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“These cookies are fun to make and especially fun to eat.” (source)

Semantically, these cookies is both to-infinitves’ object; and to-infinitves seems to be the semantic subject of both funs, as is in the sentence of "It's fun to take a walk". Is this right understanding? Or do the to-infinitves become semantic object of both funs?

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    What does "to-infinitives seem to be the semantic subject of both funs" mean? Fun here is an adjective, isn't it? Fun to make is an adjectival phrase.
    – Andrew Leach ♦
    Commented Dec 28, 2013 at 11:03
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    No, (be) fun is a predicate noun; It would be fun to swim there, extraposed from To swim there would be fun. Since fun is an experiential predicate, it can take a complement referring to the experience, which is where the infinitives come from.
    – John Lawler
    Commented Dec 28, 2013 at 21:22

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These cookies are fun to make and especially fun to eat.

As the OP suggests, this is a Conjunction Reduction of

  • These cookies are fun to make and these cookies are especially fun to eat.

Let's just take one of these, OK? It's the same structure in both conjoined clauses.

  • These cookies are fun to make.

The OP also notes that these cookies is the Direct Object of the infinitive to make and normally what one expects to be moved or missing from an infinitive is its Subject, not its DO. And indeed the subject of each infinitive is missing, but that's normal for indefinites.

The real question is how the infinitive make wound up shorn of both its Su and its DO,
and how the DO of make wound up as the Su of be fun.

And the answer is a minor governed cyclic rule called Tough-Movement.

A "governed" rule is one that requires the presence of some particular (kind of) predicate. We say that the rule is governed by the predicate; in this case, Tough-Movement is governed by the predicate adjective be fun.

A governed rule is called "minor" if it only applies to a relatively small number of predicates.
In this case, fun is one of a relative handful of predicates, all taking infinitive complements, e.g: (be) tough, easy, difficult, hard, a bitch, a breeze, a piece of cake, fun, cool, nice.

What the rule does is sort of like A-Raising,
in which the Su of an infinitive winds up as upstairs Su, e.g:

  • It seems to be a long way to Tipperary.
  • There is likely to be a unicorn in the garden.
  • The shit appears to have hit the fan.

Here the boldfaced idiomatic or dummy subjects of seem, likely, and appear (all of which govern A-Raising) are unambiguously licensed by (or "originated in", as one says when one uses "movement/raising" syntactic terminology) the infinitive complement clauses:

(Extraposition and There-Insertion have generated the It and There dummies,
and the idiom chunk subject in the last sentence clearly goes with hit the fan.)

However, this is A-Raising, a major governed rule, very frequent with many predicates.
Tough-Movement, by comparison, works exactly the same way as A-Raising, with two differences:

  1. Tough-Movement raises the Object of the infinitive clause, and not its Subject
  2. A small set of predicates governs Tough-Movement, and a large set governs A-Raising
    (these sets are disjoint, btw; no predicate governs both.)
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I think that there's a complication with the emphasiser(?) 'especially' here that deserves a mention (it's going to get one anyway).

These cookies are tasty and inexpensive.

obviously uses two coordinated predicative adjectives to modify (give some / more information about) the referent, the baked whatsits. The subject is 'These cookies'.

This new game is fun.

shows that 'fun' can be used without shame as a (here predicative) adjective.

These cookies are fun.

seems to be incomplete (the notion of food, rather than eating, being fun is rather stretched. The implication would probably be that they are a weird shape and/or colour.)

These cookies are fun to eat / These cookies are fun to make and fun to eat.

sounds fine, however, with the addition of the 'adjective complement' showing what the fun is actually associated with. Quite a few adjectives readily accept (or even require) complements. Some authorities prefer the term 'modifiers' to 'complements', as they're not always necessary. As seen in OP's example, to-infinitives comprise one type:

She is curious to know . . .

I was sorry to learn . . .

He is quick to take offence.

They are hard to beat.

He is likely to fail the test.

The complication with OP's example is the inclusion of 'especially'. All four of the adjectives above accept the intensifiers 'very', 'really' and if you'll excuse the register 'frightfully'. I'd say that 'fun' doesn't (with the possible exception of 'really' - and 'real' might be considered as acceptable, with 'fun' being so nouny). So I'm preferring the interpretation of 'especially' here as a pragmatic marker emphasising the whole sentence (which makes little difference semantically):

These cookies are fun to make. It's even more fun eating them.

These cookies are fun even to make. But oh, are they fun to eat!

These cookies are fun to make. And THEY ARE FUN TO EAT!

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  • I’m very much obliged. So your third and fourth cases (He is quick to take offence.They are hard to beat.) are to express ‘to be associated with the activity of to’s complement denoting; the first (She is curious to know) does ‘to do the activity’. Would this be in line with your answer?
    – Listenever
    Commented Dec 28, 2013 at 12:21
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    Here is a lightweight breakdown of the usual semantic tie-ins of the adjective + to-infinitive construction. You're right in saying that 'She is curious to know how to solve the problem' and 'Maths tables are good to know' for example are more different than they appear at first glance.
    – Edwin Ashworth
    Commented Dec 28, 2013 at 12:33
  • I’ve read well what you’ve linked to. And I hope you would give me another answer. In ‘He is not old enough to go to school’, which one of the two, adjective old or adverb enough, takes the to-infinitve as its complement? (Having looked up CGEL, I’ve found no case that adverbs take to-infinitve complement other than -ly adverbs. So I’m confusing which one does.)
    – Listenever
    Commented Dec 28, 2013 at 13:48
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    There comes a time when it makes more sense to consider individual constructions as if they were multi-word lexemes or at least not to analyse them too deeply. So 'ship of the desert' is an idiom for 'camel' (though the plural is 'ships of the desert' – there is some internal structure). 'Take off' in one sense = 'impersonate' (though the object may be placed between the two obvious parts of the lexeme). Here [8] is a sensible treatment of the '__ enough to __' structure (and others) – it lumps 'adjective/adverb' for 'old enough' etc.
    – Edwin Ashworth
    Commented Dec 28, 2013 at 16:27
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    @Listenever: In "He is not old enough to go to school", the determinative "enough" is a post-head modifier for the adjective "old". (Similar to [74.iii] "The furniture isn't robust enough for that kind of treatment", page 397 in CGEL.) So, your example is somewhat similar to "He is not too young/old to go to school".
    – F.E.
    Commented Dec 28, 2013 at 20:24

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