Instinctual adaptations = adapting on the fly because of what you can see the enemy having, the mechanics behind the enemy, and the potential of the enemy, without actually thinking about it.

Logical progression on a subconscious scale = taking an ability and understanding its maximum capabilities in real scenarios.

Mathematical glossary = knowing how the ability works, utilizing every possible method for it to scale, just a moments glance.

Umm...well, now that I know what you're talking about, it sounds like you're judging my gameplay skills (fair enough).

To my knowledge I do this. Not perfectly by any means, but I'm definitely capable of these.

It's a measely 35% penetration with some flat pen around 20-ish for armor and 40 for mages, get over it. Health still works anyway.

I kind of dumbed it down to make it easier to understand. What I do is actually a bit further than that, although I do frequently seem to be a hair's breadth away from victory due to unforeseen circumstances or knowing the situation and not caring. Like soloing in a 2 versus 1 lane; if I calculate that I can kill one of my opponents, I will probably go for it. Whether or not it's a good idea.

Untrue, as in the case of the example provided (added to original post), it's potential can rise up to 68% and 40 flat for armor, and mages have 40% +20 flat or so. Note, I'm not asking for mages to get just as much penetration, but something be done to help limit the penetration as it is getting out of hand and preventing fun but competitive play.

And that's why bruisers should be building damage items, instead of going full ****** and hoping being tanky as **** will make you more valuable.
The point is EVERYONE can use these items, so it's not really a good argument to say that it's invalidating everyone but adcs.
Because flash, silence, and frozen mallet are still things.
Particularly with Garen. W Q flash hit carry E R win.
The problem you're not accounting for is that without any survivability, the carries who focus full attack like you're proposing are REALLY EASY TO KILL.
So you make a tradeoff with these items, since they have no, or almost no, durability return on them. Multiple cleavers no longer stack, so returns on stacking it are minimal at best. Youmuu's ghostblade gives you no survivability, and is pretty goddamn useless on an adc.
So basically, if you're too goddamn stupid to focus the carry, yes, carries are OP.
But that's not because of the change in items. It's because you're retarded.

Damage and survivability items on bruisers is the combination you want. And sure, if your team can't get past their defense, you're gonna have a bad time.
AP Carries have massive damage outputs to compensate for comparatively low magic pen, too, so the argument that the increase in armor pen ****s APCs isn't really decent either.

Not necessarily. Carries who full attack like this are likely with other teammates, at least a support who helps with surviability, as well as carrying lifesteal (As in the example, a bloodthirster.) So while you're trying to focus them down, They're regenerating their health by that full attack. 20% from just 1 bloodthirster means they're regenerating 200 hp/second on average, and at range in most cases at that, making return pokes to them difficult at best while they kite backward.

While youmuu's doesn't give survival, note that I didn't put it on cait for that reason. I know that cleavers don't stack, but their effect still stacks 4 times correct? the caitlyn in my example is capable of surviving things with up to 50% mitigation (100 armor/mr) due to runes and masteries (which i didn't bother adding due to wanting to make a point, so i left non armor pen/hp runes empty). That still puts her effective hp regen at 400/sec if she attacks while retreating if she's in a bad spot, or if she's doing well in a teamfight.

So yes, if you ignore that I mentioned that carries, by virtue of supposed to be being played well and not allowing themselves to be focused like they're supposed to, then you're "too goddamn stupid" to realize carries can be OP as it currently stands. Yes, there are bad ADC's, but if you can assume that both sides are relatively equal in skill then it stands to reason that you won't get that chance to focus that carry. But hey, what do i know if I'm the retarded one presenting all of the math and so on to you?

I agree, damage and survivability on bruisers is better. I more frequently go black cleaver, IE, warmogs, atmas, boots, and frozen mallet on Garen, however that setup means that he would die in about 2-3 seconds due to his 3k ish health and nearly no mitigation against such a foe. Seeing as most champions suited to killing the ADC are either ranged characters like another ADC, or an assasin who actually does get the jump on an ADC (who isn't supposed to be "bad" enough to let that happen in the first place), it makes things harder to remove/focus that ADC, shy of ignoring the rest of the team, who's sole purpose is to do damage and prevent you from reaching their ADC in the first place.
I didn't try to argue anything about how it messes with APC, but APC have massive damage outputs, and they also have cooldowns they have to manage. They typically have to wait at least as much time, if not longer to do the same amount of damage as an ADC, and they usually can't drop the mitigation to nearly as low as the ADC can. (I also realize that AP can reach 600 on champions, but bear in mind most of their ratios are 80% or lower, and would equal a 400 ADC stat in that respect).

My biggest point is that I'd like to see some kind of minimum armor/MR in place or an item that can prevent that mitigation so you trade off damage for survivability to counter that damage. It would also be circumstantial, so that the person who gets more power but less mitigation can do just as much damage, whereas the person who relies on that penetration is countered more effectively. Its circumventable by both sides in this case, whereas the current system is just "buying pen? better get health..." and as my math shows, not much is gained by it.

Potential Armor penetration and shred combined, not including innate champion capabilities, has a maximum of 55.1%, leaving just a little under half of their armor intact. Other champions' shred/penetration abilities can separately scale up to 68.6%, and if you took multiple Armor Shred factors together, it could maybe reach 80%.

It could ALWAYS do this. That has not changed. The only thing that has changed is that now Flat Penetration is not made worthless by % Penetration.