The uses of the verbal suffixes -ig and -iĝ have proved to be horrendously confusing for me. After a few hours of pondering, I have come up with the following hypothesis on how each of them works:

Proposition: Many verbs in Esperanto have both transitive and intransitive meanings.

-ig added onto a transitive verb = to cause to be [past participle of the verb]
vidi – to apprehend by sight (to see, transitive)
vidigi – to cause to be apprehended by sight (to show, to display)
ex. Mi vidigas la libron al la viro, I show the book to the man.

-ig added onto an intransitive verb = to cause to [verb]
vidi – to have the ability to see
vidigi – to cause to have the ability to see (to give sight to)
ex. Mi vidigas vin, I cause you to have the ability to see (I give you sight)

-iĝ added onto a transitive verb = to be [past participle of the verb]
vidi – to apprehend by sight (to see, transitive)
vidiĝi – to be apprehended by sight (to be seen)
ex. Mi vidiĝas, I am seen.

-iĝ added onto an intransitive verb (inappropriate, but used nonetheless) = to become [verb]
vidi – to have the ability to see
vidiĝi – To become to have the ability to see (to obtain sight)
ex. Mi vidiĝas, I obtain sight.

In order for this to be a credible hypothesis, some issues must first be clarified.

1. Can the above verb “vidi” be used both transitively and intransitively as shown above?
2. Can the verb “scii” be used transitively?

The answer to second question could potentially break my hypothesis. Assuming that scii can be used both transitively and intransitively, the following meanings would apply with the suffixes –ig and iĝ added:

scii (transitive) – to know
sciigi – to cause to be known (not in any dictionary I’ve consulted)
sciiĝi – to be known (also not in any dictionary I’ve consulted)

scii (intransitive) – to be aware
sciigi – to cause to be aware (to inform, dictionary definition)
sciiĝi – to become to be aware (more simply, to become aware, also dictionary definition)

As may already be obvious, the problem that I face with this hypothesis is that the definitions for the –ig and –iĝ forms of the transitive version of scii do not exist in any of the (low quality) dictionaries which I have consulted. If it is indeed true that these meanings do not exist for the–ig and iĝ forms of the transitive scii, if it exists, one of the following must be the case:

1. My hypothesis is fundamentally wrong
2. The dictionaries are wrong for not including the omitted definitions
3. Scii has both a transitive and intransitive meaning, but the –ig and –iĝ forms of its intransitive meaning arbitrarily do not apply

Help!

Thanks a lot.

Well, above all, no verb in Esperanto are both transitive and intransitive. 'vidi' is transitive. So is 'scii'. But in spite of that, your hypothesis is right on the whole, I think. However, -ig- added onto a transitive verb can mean both 'to cause to' and 'to cause to be done'(though sometimes only the second one). For example:
Mi sciigis al la viro sxian morton. = Mi sciigis la viron pri sxia morto.
I informed the man about her death.
In the first sentence, the object of 'sciigi' is 'her death', but in the second one, its object is 'the man'. 'vidigi' also has both, but it's difficult to use the first meaning. For example,
Mi vidigis la libron al la viro.
I think it hard to change it into
Mi vidigis la viron __ la libro. (I can't find a suitable preposiion)
As for -igx- added onto a transitive verb, it is somewhat like 'se ...' in French. For example, 'levi'- 'élever'-'raise', 'levigxi'- 's'élever'-'rise'. The suffix makes a transitive verb intransitive, meaning 'to be(become) done'. Sometimes it can also mean 'to get to do', as your dictionary definition says, bur it's rare.

The meanings of -ig and -igx added onto intransitive verbs are easy to understand, and just the same as you said.

黄鸡蛋:Well, above all, no verb in Esperanto are both transitive and intransitive.

How can this be true? If "vidi" can be used both in the sense of "Mi vidas la libron" and simply "Mi vidas," it is both transitive and intransitive. Another example is scii. "Mi scias la fakton (transitive)" and "Mi scias pri la fakto (intransitive)."

I think you're both right. The lernu! coures Verbumado (which teaches this exact topic) defines a transitive verb as a verb that can have an object. It doesn't always need one.

Some verbs in dictionary have mark "vt,vn":
esperi, fidi, sopiri etc.
This means they can be transitive or intransitive.
But vidi and scii have mark "vt" - they are transitive.

leonarde:If "vidi" can be used both in the sense of "Mi vidas la libron" and simply "Mi vidas," it is both transitive and intransitive.

It's not being used in both senses, as it's transitive in both sentences. The first sentence has an explicit direct object ("la libron"), and the second sentence has an implicit direct object (i.e., the direct object is implied by the context but not spoken - typically it's the words "... kion vi signifas", although others will work in different circumstances).

The sentence "I see", as a simple statement of fact, is technically grammatically correct, but in fact would practically never be said except in a "Me Tarzan, you Jane" sort of way. As a statement that I am capable of sight and am so exercising that power right now, the sentence would almost universally be constructed as "I can see", because even in English the verb is mostly used transitively.

That said, the CEED does list some verbs as both transitive and intransitive. But the CEED, as useful as it is, I don't think is universally considered authoritative.

Maybe I'm wrong, but I would say that "vidi" works exactly like the verb "to see." "To see," when it means "to have sight," implies the direct object "things," I think. When you add "-ig-," it means "to cause to see." Adding "-iĝ-" makes it "to be seen." I'm pretty sure you can't say "vidiĝigi" or "vidigiĝi," so I say instead "vidatigi" and "esti vidigata." Words like "konatiĝi" and "bluiĝi" don't really make sense to me, so I prefer to say "ekblui" or "ekkoniĝi."

"I cause the person to see the cat" = "I show the cat to the person" = "Mi vidigas la homon je la kato" ... or, at least that's how I say it.

Sorry if that's totally wrong.

pacepacapaco:Maybe I'm wrong, but I would say that "vidi" works exactly like the verb "to see." "To see," when it means "to have sight," implies the direct object "things," I think. When you add "-ig-," it means "to cause to see." Adding "-iĝ-" makes it "to be seen." I'm pretty sure you can't say "vidiĝigi" or "vidigiĝi," so I say instead "vidatigi" and "esti vidigata." Words like "konatiĝi" and "bluiĝi" don't really make sense to me, so I prefer to say "ekblui" or "ekkoniĝi."

"I cause the person to see the cat" = "I show the cat to the person" = "Mi vidigas la homon je la kato" ... or, at least that's how I say it.

Sorry if that's totally wrong.

In different languages, words often have nuances. There are hardly two words working exactly the same in two languages. Anyway, it is right that 'vidi' works like 'to see'. However, '-ig-' and '-iĝ-' don't work exactly as any suffixes or other things in English. 'vidigi' means both 'to cause to see' (it is rare, though) and 'to cause to be seen', that is, 'to show'. And what about 'vidiĝi'? It means 'to become seen' or just 'to be seen'. The suffix '-iĝ-' has the meaning 'become', but it has the passive meaning when added onto a transitive verb. When added onto an adjective, '-iĝ-' just means 'to become', so 'bluiĝi' means 'to become blue', and 'konatiĝi' means 'to become known'. Instead, 'ekkoniĝi' should be replaced with 'koniĝi', which has entirely the same meaning but is simpler.