So, if Churchill's was killed in Manhattan by a taxi (or died in the plane crash in 1919), and Halifax became PM, it would be economics etc. that determined the outcome of WWII?

Okay, I'll play along, suppose Churchill had died in 1919. That means Chamberlain has no pressure to move right, no vocally anti-Bolshevik behind British foreign policy. Maybe, then, the British take up Stalin's offer to defend Czechoslovakia and thus don't give Hitler any concessions at Munich.

Or later, again without an anti-Bolshevik around to scare Stalin, Ribbentrop goes back to Berlin empty handed and the Nazi invasion of Poland is halted by Russian forces.

No kidding?

Washington wasn't a particularly gifted (or lucky) general, I'm sure Arnold would have performed just as well.

But there is no indication that Arnold understood the need to simply keep an army in the field the way Washington did. Arnold would have wanted to win the Revolution via "feats of arms," and when that became less and less likely...who knows?

As for Lee, you are probably right, but there is always that chance.

Hmm...so if George Washington was killed during the Seven Years War, and its Benedict Arnold instead that takes the leading role during the Revolution everything works out more or less as we know it because economics, demographics and social structures remain more or less the same?

Washington wasn't a particularly gifted (or lucky) general, I'm sure Arnold would have performed just as well. I also doubt, given that the events proceeding Arnold's treason wouldn't have taken place, that he would have been any less patriotic than Washington. No matter really, as Lee would most likely have been in charge without Washington, not Arnold.

When the crisis comes, how it is handled depends on all of the other factors, and how they react. One of these is certainly the leadership, and if they react in such a way that it damps down the crisis, or turns it to advantage, in preserving and strengthening the cultural attitudes and institutions, then the crisis is in retrospect not seen as a particularly big deal, even if it was. If the leaders, instead, turn the crisis into a grab-all for themselves (as Caesar, et al, did; as Hitler did; as FDR did), then it can lead to massive social re-ordering. This isn't always a bad thing. (FDR was, at worst, a mixed bag, and our Founding Fathers were a pretty good deal for everyone but the English.) Just as FDR turned the US far more towards socialism, reordered the economy and institutions of society, and essentially changed the American character in large part, an equally driven leader who looked towards libertarian ends (say, a Coolidge type) could have saved and restored American institutions of the time, and rebuilt American confidence, leading the 1929-1933 recession to stay as just that, a recession, albeit deeper than most. Instead, we had a progressive, and a bit of a megalomaniac (as witness his running for a FOURTH term when he knew he was dying!) who made massive changes to society. That was not foreordained.

So no, the great men are not the only influence on events, but they are a very, very major influence on events, as important as the cultural attitudes and institutions. Yes, sometimes, there are events that would arise no matter who was in place in leadership (in or out of government). Other times, though, those events arise because of who was in place in leadership.

Hmm...so if George Washington was killed during the Seven Years War, and its Benedict Arnold instead that takes the leading role during the Revolution everything works out more or less as we know it because economics, demographics and social structures remain more or less the same?

So, if Churchill's was killed in Manhattan by a taxi (or died in the plane crash in 1919), and Halifax became PM, it would be economics etc. that determined the outcome of WWII?

Certainly, one can but too much emphasis on individual actors, but I think it is nonsense to say they only add "color and texture to the fabric of history". In fact, all of the great (and not-so-great) systematic attempts to account for history using only "economics, demographics, and social structures" (if we can take that to include their philosophical underpinnings), have been dismal failures. Hegel, Marx, Lenin, Trotsky, Spengler, Hitler, and Toynbee all had a problem with the future following nothing like the course they predicted. Hegel might look at Napoleon and see "the spirit of the age" at work, but in reality it was Napoleon the man at work and he had no interest in Hegel's theories.

It seems better to me to say economics, demographics and social structure provide the context within which historical actors function. That context in many important ways limits what actions are open to historical actors (in a variety of ways), but that is not the same thing as saying they determine them. Additionally, there are important actors who have the affect of changing the context they exist within, thereby opening up previously unknown or proscribed possibilities.

Think of Mohammed. Assuming what we know about him is true (the historical parts, not the religious parts), then what would have happened had he not existed? You still might have gotten some religious leader coming out of Arabia, but he might have been not quite as driven, or as religious.

Think about it. If you don't get Islamic Arabs coming out of Arabia, then the Persian Empire either doesn't get conquered, or does so much more slowly. That gives the Byzantine Empire much more time to get through all the crap it was going through in the 7th century CE. You might still get Arab coalitions of tribes (they'd existed before), but they were generally much less long-lasting. That's not just damming the river; that'd be shifting the entire river into a new bank, with major impersonal historical factors (like religion) missing.

I didn't.

I didn't mean to imply that you did. I just wanted to emphasize that neither extreme position was correct and that the truth lies in the middle.

Influence, yes; determine, no.

I guess the question there is when does influence become determination or when does a difference in degree become a difference in kind?

Maybe not, but certainly there was a widespread public sentiment against Jews already...

The Jews and Rom would not likely have faired well in whatever strongman led government followed the Weimar Republic, but it was not just German social evolution that led to wholesale slaughter that was not even fully known by much of the populace. Any strongman would also likely have taken back the Sudetenland and at least some of the other contested territories. Whether that leader would have had the spectacular successes and equally spectacular failures of Hitler is an open question. I tend to find it unlikely, but it is of course all hypothetical.

it is also foolish to ignore the role of 'great men' in shaping those structures.

I didn't. Re-read what I wrote. Leaders may swim in the river, float in the river or dam the river but they aren't the river. Influence, yes; determine, no.

Germany between the wars was also looking for a strong nationalist leader, but they didn't of social necessity need one that would attempt to exterminate the Jews and Gypsies.

Maybe not, but certainly there was a widespread public sentiment against Jews already, and certainly the annexation of Austria, re-occupation of the Rhineland, and the reclaiming of the Sudetenland would have happened under almost any other nationalist leader. Even the invasion of Poland would likely have happened so long as Stalin and his party were in power in Russia.

The "Great Man" theory is wrong because it assumes that the decisive actions come from the man, not the other way around.

As in any single sentence summation, this is too simplistic. Rome may have had an emperor, but when and how exactly it happened matter more than you credit. The personality and competencies/exceptionalities also matter more than you appear to credit. Germany between the wars was also looking for a strong nationalist leader, but they didn't of social necessity need one that would attempt to exterminate the Jews and Gypsies.
The great man theory in isolation foolishly ignores the role of evolving social, political, and economic structures, but it is also foolish to ignore the role of 'great men' in shaping those structures.