The Israeli army has fought through, and flattened, Hamas’s first line of defense. To the rear lie the tunnels; 32 offensive ones have been detected, 15 neutralized. Ahead are the concrete mazes of Shati, Sheikh Radwan, and Jabaliya. This is where Hamas’s military wing is holed up, its most precious assets stored.

Overseeing the IDF is the security cabinet, pulling in different directions, and up above that is President Barack Obama, who, in a phone call with Prime Minister Benjamin Netanyahu on Sunday, made clear the strategic imperative of instituting an “immediate, unconditional humanitarian ceasefire that ends hostilities now.”

Adjacent, to the south, is Egyptian President Abdel-Fattah el-Sissi and the other Arab nationalists, who are likely calling, covertly, for Israel to deal Hamas a debilitating blow of the sort that would leave it only capable of crawling toward a capitulatory ceasefire agreement or risking the very survivability of its rule.

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Amid all this, the Israeli defense establishment appears split, with, paradoxically, optimists calling for a massive offensive – to either push Hamas to the brink or actually wrench it from power – and pessimists, who believe annual military conflict is Israel’s fate for the foreseeable future, advocating for a ceasefire.

When it comes to a considered regional pessimism few can contend with Professor Efraim Inbar, the head of Bar Ilan University’s Begin Sadat Center for Strategic Studies. Israel, he believes, is “in a protracted intractable conflict.” The “solution-oriented” nature of Western thought, he wrote along with Eitan Shamir in a recent assessment for the BESA Center, explains part of the failure to comprehend the nature of Israel’s military action.

“Those who forlornly ask “when is this going to end?” and use the cliché “cycle of violence,” he wrote, “have psychological difficulties digesting the facts that there is no solution in sight.”

Therefore, he submits, “Israel simply needs to ‘mow the grass’ once in a while.” An ongoing war of attrition is Israel’s fate.

Deterrent power, in Inbar’s view, is the sharp fence behind which Israeli society can thrive, and since the razors on that fence have been adequately sharpened — and will undoubtedly need to be sharpened again and again for generations — Israel ought to limit its operation to the attainment of the government’s initial goals: the restoration of deterrence, a moderate weakening of Hamas, and the exchange of quiet for quiet.

The dean of this school of thinking is Defense Minister Moshe Ya’alon. An insightful man who moved far from the left-leaning socialist views of his youth, he has developed a scathing disregard for those, like US Secretary of State John Kerry, who are always in pursuit of solutions. “Solution-ism,” Ya’alon says derisively during nearly every major address, and “now-ism” are Western fixations — he pronounces them more like maladies — that are ill-suited to the Levant and its realities.

Maj. Gen. (ret) Amos Yadlin, the son of former Labor Party education minister Aharon Yadlin, has not traveled far from his roots. He is, it would seem, a Rabin-ist, raised in the military, well aware of the necessity of the sword, but yearning for the sickle: a war-hardened optimist.

Several times in TV interviews in recent days, and on the homepage of the INSS think tank that he directs, Yadlin has called for a sharp escalation in the ground operation. Gaza should be dissected, the Hamas military wing pummeled and weakened, he wrote. The military wing is preventing the signing of a ceasefire and it, therefore, “should feel the noose is tightening.”

If the organization is toppled by these actions, he said on Channel 10, “Israel will not be a widower.”

In lieu of Hamas, he said, there are three options: the return of the Palestinian Authority, under the auspices of the Egyptian government, which would be a favorable development for Israel; the rise to power of a rival organization, which, he said, would take years, perhaps more than a decade, to attain the organizational coherence and capacity to threaten Israel as skillfully as Hamas; or “Somalization,” which would mean horrible chaos but would be “far less bad” than what exists today.

If Hamas is battered, but not to the point of rival displacement, he wrote, the key is ensuring, unlike in the wake of the past two major operations in Gaza, that the organization is unable to significantly rebuild its armed forces. This endeavor is aided by the rise of el-Sissi in Egypt, who has cut off many of the supply lines in to Gaza.

Additionally, Yadlin, like former Shin Bet head Yuval Diskin, believes that Hamas, at the onset of the operation, was at a political and financial nadir. “If, after Operation Protective Edge, it is militarily weakened as well,” Yadlin wrote, “it will be possible — together with Egypt, the moderate Arab states, and the international community — to bring the Palestinian Authority back to Gaza, ensure economic development there, and gradually lift the blockade.”

Assuming, and this may be too much of an assumption, that Israel’s leadership will not allow itself to be dragged along by Hamas and its twisted agenda, the coming days will reveal which way Prime Minister Benjamin Netanyahu, a prudent pessimist, is inclined.