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When an alchemist drinks his mutagen to gain a alchemical bonus to his Strength, thereby reducing his Intelligence, is this a temporary increase/penalty or considered a 10 minutes per level permanent increase/penalty? More directly, does the number of bombs available decrease by one while the mutagen is active?
What do you mean by "don't lose a bonus extract while it's active"?
You get bonus extracts for having a high intelligence score the same way a wizard gets bonus spells.
But as Ferious Thune pointed out you don't lose them (or bombs) for taking your mutagen.
Something to note:
When you take a strength mutagen, you get -2 to intelligence. This might prevent you from using an extract if you no longer have the minimum intelligence to use the extract ( 10 + extract level )
To learn or use an extract, an alchemist must have an Intelligence score equal to at least 10 + the extract’s level.
The two pertinent quotes from the CRB glossary under Ability damage, drain etc... are:
"Some spells and abilities cause you to take an ability penalty for a limited amount of time. While in effect, these penalties function just like ability damage, but they cannot cause you to fall unconscious or die. In essence, penalties cannot decrease your ability score to less than 1."
And:
"Intelligence: Damage to your Intelligence score causes you to take penalties on Intelligence-based skill checks. This penalty also applies to any spell DCs based on Intelligence."
So, no lost bombs per day, no bonus extracts lost, and no lost access to extracts.
The two pertinent quotes from the CRB glossary under Ability damage, drain etc... are:
"Some spells and abilities cause you to take an ability penalty for a limited amount of time. While in effect, these penalties function just like ability damage, but they cannot cause you to fall unconscious or die. In essence, penalties cannot decrease your ability score to less than 1."
And:
"Intelligence: Damage to your Intelligence score causes you to take penalties on Intelligence-based skill checks. This penalty also applies to any spell DCs based on Intelligence."So, no lost bombs per day, no bonus extracts lost, and no lost access to extracts.
By raw, it seems you are right. But I recently played the Pathfinder - Kingmaker video game on PC and my alchemist definitely lost the usage of his extracts from the intelligence penalty of his mutagen. I know the video game is not always using Raw rules from the tabletop, but that is still food for thoughts. Also, by the same RAW rules, it appears strength damage does not lower your carry capacity. Which is definitely weird to me. ( in the video game once again it does lower your carry capacity )
I think a few of these cases, like carrying capacity, are excluded for ease of play. A video game has the advantage of not needing the players to recalculate stuff.
By raw, it seems you are right. But I recently played the Pathfinder - Kingmaker video game on PC and my alchemist definitely lost the usage of his extracts from the intelligence penalty of his mutagen. I know the video game is not always using Raw rules from the tabletop, but that is still food for thoughts.
The CRPG is pretty terrible in ways you can only recognize when you look into them. On the surface it looks like a really good translation of the rules, but you will soon realize it's a very bad idea to take anything in it as evidence toward it working for real.
That's for bonuses, not penalties, which are not treated the same by the rules.