The word "unconvincible" means stubborn or close-minded. There are several synonyms for this word that can be used to convey the same meaning depending on the context of the sentence. These synonyms include intransigent, obstinate, inflexible, unbending, adamant, and pigheaded. Intransigent suggests someone who is unwilling to compromise or negotiate. Obstinate refers to someone who is unyielding or unresponsive to reason and argument. Inflexible suggests someone who is rigid or uncompromising in their position. Unbending implies a person who refuses to change their mind or be persuaded. Adamant signifies a person who is resolute and insistent, while being pigheaded suggests a person who is foolishly stubborn.