There is no uncontroversial definition of a language. However, a requirement that is often cited is that there should be rules on how different elements of a language are composed together (syntax). Another requirement is that the elements of a language should have representational content (semantics). Music arguably passes the first requirement: notes cannot be strung together in any way one likes to make music. But it appears to fail the second requirement: it is not obvious that individual musical notes represent anything at all. One might argue that sometimes there are phrases in music that do represent: for example, different instrumental lines in Prokofiev's Peter and the Wolf represent the activities of different animals. But these tend to be rather isolated cases of representation; they are not as widespread and systematic as one would expect from a language (e.g. flutes in music do not always represent birds, or indeed anything at all). Even if music is not a language in the above sense...

I agree that an alien race that differed considerably from us would be unlikely to rate our art and music the same. However, this does not, by itself, show that there is no objectivity in artistic value. If one wished to defend the objectivity of artistic value in the face of such evidence, one might use one of two strategies. (I) One might argue that the alien race is simply mistaken in its value judgements; for some reason---which one would have to independently specify---the aliens get it wrong while we get it right (or vice versa). Alternatively, (II) one might argue for the conditional claim that if the alien race truly understood our art and music, then they would appreciate it; evidence that they do not appreciate should be interpreted as evidence that they do not understand it. Again, one would have to independently specify some reason why the aliens do not understand our art and music. Without more detail on the aliens and their disagreement with us, it is difficult to say which, if either...

I agree that this reasoning seems strange. However, here's one possible justification for it. Any cause can be described in a large number of different ways. For example, a brick thrown at a window can be described as: (i) a brick thrown at a window, or (ii) the movement of a bunch of molecules through space. Which way we choose to describe a cause depends on our interests in the case. If we are interested in atomic physics, we may prefer description (ii); if we are interested in the movement of bricks in the area, we may choose description (i). Suppose that in medicine our interests are primarily to explain and treat disorders. For some disorders, it may be easier to explain and treat them by describing their causes in purely psychological language. For other disorders, it may be easier to explain and treat them by describing their causes in purely physiological language. There may also be difficult mixed cases, as you mention, in which the best strategy is to describe the causes in a mixed...

I don't think that there is a special relationship between predicate logic, as opposed to any other kind of logic (propositional, modal, etc.), and computers. But there is often a special relationship between formal logic and computers. It is often possible to set up physical relations inside a computer to mirror (formal) logical relations. The computer can then take over a lot of hard work for us: it can be used to deduce logical consequences, and to check whether particular logical relations obtain. All one has to do is look at the subsequent physical states of the computer, and read off the logical relations that they embody.

There are data that philosophers aim to respect, and their guesses/hypotheses may either fail to fit, or succeed in fitting, this data. Unfortunately, there is not a great deal of consensus in the philosophical community on exactly what this data consists in. However, many philosophers would like to count (i) our best scientific data, and (ii) many of our common sense intuitions, as data that their hypotheses should respect. One major difficulty is that it is often not possible to fit all the data at once: philosophical hypotheses may explain some data at the cost of ignoring others. Another difficulty is that there can be more than one hypothesis that explains the data, and it can be difficult to tell which explains the data best.