Short answer

The rules are not completely clear on this one, but in the absence of an exception, I would say that **your Alchemist does get additional formulae if his intelligence increases permanently**, and [the first James Jacob's quote you cite]( would seem to support this. This is no less 'illogical' than the fact alchemists get new formulae when they go up a level.

Long answer

The closest we get to RAW on this is under Ability Score Bonuses / Permanent Bonuses:

> Ability bonuses with a duration greater than 1 day a­ctually increase the relevant ability score after 24 hours. Modify all skills and statistics related
to that ability. This might cause you to gain skill points, hit points, **and other bonuses.** These bonuses should be noted separately in case they are removed. (PCR 555, my emphasis)

This is supported by James Jacobs' comment in [the first post you mention](

> All bonuses are retroactive when an ability score increases, be they bonuses to damage, to skill ranks, to hit points, to saves, to skill checks... all of them. Skill ranks not being retroactive are a 3.5 convention we specifically removed from the game because it was a weird exception to the rule, and since **now there are no exceptions to this rule**, there's no need to specifically state that skill ranks are retroactively granted if your Intelligence goes up.

Unless he forgot about spells/alchemists' formulae etc, no exception means no exception.

If you are looking for rules-based logic, I would say it is no more illogical for your Alchemist to gain a formula because his intelligence has permanently increased than it is when he goes up a level:

> An alchemist begins play with two 1st level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier. At each new alchemist level, he gains one new formula of any level that he can create. (

In terms of real-world logic you could just say that your alchemist had struggled with understanding the new formula, and it wasn't until his intelligence increased that 'the penny dropped'.