How should we distinguish between personal memories of our past (what psychologists call episodic memory) and the imagination? Aren't the mental states at the heart of both phenomena fundamentally the same?

They are, but some are true and others are not, hence the significance of the distinction. It is an important distinction, and the liberty of many people has been curtailed by courts believing that some events actually happened in the past rather than merely imagined. In fact, the legal issue often is whether something actually happened or did the witnesses merely think it happened, and as you say the actual experience in both cases is identical. Our experiences do not come with little flags which wave around and tell us they actually happened, so we are often dubious about the reality of some remembered or imagined event.

One might say, in fact, that memory is part of our imaginative capacity, or at least dependent upon our imaginative capacity to the extent it is composed of imaginative mental phenomena. One way to distinguish memories from other imaginative events, then, as Oliver Leeman suggests, is by their epistemic status. Genuine memories are true, while imaginative events generally may or may not be. But I'd add that it's possible to have imaginative events that are true but are not memories. They would be true accidentally, or by luck. For example, I might imagine that right now a Turkish fighter jet has engaged a target along the Syrian frontier--and by chance it might be so. I'd say, then, that another feature of memories that distinguishes them from imaginations is their causal history. Memories are cause by past experiences, by our past interactions with the world, ourselves, and others. Imaginations may be dreamt up at any time. But these are rather objective ways of distinguishing memories from imaginations (i.e. that memories are true and caused by our past experiences in ways that are evident in the memories). And I suspect you're looking for a subject way of distinguishing memories from imaginations. I can think of two criteria for making that distinction offhand. One is that memories fit into a coherent narrative of our lives. If I think of myself having a conversation with Socrates in ancient Athens, one sign that I'm imagining things is that I didn't live in ancient Athens and couldn't have lived in ancient Athens, and I haven't time travelled there. On the other hand, if I remember having a conversation with my mother as child in a context that fits in with other memories and beliefs I have about my past, then there's a pretty good chance that I'm experiencing a memory. But, of course, I can imagine having a conversation with my mother that never happened, too. Here, I don't there's a clear way to make a subjective discernment between memory and imagination. The strength, force, and what Hume called vivacity of the memory might help signal that it's a genuine memory. But besides fit with other memories, narratives, and beliefs together with force and vivacity, to be sure it's a genuine memory we're going to have to look beyond ourselves and seek corroboration from others, from artifacts (like diaries and photos).

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