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The sophist argues: “the soundness of a rational argument, depends on the non-existence of any sound objection to it. But how can we ever survey all objections ever raised against this argument? And even if we could somehow muster the resources to refute every objection in existence, what’s to say that some novel objection will not be raised in the future?

If all the above is granted, one must admit that rational arguments can only be judged as sound on a provisional basis. And that all conclusions stemming from such arguments are inherently indecisive.”

We say: knowing that a rational argument is sound, does indeed depend on knowing that no sound objection to it can exist. However, knowing that no sound objection can exist, does not depend on refuting every objection ever raised. Rather, we can come to know that no sound objection can exist by investigating the original argument itself. This is because, granting the argument’s validity^[1], either its premises are known non-inferentially, or they are known inferentially.

If the premises are known non-inferentially, then any objection that can be raised- whether in the past, present, or future- will be an objection against what is known non-inferentially. And any such objection can be dismissed on this basis^[2].

If the premises are known inferentially, then those premises are demonstrated using other, second-order arguments. 

Then, we recursively investigate whether any of the premises in those second-order arguments are known inferentially. If so, then we demonstrate them using third-order arguments. And so on and so forth for each inferred premise, until we reach a base case where all premises are known non-inferentially^[3].

At this point, any objection that can be raised against the original premises, will be an objection against arguments whose premises are known non-inferentially. And such objections can be dismissed as above^[4].

Useful corollary I: identifying fallacious arguments

From the above it is clear that premises which are, either directly or indirectly, known non-inferentially, cannot be rejected on the basis of a sound objection, and must be true.

For the same reason, a premise in an argument which, either directly or indirectly, conflicts with what is known non-inferentially, must be false. Thus, one way to decisively demonstrate the fallaciousness of an argument, is to show that at least a single premise that its conclusion depends on, conflicts with what is known non-inferentially.

Useful corollary II: the faith of the one who is unable to answer an objection

It is established that faith in Islam is conditioned on certitude in the truth of the religion. It can therefore be asked: “does the layperson who is presented with an objection against the religion, a disbeliever if he is unable to answer this objection?”

We say: he is not a disbeliever. As there is no contradiction between knowing that no sound objection exists, and not-knowing why a particular objection is not sound. His faith is conditioned on the former, while his inability to refute the objection is due to the latter.

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[1] In other words, assuming the argument is in a productive form, such that the truth of the premises guarantees the truth of the conclusion.

[2] Affirming such an objection, would be an affirmation that what is known to be true non-inferentially, is actually not true.

[3] Such that each premise that is known inferentially, is supported by a separate argument demonstrating its truth.

[4] Therefore, any valid argument, whose premises are reducible to non-inferential knowledge, cannot suffer from sound objections. The conclusions of such arguments are true with decisive certainty.

And the validity of the argument is likewise, either known non-inferentially or inferentially. If the former, then validity is guaranteed without need of demonstration. If the latter, the validity is itself demonstrated using separate arguments, whose premises are reducible to non-inferential knowledge.