You are definitely over-committing yourself if you mean that everything we can know is mediated through the senses – I mean, mathematics? Logical tautologies?
As with my earlier discussion of science, the key missing idea here is that of the map/territory relation. If scientists and philosophers would realize that they’re building models/maps to explain the world, and not defining rules that govern how the world/territory works, our understanding of these issues would improve drastically.
Frankly, I find it preposterous to suggest that mathematics can be known without relying on sensory perception. Show me a way to teach a child addition that doesn’t rely on sensory perception–no blocks, no pictures, no counting on your fingers. Then, and only then, will I grant that mathematics can be intuited without sensory perception. Yes, armchair philosophers can understand math without reference to specific measurements. But only because they’ve previously perceived an enormous number of examples of mathematical theory working.
Based on observation, we create a model; we test it; it works; over time we accept it as very strong theory. That’s our inductive process, for science, for math, for logic. After we have our model, we extrapolate, interpolate, and infer–deductive processes. So we can figure out that 9823+2349=12172 without measuring. But only because we’ve previously seen so many other applications of our addition theory work, without ever seeing one fail. We trust that we don’t need to test it, based on the enormity of evidence supporting the model. But our trust doesn’t make the theory true.
(Editorial note: Philosophy Bro writes casually about interesting issues in philosophy. In a previous post about Free Will, the author used a word I found offensive, and I said so in the comments. The word remains in that post, and as such I won’t link to it. However, I like the blog, and am wiling to write off one isolated case of bad judgment in linking to the site.)