Quamvis severitas iudicis multis dura videatur, honestas tamen eius omnibus clara est.

Because quamvis here introduces a concessive clause: although / even though. In Latin, quamvis very commonly takes the subjunctive.

So:

• quamvis ... videatur = although ... may seem
• not because the action is unreal, but because this is the normal grammar after quamvis

The main clause, however, stays in the indicative:

• honestas tamen eius omnibus clara est

So the sentence has a very common pattern:

• quamvis
  • subjunctive
• main clause in the indicative

Here quamvis means although or even though.

It introduces an idea that is conceded, but then the main clause gives a contrasting point:

• Quamvis severitas iudicis multis dura videatur = although the judge’s strictness may seem harsh to many
• honestas tamen eius omnibus clara est = nevertheless, his integrity is clear to everyone

So quamvis sets up the contrast, and tamen answers it.

Latin often likes to mark both sides of the contrast.

• quamvis = although
• tamen = nevertheless / still / yet

Together they make the opposition very clear:

• Although X, nevertheless Y

English can do this too, though we do it less regularly. In Latin, this pairing is very natural and common.

Iudicis is genitive singular of iudex, iudicis (judge).

It depends on severitas:

• severitas iudicis = the severity / strictness of the judge

So this is a genitive showing possession or association. A native English speaker can think of it as equivalent to either:

• the judge’s strictness
• the strictness of the judge

Because severitas is the subject of videatur.

In the concessive clause:

• severitas iudicis = the judge’s strictness
• dura videatur = may seem harsh

So the thing that seems harsh is severitas, and that is why it is nominative.

They agree with the nouns they describe:

• severitas is feminine singular, so dura is feminine singular
• honestas is feminine singular, so clara is feminine singular

This is standard adjective agreement in Latin:

• same gender
• same number
• same case

So:

• severitas ... dura
• honestas ... clara

Multis is dative plural because with videor (to seem), Latin often puts the person affected in the dative:

• multis dura videatur = may seem harsh to many

This is very idiomatic Latin. English uses to many; Latin uses the dative for that idea.

So:

• severitas iudicis multis dura videatur = the judge’s strictness may seem harsh to many people

For a similar reason. Clara est omnibus means is clear to everyone.

Latin commonly uses the dative with adjectives like clarus when something is clear, evident, or known to someone.

So:

• omnibus = to all / to everyone

This is not the subject. The subject is honestas.

This is a very common learner question.

Latin uses:

• suus, -a, -um for a reflexive possessive: his/her/its own, referring back to the subject of the same clause
• eius for his/her/its, referring to someone else

Here the main clause is:

• honestas tamen eius omnibus clara est

The subject of this clause is honestas, not iudex. Since the possessor is the judge, and the judge is not the subject of this clause, Latin uses eius, not suus.

So:

• honestas eius = his integrity
• not honestas sua, which would refer back to the subject honestas in a reflexive way and would not make sense here

Both are abstract nouns ending in -tas:

• severitas = severity, strictness, sternness
• honestas = honesty, honorableness, integrity, moral uprightness

In this sentence they are being contrasted:

• the judge’s strictness may appear harsh
• but his integrity is obvious

So the sentence contrasts outward harshness with inner moral worth.

Yes. Very literally:

• dura = harsh
• videatur = may seem / may appear

Together:

• dura videatur = may seem harsh

Depending on context, English might also express it as:

• seems harsh
• is regarded as harsh
• appears harsh

But grammatically, videatur is simply the passive form of video used in its common meaning seem.

Latin word order is much more flexible than English word order because Latin shows grammatical relationships mainly through endings, not position.

This sentence is arranged for emphasis and balance:

• Quamvis begins the concessive clause
• severitas iudicis puts the first key idea up front
• multis dura videatur delays the verb to the end of the clause
• tamen marks the contrast at the start of the main clause
• honestas ... clara est presents the stronger counterpoint

A rough structural outline is:

• Although [the judge’s strictness] [to many] [harsh] [may seem],
• nevertheless [his integrity] [to everyone] [clear] [is].

Latin often places important adjectives and verbs later for emphasis.

Yes. In natural English, both are possible depending on style.

The Latin dative here expresses the people from whose point of view something seems harsh or is clear:

• multis = to many / in the eyes of many / for many
• omnibus = to everyone / for everyone / in everyone’s view

So the exact English wording can vary, but the Latin grammar remains the same.

Classical Latin does not have definite or indefinite articles.

So Latin simply says:

• severitas iudicis
• honestas eius

and English must decide whether to say:

• the judge’s strictness
• a judge’s strictness
• his integrity
• the integrity of the judge

In this sentence, context clearly favors the judge’s strictness and his integrity.

Yes. It creates a neat contrast:

• multis = to many
• omnibus = to all

So the sentence says something like:

• his strictness may seem harsh to many
• but his integrity is clear to everyone

That is a carefully balanced idea. The first judgment is limited and subjective; the second is universal and certain.

This contrast strengthens the sentence’s point: people may disagree about his sternness, but no one can miss his integrity.