So is there a reason to give intelligence to an Eidolon? Does it grant them bonus skill trainings since I do know they do not gain additional languages.
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It can make RKs due this.
An eidolon more intelligent than you can RK better than you because your KAS is Cha and not int and it's not unlikely that the summoner doesn't invest into Int.
It's also allows the player to have an additional check in case of failure. If your Eidolon that is more Intelligent than you fails its RK you can try to RK yourself for the same thing because it's your Eidolon that is restricted to do new checks not you.
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So is there a reason to give intelligence to an Eidolon? Does it grant them bonus skill trainings since I do know they do not gain additional languages.
This is a very strangely worded question.
Yes there is reason to boost INT on an Eidolon. It will increase their INT bonus for their INT-based skills.
No, the INT bonus is not going to give more trained skills or known languages because those are locked to the stats of the Summoner rather than calculated from the Eidolon's attribute numbers.
But you already mentioned that. So I am guessing you are asking about what benefits the INT bonus on skills and such is going to do for the Eidolon.
The one you didn't mention is that Spell attack and DC are also copied from the Summoner rather than calculated from the Eidolon's attirbutes. I am guessing that is because most of the Eidolon stat arrays are light on mental skills and the developers didn't want to nerf Eidolon spellcasting too much.
It can make RKs due this.
An eidolon more intelligent than you can RK better than you because your KAS is Cha and not int and it's not unlikely that the summoner doesn't invest into Int.
It's also allows the player to have an additional check in case of failure. If your Eidolon that is more Intelligent than you fails its RK you can try to RK yourself for the same thing because it's your Eidolon that is restricted to do new checks not you.
Eidolons are really nice for out of combat RK checks, at least at early levels. The number of times the spirit wolf knew a thing the party's wizard, summoner, and thaumaturge didn't became a running gag for us.
Another fun sneaky little edge is that the summoner/eidolon can use any runed up weapon you find. It doesn't matter if its on a crappy little mace-- until an opportunity to transfer it emerges, you can still give your eidolon the happy juice.
No. There is no mechanical reason to do so unless you feel like role-playing an intelligent eidolon who wants to roll for intelligence based skills.
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So is there a reason to give intelligence to an Eidolon? Does it grant them bonus skill trainings since I do know they do not gain additional languages.
Eidolons get much less from attributes than other PCs: No extra skills/languages from Int, no hp from Con, they don't roll initiative, they don't use their attributes for spellcasting, they have harder time building long skill feat lines (like Intimidation) and it's less impactful for them to be affected by a good portion of the save-based effects. So besides Str and Dex, they can roughly do however they want.
Intelligence is interesting because the Summoner is in general bad at it so if you want to cover more ground it can be useful. It's also necessary if you want to build a Disturbing Knowledge Eidolon, but that's a high level build so not necessarily what people are looking for. Now, high Int Eidolons are rare, you just have the Dragon and the Construct, so most Eidolons won't raise Int.
Where does it say Eidolon do not gain extra skills from INT Mod?
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The only way to Eidolon get new skills is via Dual Studies and it progress very poorly.
Where does it say eidolons don't get languages from intelligence?
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And before anyone asks:
Eidolon Spells - "An eidolon that has spells also gains the Cast a Spell activity. It doesn't have its own spell DC or spell attack modifier; if it needs to Cast a Spell, it uses your spell DC and spell attack modifier."
And before anyone asks...
:P
And before anyone asks:
Eidolon Spells - "An eidolon that has spells also gains the Cast a Spell activity. It doesn't have its own spell DC or spell attack modifier; if it needs to Cast a Spell, it uses your spell DC and spell attack modifier."
Yes which means now they have taken attributes off damage for most cantrips, the only mechanical reason to give your Eidolon Charisma is to use the Charisma skills. Which is annoying as the caster Eidolon was the high Charisma option.