The formation of an adjective indicating capability or fitness is normally formed nowadays by adding the suffix –able to a verb. For example, you may find “American Idol” watchable, Lady Gaga listenable, and Gummy Bears desirable. To each his own.
But, for reasons we need not go into because no one really knows them, some adjectives were formed historically by adding –ible instead of -able. Thus, I find “American Idol” incomprehensible, Lady Gaga unintelligible, and Gummi Bears inedible.
If you can connect two objects, they are connectable, but if you wish to make a hobby of collecting those objects, they become collectible. Don’t ask why, that’s just the way it is.
The even more unfortunate fact is there’s no rule about which adjectives are spelled which way; it’s just something you have to memorize. You may find this state of affairs indigestible, but it’s nonetheless incontestable.
The Bard of Buffalo Bayou is incorrigible, but no less blamable, in his savage outpourings:
My income tax is truly terrible,
And my distress is ineluctable,
Each year when it becomes unbearable
To find expenses non-deductible.
By now that outcome should be guessable,
But it is always unexpectable.
Too bad my money’s inaccessible
And my taxes uncollectible.
My dear, I find you irresistible,
To me, your love is indispensable,
But why your telephone’s unlistable
Is something that’s incomprehensible.
My love’s so great it’s unassessable,
And I hope that it’s permissible
To say I find it inexpressible
That you’re so huggable and kissable.
My grades are just passable,
That it makes me irascible
Is strongly assertable.
It’s just not acceptable
That things indiscernible
Are quite imperceptible
And largely unlearnable.