Solution 1:

So foolish, unreasonable, or out of place as to be amusing.

Here are some more examples of this construction. This time in full sentences:

  • This action was so forceful/beautiful/thoughtless/terrifying as to cause the audience to burst into tears.

  • She sang so beautifully/movingly as to cause her audience to take to the aisles.

We’ll revisit these sentences below. Before we dive in, however, a brief diversion:

A diversion

Some words, rather than having a meaning of the sort you can look up in a dictionary, can only be interpreted from the context in which they occur. This might be the physical environment or the actual conversation that they occur in. In order to interpret them you often need to orientate yourself to the position of the speaker or intended listener.

Examples of this are the words I and you. To illustrate, I at the moment of speaking, as you read this, refers to 'Araucaria'. You know this because you understand that the word I points towards the person who is speaking (or writing) in order to show who it is meant to refer to. Generally speaking the word I does not mean Araucaria

Another word like this is today. At the point of writing, today refers to 26th of June 2014 (British Summer Time). If you look up today in a dictionary, it won't say "26th June ... ." To understand today you orientate yourself to the position of the speaker at the time of speaking. You understand that the day that they intend to refer to, is the day during which they are, or were, speaking.

The term for this kind of linguistic pointing is deixis. I and you, this and that, yesterday and tomorrow are deictic words. That is a useful word to consider at this point. An important point here is that in order to understand that, we need some form of contextual clue to grasp what the speaker is referring to. We might get the clue from the rest of the conversation - or we might get it from the physical environment we are in.

For example, someone might say Give me that whilst pointing at a banana. We understand that the speaker is using the word that to represent a certain banana. However, we don't understand this from the conversation itself but through the speaker physically pointing towards the intended referent. If the speaker was standing in a greengrocer's we wouldn't understand what they were referring to if they did not point! Deictic words like that require that some kind of clue is given to facilitate their interpretation.

So (x)

Back then to so ... as to. In the definition in question, so is a deictic adverb. It is also a degree adverb; it points to the size, extent, measure or degree of a property. This property usually appears in the sentence in the guise of an adjective:

  • This action was so forceful/beautiful/thoughtless/terrifying as to cause the audience to burst into tears.

In the example above so is syntactically and semantically modifying the adjective that comes after it. However, as with other adverbs of degree such a quite, rather and extremely, so also commonly modifies adverbs:

  • She danced so forcefully/beautifully as to cause the audience to ...

As mentioned above so refers to the extent of the property described in the word it is syntactically modifying. Crucially, in a normal sentence ( - not an exclamation) the speaker must indicate how big or small this is. They must provide some kind of index which explains how great this extent actually is. In the same way as previously discussed with that, this information may come from the environment that the speaker or listener finds themselves in, or it might come from the text of the conversation itself.

A fisherman, for example, telling his friends about a fish that got away, may hold his hands apart in front of him and say:

  • "It was about so big, and it had...,

Or someone wanting to indicate how tall a particular plant is may hold their hand out above the ground and say:

  • "It's about so tall ...

Which may shortly be followed by:

  • ... and about so wide."

Here the index is provided physically by the speaker’s hands.

When no such environmental clue is given, the exact measure or degree that the word so represents must be provided in the conversation itself. In the construction we are talking about, this extent is explicitly explained in the phrase beginning with as to.... Consider the following example:

  • His ears were so big as to block out the sun.

Here the phrase to block out the sun doesn't only tell us a potential result of the ear situation. The result itself, as described in the phrase, fulfils the linguistic function of providing the required index for the 'extent' of the bigness. In other words, it has the function of informing us of the 'extent' represented by the adverb so. This, as we have described, is a mandatory feature of the use of this word in non-exclamations.

As ...

The preposition as often appears in comparative structures concerning equality:

  • as heavy as an elephant.
  • (not) such a heavy animal as an elephant.
  • (not) so heavy as an elephant.

In the first example, you may notice that there are two forms of ‘as’. The first is a degree adverb modifying the adjective heavy. The second, which we are currently concerned with, is the preposition. This particular as normally introduces something which is being equalled (or surpassed) in some way by another item in the sentence. So in the sentence:

  • Bob is as tall as Bertha.

Bertha represents an entity whose ‘tallness’ is at least equalled and maybe surpassed by Bob. In all these constructions the as phrase has an indexing function where it sets some kind of benchmark which is met (or, where negation is involved, not met).

In the so (x) as to (y) construction, this benchmark indicates the intensity of the degree adverb so. It tells us that the ‘extent’ of the x-ness meets or exceeds the level required to cause ‘y’ to occur.

As, like other prepositions, can take different complements. When used with this indexing function, as often takes a clause in which material - echoing sections from the superordinate clause - has been deleted:

  • Bob is as tall as Bertha (is tall).
  • was not so heavy as an elephant (is heavy).
  • The second party was not such a success as the first (party was a success).

