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When one moves from Natural language to a logical one, then the motivation , to my understanding is to cut down the amount of ambiguity which can be there in communication.
However, I find it that many things of beauty in real life, derive their allure from being able to interpretable in many different angles (eg: a painting, or a music), so would it be beyond the scope of logic to be used as a model to describe such qualities of Art?
It seems possible from your comparison of natural language to logic that you are asking whether the notation typically used in mathematical logic is adequate for talking about art. If so, then the answer is that the notation of mathematical logic is a highly idealized and restricted language that is not only not adequate for art; it is not adequate for hardly any of the communication that natural language is used for. For one thing, it contains only assertions, while natural language contains many other types of sentences and speech actions. For another thing, the notation of logic has no facility for double implication, irony, non-literal speech, or other features commonly employed as part of human communication.
On the other hand, if you really mean logic as opposed to language, then you are probably referring to the predicate calculus or at least to some deductive logic expressed in a formal language, because although there have been attempts to formalize non-deductive logic, to my knowledge it has never been successful. So if you are asking whether art is "beyond" deductive logic, then, once again, practically all reasoning that people do is beyond deductive logic. Deductive logic isn't even adequate for deciding what you want for lunch.
Finally, if you are asking whether logic can be applied to reasoning about art at all, then the answer is yes. Logic is just the study of correct reasoning. Assuming the reasoning you have in mind has a correct and an incorrect form, then logic applies to it. However, it is arguable that, at least in making aesthetic judgments, there is no right and wrong thinking, that such judgments are entirely subjective. In this case logic would not apply to that part of art just as it does not apply to deciding whether you feel pain or not.
ADDENDUM
Another answer says that logic is a formal set of rules, whereas my answer says logic is the study of correct reasoning. Actually, both definitions are correct, even if they are inconsistent with each other. Unfortunately, the word "logic" is overloaded and often ambiguous even in the context of philosophy. If the context doesn't make it clear what you are talking about, knowledgeable readers might think that by "logic", you mean any of the following:
There are two additional things people often think you mean by "logic", but I would not call these people knowledgeable in the area of logic:
Logic is the formal set of rules that represent the mechanism of thinking, reason.
Art has, in the sense of this question, moreover, an aesthetic load (a work of art is an object that is appreciated by its beauty). The meaning of the term art is more general than just aesthetics*, but that's out of the scope of the question.
Your question seems to suggest that logic should be able to explain art, or to describe it as a set of logical propositions in a logical set.
Describing art with Logic is impossible. But not because art is "beyond logic". Logic has possibly all necessary primitives to express any kind of mental process. Describing art with Logic is impossible because art is the result of a huge load of subjective components (feelings, emotions, sensations, experience, environment, etc.) that cannot be described by logic because the expression would be humongous. Such would be the equivalent of trying to describe love by writing all the chemical and electrical reactions that occur in every cell of our brain that occur when we feel in love.
If the mental art appreciation process would be simpler, a logical description of art could be proposed. For example,
if:
subject_sees(green_color);
then:
activate(beauty_bit);
So, art is not beyond logic, but beyond of our capacity to describe it by means of logic.
* See a simple definition of art here, pg. 98, paragraph 5, by J. S. Mill, in line with Mario Bunge's definition. In synthesis, science is essentially the theory (e.g. know how to make a shoe or knowing music theory), technique is applied science (e.g. have the ability to apply such theoretical knowledge with my own hands, and actually, not theoretically, but practically, creating a shoe, or playing a song) and art is needs fulfilment by means of technique (e.g. not only knowing the theory, not only knowing how to use my own hands to make a shoe or play a song, but making a product that pleases others, making a product that satisfies some other's necessities, including emotional ones: "hey, I love this shoe", "this song makes me cry"). Such is the sense of the term in the expression state of the arts.
No.
Imagine an artist who is somehow free from any logical thought process during the composition of an abstract painting.
None of their daubs, strokes, blotches, sprays or scratches are governed by any conscious attempt to evoke a particular emotion from either the painter or the viewer. No conscious logic (other than perhaps the knowledge that applying paint to the canvas will result in a viewable painting) has been employed by the artist.
The result? Like much of, if not most art, the result is a work that is interpreted differently by everyone who views it.
What can we conclude from this? Does the fact that the resulting piece was unpredictable mean that it was divorced somehow from logical processes? No. It merely represents an artwork that was created without reflection by the artist as to what logical processes were occurring during its creation.
Does the fact that the interpretation of the artwork is unpredictable and almost infinitely varied mean that its appreciation is divorced from logical mental processes? No. It merely suggests that these processes are highly complex and occur within the viewer at an unconscious level.
Were we to have access to all the available information, we could likely determine precisely why particular hues in particular arrangements influence us the way that they do. These arrangements constitute visual stimuli which cause responses in us that we have no reason to believe are somehow divorced from the law of cause and effect.
And... if we truly want to remove as much romance as possible from the artistic process, we could extend this contemplation of cause and effect to the realms of determinism (which is a very logical - and theoretically predictable - process), which suggests it would be illogical for the painting to be created and viewed in any ways other than the ways in which it was.
Quantum indeterminacy may throw a spanner in the works here, although possibly not at the macro level at which our minds operate. It might be possible to allow for quantum indeterminacy whilst still being able to (theoretically) demonstrate exactly why one person's Kandinsky is another's Klee.
