That would be an stupid idea, because that would make him his heir. Which means, all Ptolemy needs to do, is kill Alexander, and he would be in charge. Even if Ptolemy did nothing to Alexander, he would be seen as a possible murderer.
On the plus side, his claim to rule would be a lot more legitimate.
Alexander would have killed him years ago if Ptolemy had actually been his half brother.
Besides, if I remember correctly, the whole "Ptolemy is Alexander's half-brother" story was a propaganda device invented after Alexander's death. Claiming some sort of special connection to Alexander was necessary when the huge empire was up for grabs by so many powerful men. Robin Waterfield in "Dividing the Spoils" explains that Craterus invented a story about saving Alexander's life and Seleucus claimed to be conceived by Apollo, thus being Alexander's divine nephew. (p. 50)
Alexander would have killed him years ago if Ptolemy had actually been his half brother.
Knowing Philippos II, it seems to me that it's very possible that Ptolemaios was indeed his bastard.
The behaviour described above is most certainly real, but applying it to Ptolemaios ignores that he stands out for not claiming Alexander's legacy, and explicitly didn't aim to gain imperial hegemony. He wisely chose to rule Egypt, accentuating (fabricated) continuity with the Pharaonic past.
Alexander was known for weird personal points of honour (and dishonour). He didn't kill Arrhidaios, either, even though the guy could obviously be used as a pawn by any crafty enemy. He occasionally killed people without a truly logical reason, because he felt slighted, and he sometimes let people live even when they could be major threats-- by all accounts because of some particular sense of honour or personal loyalty. @Lalli correctly states that it would make sense to kill all potential threats, based just on the recurring Macedonian theme of messy successions, but we know Alexander didn't do that. He never acted based on what was sensible, but instead based his actions on some internal motivation that apparently wasn't even understood by his contemporaries, and remains subject to interpretation to this day.
Anyway, none of this means that the story is certainly true, but dismissing it out of hand seems far too hasty to me.[/USER]
I’m gonna quote my own post on the matter.
Perhaps Alexander had genuine affection for Arrhidaios, but affection or not, Alexander was first and foremost a pragmatist, if he had believed Arrhidaios could have endangered him, he would have killed him right away.
Rumor of Ptolemy being Philip’s son only started when Ptolemy himself was in Greece, coincidence? I doubt it. Nobody before then seemed to have ever seen Ptolemy as a Argead, and I doubt any of the other surviving diadiochi ever took his claims seriously, or else they’d have at least attempted to discredit them.
That's your view; it doesn't convince me. My reading is that Ptolemaios was very sensible in limiting his ambitions, and never once attempted to posit an imperial claim. His attempt to gain control in Greece was pure opportunism, brought about by the circumstances. He never showed any sign of seeking to claim imperial hegemony, and the way he portrayed his reign didn't allude to anything like that. If he'd vassalised Greece, he'd have been King of Egypt and Greece, instead of just King of Egypt.
On the contrary. Although Alexander was at times utterly ruthless, he was never sufficiently consistent in this to ascribe it to a leading drive of pragmatism. Alexander was in fact nothing so much as a total romantic, who deliberately patterned his behaviour on what he thought a semi-divine God-Emperor should be like. And that wasn't a clever strategy either, because most people he encountered totally failed to understand what he was getting at. (Which is to be expected, when you live your life as if the Iliad is an instruction manual.)
Considering that this whole thread has already gone over the fact that if you intend to limit your ambitions, broadcasting your supposed relation to Alexander mostly does you a disservice (it paints a target on your back), the fact that he only brought it up when it became an advantage is no surprise. And when you're looking to mary a princess of the royal blood, it is an advantage. Can that mean he made it up then, to serve his designs? Yes. Does it have to mean that, as you suggest? No.
My point is that there are various readings of the historical record here, and ruling one of them out because you just don't believe that one is no more than a subjective interpretation. Don't confuse it for (near-)certainty.