However, in the so (x) as to (y) construction, there is no repetition of this type of material from the main clause, whether it is deleted or not. Here a finite clause is not possible with the same meaning:

  • She danced so beautifully as that the audience clapped. * (wrong)

The clause after as must be a non-finite infinitival clause. In the examples given these all begin with the word to. It would be tempting to think that the to here actually belongs to some kind of as to phrase. It does not!

To

There is simple evidence from negative clauses that shows that to belongs with the following verb phrase, not with as:

  • so small as [not to be seen distinctly without a magnifying glass].

The word not here precedes to. It is the entire verb phrase following not which has been negated.

Further note that there is a missing subject in all so (x) as to (y) clauses:

  • The music was so awful as to cause the revellers to stand still.

Here the subject of the verb CAUSE is understood to be the music. In such sentences, the subject of the subordinate clause is always understood as being the same as the subject in the main clause:

  • The music was so awful as (for the music) to cause the revellers to stand still.

  • It was so foolish, unreasonable, and out of place as (for it) to be amusing.

If we wish to introduce a completely different subject, it is necessary for it to be introduced by the subordinator for (a relatively rare occurrence):

  • It was not so serious as for the government to take any action.

Here the subject of the main clause is it, which may refer to a specific situation. We have a different subject for the infinitival clause, the government, and this clause is therefore mandatorily preceded by for. This demonstrates again that to in this construction is part of the verb phrase, it is not part of an idiomatic as to phrase.

'so (x) as to (y)' and 'so (x) that (y)'

The Original Poster noted that so (x) as to (y) and so (x) that (y) constructions are similar. They are, but they are certainly not the same. There are important semantic and grammatical differences. First, however, let us consider the similarities. Firstly, the function of the as and that clauses are the same. They both provide an index for the interpretation of the adverb so. Secondly, the clauses both describe some kind of result.

However, as the OP also noted, the grammar of the two constructions is different. Here is how it’s different: firstly, as in the first construction is obligatory, that in the second is not:

  • so foolish as to be amusing.
  • so foolish to be amusing. * (wrong)
  • so foolish that it is amusing.
  • so foolish it is amusing.

This mirrors the fact that as in the first construction is a preposition and heads the phrase. That in the second is a subordinator and merely marks the phrase that follows as subordinate. Moreover, the verb in the as construction, as we noted, is non-finite. It has no tensed verb. Instead it uses an infinitive. The clause cannot stand on its own:

  • To cause her to burst into tears. (not a full sentence).

The clause marked by that on the other hand is a finite clause with a verb that has tense. The clause can stand as a sentence in its own right:

  • It is amusing.

Lastly, we previously noted that the subject in the as phrase is omitted in a so (x) as to (y) sentence. The subject in the clause with that contrastingly must be overtly stated:

  • It was so foolish as to be amusing.
  • It was so foolish that it was amusing.
  • It was so foolish that was amusing. * (wrong)

So much for the grammar. The OP also wondered about the semantics of as and that. Well, as, as discussed above introduces some kind of benchmark which is met or exceeded. That appears to have no meaning at all - a point reinforced by the fact that we can miss it out altogether without it affecting the meaning of the sentence. More fundamentally important however, is that the two constructions do not mean the same thing. They do not have the same truth values. Consider the sentence below:

  • My pet cobra had a venom so powerful as for its bite to kill a grown adult in less than thirty seconds.

Because the verb in the subordinate clause is an infinitive, it gives a theoretical meaning to the proposition it introduces. The proposition may or may not have actually occurred. The result shown, which is of an adult dying from the venom within thirty seconds of being bitten, is hypothetical, not factual in the sense of describing a real individual who died. In the construction with that the verb is tensed. This usually encodes that the sentence be considered as a factual state of affairs, not a hypothetical one. Compare the example above with the following:

  • My pet cobra had a venom so powerful that its bite killed a grown adult in less than thirty seconds.

This sentence is rather more alarming than the first, because it involves a factual, not notional fatality. The so (x) as to (y) construction implies a notional result, the so (x) that (y) sentence on the other hand entails a factual result.

Conclusion

In so … as to sentences, so is a deictic adverb of degree. So receives its interpretation from its intensity being indexed by a notional result (which may or may not be interpreted as having actually happened). This result is described in a non-finite clause headed by the preposition as. Where to follows the preposition, the subject of the clause is omitted, and is interpreted as being identical to the subject of the main clause. The to in this construction is part of an infinitival verb phrase, it is not part of an as to idiom, or an as to subordinator. Although so … as to sentences bear certain similarities to so … that sentences, they are materially different constructions, both in terms of meaning and form.

Solution 2:

The word so is an adverb that means, in this context, to such a great extent. For instance, you might say:

He was driving so fast that he lost control of the car.

This is the sense that applies in the sentence you quote. The phrase as to be is simply another way to say that it is. So your sentence is saying that someone is very foolish, to such a great degree that it is amusing.

This use of so is mostly unrelated to its use as a conjunction that means therefore.