Let us try to confront the issue of the numerical relationship between the forces in 1948 straight on. Even during the first part of the war, which was a struggle between the two local communities, when it came to armed fighters, the Jewish yishuv (pre-state community) actually had an advantage over the local Palestinian community, despite the fact the Palestinian population was twice the size. Not only did the leaders of the Jewish community know this, it was also assumed by British and American military experts. This was true until the neighboring Arab states entered the picture. The yishuv was more organized, had prepared its fighting forces and their strength was exagerated by British intelligence services, who claimed that the Haganah had two or three times the amount of arms it actually had. All of this led to the perception that the forces weren't equal.
The irony is that from December, 1947 till March, 1948, there was a very difficult war, in which this Jewish military advantage was not expressed because of strategic errors. Most of its efforts were devoted to maintaining transport and communication links, in the belief that maintaining these would contain the fighting. The initial clashes took place in urban areas, the cities and mixed towns, while rural Palestinians were much slower to get involved. This was a repetition of the situation in the 1936-39 Arab rebellion. The turbulence began in Jerusalem, Jaffa and Haifa, but once rural farmers and villagers became involved, the situation became much more difficult.

Paradoxical Situation

The approach of the Zionist leadership, throughout the days of the British Mandate, had been to downplay the significance of the "intifada", to use the contemporary term for rebellion. This held true for l947-48 as well. In the first few months of the struggle, the initiative, timing, etc., were all on the Arab side. This indicates that the Jewish interest was to prevent and contain the rebellion, not to exploit an opportunity to gain advantages.
The pattern of the first few months of the war suited Palestinian fighting capabilities. They couldn't activate large, organized forces, or attempt to capture a town or village, but they were able to carry out partisan actions against convoys and isolated communities. This led to a war of attrition and high loss of life, particularly in the Palmach, the yishuv's organized commando unit and the only force which could carry out serious attacks.
We should note the paradox that when the yishuv had a numerical advantage in the first months of the war, it wasn't translated into advantages in the battlefield. This actually caused the US and others to have second thoughts about the creation of an independent Jewish state.
At this point, the leadership of the yishuv changed tactics to concentrate forces (the Nachshon Operation) and conquer territory, which had not been done during the sisyphean struggle over the transportation arteries. The decision to change tactics was taken as soon as they realized the previous strategy wasn't working and the international climate was beginning to change towards the establishment of a state - the US was preparing a trusteeship proposal, and looked as if they were going to convene the UN General Assembly.
It took essentially one month, April, to destroy the military force of the local Palestinian community. Beginning with the conquest of the village of Kastel, the Israelis soon took control of the mixed cities, and the route to Jerusalem was opened.
The British Mandate ended on May 14, 1948 (the date of the declaration of the State of Israel), and if it weren't for the invasion of the Arab armies, all of the area west of the Jordan River would have been in the hands of the Jews within two weeks. This would have meant ruling over another nation, with all the potential implications and consequences as we can see today. We shouldn't forget the cruel nature of such struggles, which are essentially civil wars, as witnessed recently in the Balkans. Such a development might have led to expulsion, if not total destruction.
Of course, all of these "what if" scenarios can be played from both sides, since on our side there are always claims about "what they would have done to us" if the Arabs had won. Such a war, of total victory and total defeat, leads to a zero sum game, with potentially disastrous consequences.

The Five Arab Armies

The entrance of the Arab armies was motivated, first and foremost, by the desire to save the Arab community in Palestine. This is not emphasized in our narrative, though perhaps it is presented to a greater degree within the Arab narrative. This doesn't mean that this was their only goal. If, after their entrance into the war, they had achieved a series of rapid victories, would they have stopped there? No.
The Arab leaders couldn't refrain from entering the struggle because they weren't ready for, or were afraid of, the UN's response, i.e. the response of the two rival super powers, both of whom supported the UN Partition Plan. Remember, we are not talking about contemporary Egypt, but King Farouk's Egypt, King Abdallah's Jordan (which the British recommended should not enter the fray, despite general assumptions to the contrary), King Faisal's Iraq, a very different Syria, and Lebanon. These were not today's well-armed Arab states. And if today you can see how wary they are about antagonizing the American super power, you can imagine the constraints they felt then, given their dependence. If the USSR had been on the other side, we could imagine a scenario in which the Russians would have encouraged the Arabs. But that didn't happened. The Russians were clearly on the side of the partition plan.
So where did the Arab states find the courage? In my view, the answer is they were confronted with an internal consideration, public opinion, demonstrated on the streets. They were also bound by a series of decisions that had been made, beginning in l945, but particularly in 1946-47, which said that, under certain circumstances, they were committed to defending the Palestinian Arab side in a conflict. They were also trapped by slogans that they themselves had encouraged. But the primary factor was the collapse of the Palestinian Arab community, which forced the Arab armies to get involved. All of this was wrapped in their commitment to prevent the establishment of a Jewish state.