"... However, I find it that many things of beauty in real life, derive their allure from being able to interpreted in many different angles (eg: a painting, or a music) ..."
You can certainly use unambiguous language to express the idea of being interpretable from many different angles.
This is obviously a subject on which there are many different opinions, but it doesn't seem unreasonable to suppose that there is some rational, evolutionary reason for our aesthetic sense. One possibility that fits many cases is that it is the response of our pattern recognition facility. We get a pleasurable feeling when we look at something that initially appears complex, chaotic, and random, and we suddenly spot the patterns and relationships that simplify it, generating all that apparent complexity from simple rules. Or conversely, when a simple insight or observation conveys a wealth of hidden background information and context.
So on a simple level, we like symmetry. Regular, repeated patterns have been used for decoration for millennia. A simple regular pattern of squares is slightly more attractive than random splodges. But then we like more complicated symmetries even more - the decoration of the Alhambra Palace in Spain shows many examples of this. And it explains the universal human response when mathematicians first developed fractals - not just translation, reflection, and rotation, but also at different scales. We recognise and process fractals in nature the same way. Music is also about spotting many different symmetries in apparent complexity - repetition in the beat, in the melody, in the sequence of themes (e.g. verse/chorus), the same theme played at different speeds, pitches, or by different instruments, and so on. We like music that allows us to simplify their apparent immense complexity by spotting the many relationships between the parts.
And we also enjoy the converse process, where a long, complicated and emotionally-significant story is expressed in a few simple words, or a poignant image. The bigger the background picture we can construct from the brief detail shown, the more angles we can find through which to interpret it, the more we like it.
This can be partly described using the mathematics of information theory as something like the data compression ratio - the amount by which our insight has shrunk the apparent complexity. But it is not just the ratio, but also the novelty and cleverness of the insight itself that gives us pleasure.
There's an obvious evolutionary reason why this should be rewarded. The world we see around us is immensely complicated, and we need to simplify it and spot the patterns and relationships that connect all this complexity to the underlying motives and themes. We need it to spot the slight anomaly that doesn't fit the rest of the pattern. Our aesthetic sense trains us to be constantly on the lookout for patterns and hidden relationships. Art stimulates that aesthetic response by presenting us with extremely compressible patterns.
Artists often have this idea that the sciences are blind to beauty; that they take out all the emotional significance in things by reducing them to the empty jiggling of atoms and shuffling of numbers. I suspect this is what you mean by 'logical' language exluding the expressive opportunities inherent in ambiguity. And yet, it has been constantly noted by physicists and mathematicians themselves that their aesthetic sense of beauty in the equations is what guides and motivates them.
It's not often they manage to express that sense of beauty in terms other people can understand and appreciate. When those first pictures of the Mandelbrot set and other fractals came out, the public reaction to them was notable - mathematical beauty is not normally so accessible. But art is fundamentally about spotting patterns and relationships, and so is mathematics. I would argue that the languages science has developed for studying those patterns and relationships are very much capable of dealing with matters of beauty, symmetry, complexity, and seeing things from many different perspectives.
I would instead rather be asking: "Is 'Logic' beyond 'Art'?" Personally, I see mathematics as being an art - pursued for many of the same reasons. But to the extent that they are in conventional usage considered different things, I see 'Logic' going much further and deeper into revealing the hidden relationships between things than what we commonly describe as 'Art'. But as I said earlier - there are many opinions, and this has often proved a controversial one.
No. Art is not beyond logic.
First, what is art is inherently an very broad idea. So broad, it's a highly contested concept.
Art is a diverse range of human activity, and resulting product, that involves creative or imaginative talent expressive of technical proficiency, beauty, emotional power, or conceptual ideas.
So, beauty, art, and aesthetics are not limited to painting and poetry (PhilSE).
Secondly, depending on your definition of logic and judgment, aesthetic judgments themselves are rational (PhilSE). From WP:
Judgement (or US spelling judgment)1 is also known as adjudication which means the evaluation of evidence to make a decision.
Simply put, art critics use reason when explaining their opinions.
Therefore, because logic and art are not separable categories, and people use logic when evaluating art, it is not in any sense beyond.
The tension you're noticing is not between art and logic but between art and determinacy.
You are equating logic and determinacy, but they're not the same (even if there's a lot of overlap). For example, something can be determinate and illogical, like the assertion that 2 + 2 = 5; there's no ambiguity about it, but it's positing an obvious contradiction of mathematics. On the other hand, something can be ambiguous as well as logical, like the expression "actions speak louder than words". We know what the expression means (maybe some don't) and it makes sense, but if interpreted to the letter we'd be left wondering how abstract entities such as "actions" can speak while lacking mouths. Even better are those sayings which are made to seem like paradoxes at first glance, but which when analyzed thoroughly reveal some deep truth succinctly wrapped in an aphorism. Proverbs 26:4-5, for example, is worth much meditation. Mathematics in general tries to be as determinate as possible so that mathematicians spend more time seeing whether a proof works than debating what each term means before they can get to the proof.
With that said, art is not at odds with logic in a broader sense, since art which strives to be harmonious, well-structured, coherent, truthful, and the likes could be said to be logical. And when such a work of art allows itself to be interpreted from multiple angles, often it's to present a coherent whole which is greater than the sum of its parts. That doesn't need to mean falling into illogical or absurdity, and I'd even say that much art which deliberately tries to be absurd is art which fails to understand what makes something truly deep.
