I agree. This is my point from the beginning. But note that “unfalsifiable” has sense only in the context of empiricism. The solipsist claims for an evidence similar to “I exist”.
Okay. But it's important not to confuse "no certain proof" with "no evidence," even when dealing with unfalsifiable propositions. Not seeing a ninja in the room with me is evidence that there is no ninja here. Not seeing one after a thorough search is stronger evidence. That's true even if it "could be" that the ninja has amazing agility and jumps behind me each time I turn to look somewhere, and moves very silently so I never hear the jumping, and can cling to the ceiling if I back up against the wall, and then drop unseen behind the furniture if I look up at the ceiling, and so forth. Absence of evidence is evidence of absence; it's just not proof.
Seeing an elephant is evidence of an elephant. Sure, it could turn out to be a hallucination of an elephant or a picture of an elephant or a dream of an elephant or a chance elephant-shaped juxtaposition of rocks. But if others see an elephant in the same place, and it's three-dimensional and moving and palpable and smells like an elephant, and it doesn't go away if I think about something else, and it continues to behave like an elephant over time, and doesn't transform into something else or start talking or take flight, evidence that it's an elephant accumulates, even though like the absence of a ninja in the room it never reaches absolute proof if someone is determined to endlessly embellish some alternate explanation. (9/11 Truthers can give some pointers for how to do that. Ask them about those full-scale full-motion real-time broad-daylight hologram jetliners sometime.)
Since that “the solipsist” is only a logic figure it is difficult to imagine what would be his behaviour in day to day life. In theory, the solipsist would behave in the same way that “normal” people. He would establish some relations among ideas —we would say “things”— and predict his future occurrence in the same way that you an I do it. It would be surprised bay not predicted events —like you and I— and search for possible mistakes in the prediction. He would be sceptic about miracles, given that miracles don’t occur in his deductive system. That is to say it would not be distinguishable from other people except by his annoying mania of debating the existence of real world.
I suppose that his belief could arose some problems of psychological order. I imagine that truly believing that you live in a ghostly world must affect you. But if we take a look at the life of Bishop George Berkeley, who was a convinced idealist, it does not seem that he was much affected by his subjective idealism, which is the closest thing to the solipsism I know. Which suggests that he didn't quite believe it. Perhaps his idealism was a way to annoy the rationalists —and he did succeed!— or to draw attention because he was bored of ecclesiastical life— and he also succeeded. I don't know about that.
Well, the only solipsists we're likely to meet are the ones who still act as if breathing and avoiding being in the path of speeding busses is necessary. Presumably any who didn't, wouldn't stay around very long. (That is, the idea that they continue to be ideas of living people wouldn't remain very long.)
Which makes the whole thing, as I said before, a semantic issue in the end. Once they acknowledge cause and effect, whether they attribute that to particles obeying quantum equations or shadows on the cave wall cast by the mysterious actors in front of the fire or concepts in the mind of God obeying the will of God or pure will creating and acting upon mental representations or sprites in a grand computer simulation following the simulation's program or their own ideas following mental patterns of behavior that happen to be consistent for no particular reason or ducks behaving according to their mysterious fundamental duck nature, it ceases to matter. A chemist says a rock is made out of atoms; a solipsist says an idea of a rock is made out of ideas of atoms; I say a duck that seems in every perceivable way to resemble a rock is made out of many tiny ducks that seem in every particular way to resemble atoms. What accolades or attention do such word substitution exercises deserve?
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