What Were the Goals of the Arab States?

What were the war goals of the Arab states - to destroy the yishuv, to prevent the establishment of the state, to capture all of the western Land of Israel? My answer is no, and it has been reinforced by studies carried out in recent years by Israeli scholars.
Jordan was forced to follow the lead of the Arab states, based upon the aforementioned background. But once the opposing Jewish forces turned out to be stronger than anticipated, King Abdallah changed his plans and tried to arrive at an agreement with the Israeli leaders. The others accused him, with no small amount of justification, of only looking out for his own interests - which were to take control of the territory that had been set aside for an Arab state - the West Bank.
The Iraqi and Syrian maneuvers in the north were a little confusing when it comes to analyzing their intentions, but the primary riddle has been - why did the Egyptians stop advancing at the point they stopped? No Jewish force blocked their advance from the south. There were some Israeli counter attacks against them, which failed. One can say that they had a deterrent impact on them, particularly since they involved the first use of planes (two of which were downed). But for some reason, the entire line of their advance stopped at a point that had not been meant to be a part of the Jewish state - including kibbutzim like Nirim and Yad Mordechai, which were supposed to be within the area of the Arab state. The Egyptians stopped at what was to be the border of the partition plan.
As I see it, the explanation for this is as follows (though it can only be completely confirmed when all the military and government archives are opened). The partition plan was based on a division of three areas, which were to be attached at two points. Three segments of the Jewish state - the Upper Galilee which was to be connected around Nazareth with the Zevulun Valley, the Sharon area, which was to be connected with the Negev area around Be'er Tuvia and the Negev Entrance area.
The Arab area in the Gaza Strip was to be connected at some point to Judea and Samaria, which was to be connected at another point with the Lower Galilee. Each state had three strips, which were connected by the same points, like a bikini. If we had wanted to take control of areas meant for the Arab state, it was necessary to take control of these connecting points, to prevent the bi-section of the Jewish state.
The goal of the Syrians, Lebanese and Iraqis was to reach this connecting point from the north - to reach Nazareth. That was the way to gain control of the passageway to the Arab area. If they had succeeded, it would also have meant the bisection of the Jewish state.

Saving the Arab Community

Why is all of this important? Because I want to emphasize that the Arab military goals were not the goals that are stressed in our literature - the conquest of the entire territory, but rather more limited goals. Along the lines of President Sadat's limited goals when he initiated the Yom Kippur War in 1973. This is the answer to the question of whether they were such heroes when they decided to invade. My answer is no. They didn't dare plan, in advance, to take control of the area that was designated for the Jewish state in accordance with the UN partition plan. They arranged a plan, which, at least in the beginning, could be justified before the UN, if it responded harshly to the situation. If they were asked, "What are you doing in the land of Israel?", they would respond that "We were invited by the Arab side to save the Arab community, and we only entered the Arab territories, not the area of the Jewish state." I anticipate that when the Arab war plans are revealed, that is the picture we will get. This explains why the Egyptians stopped at the point they did.
The leadership of the Jewish state didn't understand this, and there was no reason for it to do so. That is the privilege of historians. Still, correct behavior does not always follow from understanding. After all, we also have to take into account the dynamics of how things develop. Let's assume that the Arab armies didn't encounter strong resistance, would they have stopped at the borders of the Jewish state and not proceeded further? Did we stop in 1967? We also had all sorts of plans concerning borders and peace, but a different dynamic emerged. Instead of maintaining the territories as a card in exchange for a future peace, we established settlements.
This wasn't a preconceived scheme. There were pressure groups, dynamics, and as usual, a political leadership which was dragged along and did not lead.
While I can say that the Israeli narrative that there was a threat to the existence of the state was incorrect, and that the plans of the Arab armies were limited - I can't say that they wouldn't have gone beyond those limitations if circumstances had permitted. Force doesn't stop - it can't suffer a vacuum. The same was true for Sadat in 1973. If the Egyptian army had been able to advance and conquer all of Sinai, wouldn't it have done so, despite the limited war plans? Wouldn't he have responded to the demands of the generals to continue beyond the Mitla Pass? This is how the dynamic works - the dynamics of power, as I understand them from history.
I'm not saying that we should have responded only in accordance with the limited goals of the Arab armies. We acted in accordance with our fears. And, of course, we could not afford to lose. But, after the victory in the War of Independence, there was no need to continue to declare, with drums and bugles, that it was a war in which the Arabs intended to destroy us, to throw us into the sea, etc. That was not the case.

