Is “faith”, "substance" or “certainty” more appropriate in this sentence and why? [closed]

Solution 1:

Certainty in someone's sincerity is not a correct expression. You don't have certainty in something but of or about something.

• There is no such certainty about the fourth match on the coupons. Times, Sunday Times (2009)
• I began to realize the certainty of freezing to death if I remained where I was. (Collins)

Longman records as phrases:

certainty of (doing) something

• the certainty of being caught

certainty that

• There’s no certainty that he’ll remember.

In can be used after certainty but, most of the time,¹ not as a repository of your certainty, but as a framework rather, as in

There are few certainties in life. (Cambridge)

or as the quality of being certain present in something, as in

Somehow, the certainty in Tonnison's voice affected my doubts. (inspirassion)

^{1 See comments.}

As for "faith", it is not at all restricted to religion. Most dictionaries record the religious meaning as second, the main being:

complete trust or confidence in someone or something.

• This restores one's faith in politicians. (OxfordL)

In is the most common preposition with faith, and that is because to have faith in something is an idiom:

to believe that (someone or something) deserves to be trusted

• His parents have always had faith in him.
• We had faith in her ability to succeed. (M-W)

Solution 2:

"Faith" would seem to be historically primarily associated with religion, but, if so, modern usage has shifted its domain of application; it can be seen that the most important context where the word is used is not religion but the context of some sort of belief that can be put into certain facts; the first sense defined in the OALD is that one.

faith 1. [uncountable] trust in somebody’s ability or knowledge; trust that somebody/something will do what has been promised
♦ If the company can retain its customers' faith, it could become the market leader.
faith in somebody/something I have faith in you—I know you'll do well.
♦ We've lost faith in the government's promises.
♦ Her friend's kindness has restored her faith in human nature.
♦ I wouldn't put too much faith in what she says.
♦ He has blind faith (= unreasonable trust) in doctors' ability to find a cure.

It can be seen in the SOED that the word has its general meaning already in Middle English and that it takes o its religious sense only in Late Middle English.

I 1 Confidence, reliance, belief, esp. without evidence or proof (Foll. by in) ME
[…]
3 Theol. Belief in the doctrines of a religion, esp. such as affects character and conduct. LME

"Certainty" could be used but the preposition must be changed.

• If negotiations are to prove fruitful, there must not only be sincerity on each side, but there must also be certainty as to the sincerity of the other side.

"Certainty" fails to connote the idea of trust associated with faith; whereas "certainty" implies more factual phenomena, "trust" relies on phenomena that are not so tangible.

The awkwardness felt relative to the idea of "the substance in someone's sincerity" is understandable as sincerity is not a concept that lends itself to being described in terms of substance; it is only the appraisal of a match/mismatch between a stance of an individual and a state of mind of his/hers that is made up of levels, of certitudes/incertitudes, of likes/dislikes, and which, according to how the stance reflects the particular weighs of these opposites, can be considered as categorizing the individual in question as either not very sincere, hypocritical, sincere, very sincere, etc. The concept of substance is foreign to the idea of appraisal: the essence of the idea in the decision about how well founded is this match/mismatch is uniquely that of a judgement.

As shows the most frequent vocabulary on the model "< xxx > of his sincerity", that is the words

"doubt", "pledge", "evidence" and "suspicion",

what matters is the truth of a jugement. The word "evidence" could have been used also.

• If negotiations are to prove fruitful, there must not only be sincerity on each side, but there must also be some evidence of the sincerity of the other side.