conviction / persuasion
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conviction
A firm inner certainty or strong belief in the correctness of an idea, opinion, or fact.
Ich handle aus der tiefen Überzeugung, das Richtige zu tun.
I act out of the deep conviction that I am doing the right thing.
'Die Überzeugung' (conviction/persuasion) is the noun related to the verb 'überzeugen' (to convince). It describes the result of convincing: the state of firmly believing in something.
Seine Argumente waren so gut, dass sie mich überzeugt haben.
His arguments were so good that they convinced me.
To describe the content of the conviction, a subordinate clause with 'dass' (that) or an infinitive construction with 'zu' (to) is very often used.
Ich bin der festen Überzeugung, dass wir dieses Projekt schaffen werden.
I am firmly convinced that we will complete this project.
Common adjectives that emphasize the strength of the belief are 'feste Überzeugung' (firm conviction) or 'tiefe Überzeugung' (deep conviction). Another typical phrase is 'aus Überzeugung handeln' (to act out of conviction).
Sie ist Vegetarierin aus tiefster Überzeugung.
She is a vegetarian out of deepest conviction.
The process of forming an opinion is often expressed with the fixed phrase 'zur Überzeugung gelangen' or 'zur Überzeugung kommen' (to come to the conviction).
Nach langem Nachdenken kam ich zur Überzeugung, dass ein Umzug die beste Lösung ist.
After thinking about it for a long time, I came to the conviction that moving is the best solution.
opinion
'die Meinung' and 'die Überzeugung' are close in meaning because both express what someone considers right. The difference is in the strength. An opinion can be rather casual or provisional. A conviction is firm and deeply rooted inside. Learners may confuse the words because a strong opinion can seem almost like a conviction. If someone is simply saying what they think, you usually use 'Meinung'. If someone is very sure and firmly believes in it, 'Überzeugung' fits better.
Sie hat die feste Überzeugung, dass ehrliche Arbeit wichtig ist.
She has the firm conviction that honest work is important.
Im Büro hat meine Schwester ihre Meinung zu dem neuen Plan gesagt.
At the office, my sister gave her opinion on the new plan.