What is necessary is what must be the case in every possible way the world could exist.

Our imagination is not necessarily completely capable of determining the limits of imagination.

Therefore, it is possible that what we can not imagine is infinite.

It is necessary that something is going on or happening here, now, for me to have written these words.

It is necessary that one thing and one more thing are two things.

I have attempted to explain mathematics using the idea of points and that points can be formulated appears necessary.

Logical formulations such as [if A then B] also are necessary in that, just by positing the assumption [if A], we are creating a reality in which there is some thing, [A] and if it is the case that [A] then it will also be the case that [B], whatever [B] actually is.

Simply by positing the conditional, we are bracketing off some aspect of the particular reality we find ourselves in, and assuming it will be so.

We can imagine that the observable world described in physics, for instance, could be different.

Perhaps, if it were different, we could not exist in a way that would allow us to develop.

Or, perhaps in many possible schemes of scientific reality, intelligent life can develop.

We could be completely ignorant of these possibilities because our conceptual and representational mental capacities may be limited in ways we can not now comprehend.

Whether or not consciousness is necessary, for one or for all or in some things or in everything, is one of the most daunting and intractable problems for beings.

There seems no ultimate test concerning the necessity of consciousness, whatever the word "consciousness" is meant to refer to in a public sphere.

I have an essay on qualia, here, which deals in depth with this issue and the possibility of philosophical zombies.

Qualia is just another word for sensory experience or particular facet of conscious experience.

Necessity is not something that applies to inductive reasoning or science.

Science is the study of the particular possible ways the world is given to our ability to observe it.

There could be infinite ways in which empirical reality is constituted, though, there may be few that give rise to intelligent beings.

Perhaps the particular way the world is, is precisely the best way to cause life to evolve.

But, maybe there are more and better universes where the particular form of reality is even greater in terms of the ability to create self-awareness through complexity.