Quarky's definition of synchronicity is the same one that we do find a lot, but it's actually about a subjective mental event, a reaction (often a shared one) to a coincidence, and as such, it belongs in that category and class of events.
I disagree. I see synchronicity used to talk about some other connection (than normal causality), like "resonance" or "astrology" and so on. Even in the Merriam Webster definition it's obvious that they're talking about a connection that is not conventional causality. If the word only meant what Quarky says, the term "apophenia" would cover it.
ETA: I also think the notion of saying synchronicity only claims a personal subjective meaning (rather than an inherent meaning) in the events is problematic (or even dishonest). For example, Quarky gave the example of a person attributing a personal and subjective meaning to a fly disturbing a person who was considering whether or not to get up and mow the lawn. Trouble is, that "personal subjective meaning" was that the universe was telling him to do something. That's actually a claim about the external world (and it's wrong). So claiming that it means something to you personally is just a way to worm out of a claim about objective events.
Similarly, someone who believes in astrology plays that same game when they say that it's not that the apparent position of the planets against the constellations actually causes things on Earth. It's rather that a person can ascribe personal and subjective meaning to those patterns. However, the personal and subjective meaning they're ascribing is in fact that the planets are affecting things on Earth.
To count as synchronicity, the events should be unlikely to occur together by chance"(per Wikipedia), but ALSO proof that a whole lot more of these events are really happening than chance would dictate.
And, of course, we've shown over and over that with the arbitrary rules of deciding what events are meaningful, such events are not actually happening more often than chance would dictate.
Again, the Skeptic's Dictionary
entry on coincidence is right on point. Remember Uri Geller's e-mail about all the "elevens" associated with the events of 9-11? It seems uncanny--as if this many things associated with the event coming to "eleven" that there must be some meaning of significance--until you realize that the rules are completely arbitrary. You could play this game with any set of random data (and that's not even counting the "hits" that get included that are flat out lies or misremembered events).
Look at what Rodney did with the coin tossing thought experiment. He asks what the odds of a patterned outcome are, and we point out that the odds of any particular outcome are identical. He then lumps a large group of outcomes and shows that the odds of getting an outcome from that large set are not so long. That's just playing games with arbitrary rules. It's doing the same sort of thing Geller did with the "eleven" stuff.
"Synchronicity" is actually coincidence plus a personally meaningful subjective experience.
Again, that's apophenia. Synchronicity is the claim of inherent meaning or significance to these events.
Jung really thought there was something going on (and he also believed that Rhine had statistical evidence for ESP). He believed "synchronicity" was evidence of an acausal connection or acausal objective significance. This of course is just as logical as saying the coincidence had an acausal cause.
