Mendacium contemnendum est.

Mendacium is a neuter singular noun from mendacium, mendacii, meaning lie, falsehood, or sometimes deceit.

In form, mendacium could be either nominative singular or accusative singular, because neuter nouns of the second declension have the same form in those two cases.

Here it is understood as nominative singular, because it is the subject of the sentence:

• Mendacium contemnendum est = A lie must be despised / Falsehood is to be despised

So even though the form could also be accusative in another sentence, here the syntax shows that it is nominative.

Contemnendum is a gerundive: a verbal adjective built from the verb contemnere.

The verb is:

• contemno, contemnere, contempsi, contemptum = to despise, to scorn

The gerundive often carries the idea of necessity, fitness, or that which is to be done.

So contemnendum literally means something like:

• to-be-despised
• deserving to be despised
• needing to be despised

Because it is an adjective, it must agree with the noun it goes with.

Because it agrees with mendacium.

Since mendacium is:

• neuter
• singular
• nominative

the gerundive must also be:

• neuter
• singular
• nominative

That gives contemnendum.

Compare how it would change with other nouns:

• vir contemnendus est = the man must be despised
• femina contemnenda est = the woman must be despised
• mendacium contemnendum est = the lie must be despised

So the ending is there because of agreement, not because the meaning of the verb itself changes.

This is the passive periphrastic.

It is made from:

• a gerundive
• plus a form of sum (to be)

So:

• contemnendum est = literally is to be despised

This construction usually expresses:

• necessity
• obligation
• sometimes strong recommendation

So the whole sentence means something like:

• A lie must be despised
• Falsehood should be despised
• A lie is to be despised

Because the passive periphrastic needs a form of sum to complete the idea.

Without est, contemnendum would just be a verbal adjective meaning to-be-despised or deserving scorn, but it would not make a full statement.

With est:

• contemnendum est = must be despised / is to be despised

So est is what turns the adjective into a full predicate.

It can mean both, depending on how literally or naturally you translate it.

The Latin construction itself is is to be despised, but in English that often sounds stiff. So the usual idiomatic translation is:

• must be despised
• should be despised

The difference is mostly one of English style:

• is to be despised = more literal
• must be despised = stronger, very common
• should be despised = sometimes a little softer

So if the meaning has already been given to the learner, the main thing to know is that the Latin grammar expresses necessity or obligation.

Latin often leaves that unstated when the statement is meant generally.

So Mendacium contemnendum est means something like:

• A lie must be despised
• Falsehood is to be despised

without explicitly saying by us, by everyone, or by good people.

If Latin wants to say who has the obligation, it often uses a dative of agent with the passive periphrastic. For example:

• Nobis mendacium contemnendum est = We must despise a lie
  literally, To us a lie is to be despised

In your sentence, that dative is simply omitted because the idea is general.

It can easily be understood generically.

Latin often uses the singular to talk about a whole class or idea. So:

• mendacium can mean a lie
• but it can also mean lying / falsehood in general

That is why English translations may vary:

• A lie must be despised
• Falsehood must be despised
• Lying is to be despised

All can fit the Latin, depending on context.

Because Latin is not saying merely to despise a lie as an action. It is making a statement of necessity about the noun mendacium.

The gerundive is especially useful for this idea:

• mendacium contemnendum est = a lie must be despised

If you used an infinitive, you would get a different structure and usually a different sense. The Latin here is focused on the noun as something that ought to receive the action.

That is one of the most important uses of the gerundive: it lets Latin say that something needs to be done to a person or thing.

The basic verb is:

• contemno, contemnere, contempsi, contemptum = to despise

The gerundive is formed from the present stem plus -ndus, -nda, -ndum:

• contemn-
  • -endum = contemnendum

So the pattern is similar to other gerundives:

• amandus = to be loved
• monendus = to be warned
• regendus = to be ruled
• audiendus = to be heard
• contemnendum = to be despised

Knowing the dictionary form helps you recognize where the gerundive comes from.

Yes, Latin could vary the order.

Because Latin marks grammatical relationships with endings, the words do not have to stay in one fixed English-style order. So these would mean essentially the same thing:

• Mendacium contemnendum est
• Contemnendum est mendacium
• Mendacium est contemnendum

The choice of order can affect emphasis or style, but not the basic grammar.

With mendacium first, the sentence may feel as though it starts with the topic:

• As for a lie / falsehood, it must be despised

So the order you see is natural and straightforward, but not the only possible one.