The Few Against the Many: Phase 2

Now we reach the question of "the few against the many" in the second phase of the war. When the Egyptians reached their intended target line after two weeks of fighting, stopped, and encountered resistance, the question is whether they had enough force to retain the line. To ensure that they wouldn't go beyond this line, it was essential that the Jewish yishuv had a counterbalancing force, and such a force existed. The true miracle was that we placed the same number of soldiers in the battlefield as the entire Arab armies. The same number of divisions and soldiers, about 29,000 men. We had the same number of infantrymen. If this had not been the case, our situation would have been very grave.
This was the main factor - soldiers were more important than weapons and equipment. Remember, we are talking about primitive weapons, not the sort of technology that the Americans or Israelis are capable of putting in the field today. The miracle was that a Jewish community that numbered 650,000 people was capable of mobilizing a fighting force equal to the combined Arab armies which came from nations with a combined population of 30 million people. Egypt alone had a population of about 19 million.
The Arabs had a much larger military potential than the force sent to Israel. But much of those additional forces had to remain behind to defend the regimes, and they didn't really have that much in reserve. The additional amazing factor was that, in the course of the war, the IDF actually tripled its manpower. It became an army with over l00,000 mobilized soldiers. Two-thirds came from the new immigrants, and the rest were somehow squeezed out of the yishuv. Most of the increase was not in the infantry (which did not increase significantly) but in the supportive units, logistics, the navy, the air force, etc. This is the ratio of modern armies - one to three.
Why didn't the Arab armies increase their forces as well? The outcome of the war was determined when they didn't succeed in taking control of the areas of the Jewish yishuv. They didn't bring enough forces to even attempt this. The commanders of the Arab armies knew that they weren't sufficiently prepared, but they hoped that things would work out against a Jewish force that really wasn't a full-fledged standing army, and which lacked heavy weaponry.

The Role of the British

It is interesting that the narratives of both the Israelis and the Palestinians say that the British helped the other side. This to me is proof of the fact that they didn't help either side, at least not in an organized, planned manner. It was the local commander who frequently determined things, depending upon his level of empathy or antipathy for one of the sides, although at the higher levels, there was an attempt to be impartial.
In Haifa, there was a pro-Zionist orientation. The British commander, General Stockwell, actually told us when he was leaving. So we were ready, and the Arabs weren't, and within two or three days, Haifa was in our hands. And he was ready to offer trucks to the Arabs, for evacuation. It might have been a humanitarian measure, but it only served to increase the panic. On the other hand, when we conquered the Sheikh Jarah neighborhood in East Jerusalem, the British forced us to withdraw. They tried to maintain a certain balance.

Israel Changed the Equation

On the Arab side, it was natural for them to believe that they had the advantage. They did have an absolute advantage in heavy weaponry - tanks, armored vehicles and artillery (particularly the Jordanians), and they had planes and a navy (the Egyptians). There are claims that they had problems with their ammunition and corruption, but the main factor was that Israel changed the equation. Despite the arms embargo declared by the Western powers, the Israeli army succeeded in getting weapons, thanks to the Russians. In this respect, the Israeli narrative that states the Czech weapons we received, with Russian backing, were critical to the war effort, is correct.
We also received additional, smuggled weapons from American and European sources. But the Czech weapons were critical - light arms and planes, the basis for the small Israeli air force. We also acquired tanks and even ships. The Czech assistance was already a factor during the first phase, when 5,000 rifles arrived on the eve of Operation Nachshon. The embargo hurt the Arab side more than it hurt the Jews. It worked in Israel's favor, because it prevented the Arab armies from replenishing their equipment. This particularly affected the Egyptians and the Syrians, since we can assume that the British continued to help the Jordanians. The fact is that we weren't able to remove them from East Jerusalem, or Latrun. After ten days of fighting over Ramla and Lod (Lydda), we arrived at a modus vivendi, which enabled us to turn our efforts against the Egyptians, Syrians and Iraqis. The Egyptians were the primary threat. The war began and ended with them. If they said they wanted war, there would be a war, if they say they wanted an agreement, the war ended. This is as it would be in the future as well. So the first cease-fire was signed with the Egyptians. Just as in the peace process, Egypt was the focal point.
To conclude, the fact that it wasn't a situation of "the few against the many" prevented the Arabs from winning. This was reinforced by an arms embargo that worked against the Arab side, and enabled the Israelis to overcome the advantage that the Arab armies had in the sphere of weaponry.