Mathematical — I like sushi

Like monads?

Logic is mathematical not lingual. It is only applied to language in the same manner it is applied to numbers, but obviously language and mathematics are completely different breeds of thing.

No one can argue over the answer to a calculation, but many can argue over the answer to a question like 'Are people like dogs?'

Language befuddles us as philosophers because we invest into language more than what language actually is, which is a tool for thinking, creating, and communicating. Language is a cultural and biological artifact. But because all of our thoughts are linguistic, to us words appear elemental. It then becomes the seemingly natural task of philosophy to decide the nature of these elementals of thought.

Well, if we are only discussing language/confusion generally then I apologize, but if it is specifically Wittgenstein’s famous quote in the Philosophical Investigations, then it might help to see the context:

[ Philosophical problems ] …are solved …by looking into the workings of our language, and that in such a way as to make us recognize those workings: despite an urge to misunderstand them. …Philosophy is a battle against the bewitchment of our intelligence by means of language. — PI, #109

It is not language that “bewitches” us; we already have “an urge” (for purity, certainty) which is the cause of our being charmed out of thinking clearly. Language is the “means” by which we “battle against” focusing only on a response to doubt. It is a reference to his method of looking at examples of what we say in specific situations (in a sense, what @Shawn proposes as: “the study of logic”, though more, studying the logic of our ordinary language). The reason it works is because language and the world are tied together (except when that breaks down) in a way that examining what we say, shows us (it is a record of) our interest in each thing, the criteria we use to judge it (the “workings”).

Now of course he does also point out that our forms of expression get us into problems. One is that we use analogies that make things look simple. The relationship between a noun and an object (see @Joshs above) makes us imagine a framework where all words refer to (point to) objects, and then we force the framework onto everything else that isn’t an actual object, like imagining “ideas”, “sensations”, “meanings”, or “reality” as things. Also, the desire for simplicity and certainty is the motivation of @fdrake’s observation that we, for example, want “I know” to have only one generalized sense.

I would only pointedly argue that the answer the PI is fighting against is for philosophy to abandon our regular expressions (to be more certain)—go “outside the box” as @Pierre-Normand’s authors call it—but should, rather, root out the urge to do so itself in appreciating the ways language is rational, clear, and precise enough in a multitude of ways.

Regarding the statement about philosophy being the bewitchment of our intelligence by the means of language, then why is that so?

*True* spoken language is an extremely important part of our intellectual life and our subsistence. I think the context of this fact is why most philosophers orate before they write. Certain visual and language symbols are 'built-in' to our social development, and words 'appear' to us as imaginary objects that are ready-for-the-taking. This is proven in tribal communities where common visual and language forms are found in completely isolated environments. They are there for us as the concrete substance of our lives, past and future. Because of this physiological significance, they have the flavour of the infinite. The physiological meaning of a word is both psychological and imagined; the imagination encompassing the internal synthesis of the past, present, and future, the psychological as the external realization of necessity and power. The imagination can never be ignored or taken away the way conventional logic can, and power can never be argued with.

The question of why language mediates philosophy, is generally pointing to a derivation of language from necessity and specificity; a psychological reality. It is the dissolution of abstract universals into subjective universality. It's where a statement like 'This bottle contains soap' finds itself in a complex web of particularities, each reflecting in a complex network of representations. As previously mentioned, nobody can use language convincingly to express doubt that the bottle is a bottle and that it contains soap, and this is more than just due to convention, but as a past and a future that together express themselves in the determination; and they must also do this internally. The imagination can doubt the bottle is a bottle, which is why it can't be ignored, and imagination and philosophy go hand-in-hand. I think this was where de Saussure was coming from when he stressed the difference in diachronic and synchronic meaning.