are internal and don't seem to necessarily entail physical "public" activity, although the converse seems to be true. — jancanc

Why internal vs external? Don't you think that, for the most part, this way of describing our every day experience misleading. For example, when everything is going well with our jobs, our sports, our band, our transport, etc. there doesn't seem to be any experience of the internal or external.We are simply there, involved in a meaningful world with shared moods, feelings and understandings. And the better things are going and the more involved in the situation we become the less and less our experience is "subjective" and the less and less is there any internal/external experience. It is when we abstract from the situation and attempt to do philosophy, science, or try and overcome some impediment to our tasks, or become self-conscious for whatever reason, that the internal/external distinction (which is an ontological distinction) can then be derived. In my experience, the internal/external distinction is always derivative, derivative of a more basic shared, involved and public experience of our worlds. This latter experience is called being-in-the-world.

Why internal vs external? Don't you think that, for the most part, this way of describing our every day experience misleading. For example, when everything is going well with our jobs, our sports, our band, our transport, etc. there doesn't seem to be any experience of the internal or external.We are simply there, involved in a meaningful world with shared moods, feelings and understandings. And the better things are going and the more involved in the situation we become the less and less our experience is "subjective" and the less and less is there any internal/external experience. It is when we abstract from the situation and attempt to do philosophy, science, or try and overcome some impediment to our tasks, or become self-conscious for whatever reason, that the internal/external distinction (which is an ontological distinction) can then be derived. In my experience, the internal/external distinction is always derivative, derivative of a more basic shared, involved and public experience of our worlds. This latter experience is called being-in-the-world. — bloodninja

Sure, I think can see what you mean, and, if I am interpreting it correctly, I do agree to a very large extent. Fundamentally, for me, everything is essentially "internal", or a product of our our consciousness. One questions: how do you reconcile a notion of "public experience" and "being-in-the-world"; is this like a "pre-discusive" consciousness? pre-reflective?

What is the difference between a feeling (feeling love, anger, fear, etc) and an activity (or the participation in an activity) (e.g., a football match, a walk in the park, etc) (I do understand that feelings entail internal brain activity, yet I'm using "activity" to mean external, observable physical activity)? — jancanc

"Activity" (in the observable sense) refers to the behaviour one takes in a particular situation. In this sense, "activity" involves intentions, whereas "activity" in the "brain actiivty" sense (or "feeling" sense that I mention below) is a description of the facts of mental events.

"Feeling" refers to the conscious experience of particular states of physiological activity (ranging from less-aroused to more-aroused activity). This experience also involves nonconscious processes.