Meaning of "appear" in "She appears to have had two children" [closed]

What is the meaning of appear in the following examples:

1. She appears to have had two children.
2. He appears to have been elected as the first pope outside of Europe.
3. Their aircraft appears to have crashed near Kathmandu.
4. Their offer appears to be the most attractive.

Or, for example, when you try to open a file in Autodesk Simulation Mechanical, you see an error message like:

Warning: [file] appears to be open already.

Solution 1:

Here, the sense employed is #2 from the ODO link you provided:

Seem; give the impression of being:

[WITH INFINITIVE]: she appeared not to know what was happening

Note the example given matches your own.

In practice, this rhetoric is typically used when we want to state a fact while simultaneously conveying mild surprise, or distancing ourselves¹, from the reality of that fact.

If you need a mnemonic, consider that when a person appears at a party, it is as if they have suddenly, unexpectedly "popped into existence". Similarly for these facts. They're true, but mildly surprising.

¹ _{The alleged baby-candy-stealer went on to state...}

Solution 2:

Appear is an unusual verb in a number of ways:

• it's a sense verb of sight, but isn't restricted to visual appearance;

• it's a flip verb, in that the subject isn't the perceiver but rather the source of the percept
  (like that scares me rather than I'm scared of that);

• and it's so close to the meaning of seem that it has virtually the same syntax as seem,
  which is quite a lot of syntax indeed.

It's hard to figure out the meaning, because there isn't very much. Seem and appear are one-place (intransitive) verbs that take clauses as their logical subjects, and essentially say nothing about the subject clause, except that it represents a guess.

But English does not like long sentences with the verb last. So there are syntactic rules like Raising to break these awful sentences into something that sounds like English.

• *For their offer to be the most attractive seems/appears.
      === Subject-Raising ==>
  Their offer appears to be the most attractive.

• *For Harry to have won seems/appears.
      === Subject-Raising ==>
  Harry seems/appears to have won.

• *For there to be a party tonight seems/appears.
      === Subject-Raising ==>
  There seems/appears to be a party tonight.