In a world of blind people, c would be the speed of sound

Mmmm ... even totally blind smart people would notice that the Sun's infrared radiation travels faster than sound.
They could probably build instruments and arrive to a world view not very different from ours, much like we have to build instruments to "see" gamma rays, X-rays or even radio waves.
And we do have an organ that detects gravitational force (or rather, its acceleration effect on masses): it is the semicircular canal, the little accelerometer in your inner ear.

Also relevant: Occam's Razor

Imagine a object moving at a constant speed that emits a constant tone. To an listener on that object, the tone remains constant. To a listener that stands near it, the tone will first grow higher in pitch and then lower as it passes you.

Imagine a point. Imagine all the points that are a unit distance from the original point. Let us give this collection of points the name 'circle'.

The distance an object travels when it is thrown is a function of the initial velocity of the object and the angle at which it is thrown.

None of these concepts involve the faculties of our vision. Advanced concepts in math and physics do not require sight. Indeed, even the physics that we now probe, it is impossible to use sight to 'see' these things. Indeed, if a being is so limited in its imagination that it cannot conceive of these things without some tangible (is a circle tangible?) evidence, it is possible to draw them out on a metal sheet, or carve them in wood or wax so that it can be felt with hands.

Do not prejudice yourself with the senses that you have - the logic necessary to grasp upon foundations of math, geometry, and calculus (and thus physics) are easy to come by.

Let us imagine a scientist, who through some disability is prevented from using the tools that you and I use every day. It is difficult for him to write on paper, to type on a keyboard or to use a calculator. Yet, without these tools that we use and depend on, he has found different ways of thinking that go far beyond the limits of the tools that we use. His name is Stephen Hawking.

Let's imagine a race of humans who evolved without sight.

They didn't survive. Natural Selection swung her broadsword and it was all over. Apes rule the earth.

That was a smart-ass answer, but it's got its share of truth. In order to evolve to be a species we consider intelligent (never mind the one that dominates the planet), it is necessary to develop a dominant sense, such as vision, that allows for the location and identification of distant objects.

• If a creature evolving under earthly conditions has developed the requisite intelligence to derive, study, and share complex physical laws like the universal speed of light or the universal theory of gravitation, it will also have developed vision or a comparable sense (like sonar).
• If a creature evolving under earthly conditions has not developed vision or a comparable sense, it will not have developed the requisite intelligence to derive, study, and share complex physical laws.
• If you found a society of creatures (such as ours) that had already developed a dominant sense of sight and stripped it from them along with all of their knowledge of complex physical laws, then yes, they would probably have a difficult time re-deriving said laws. They would also have a hard time surviving, having lost something upon which their survival had relied throughout their evolution. Their inability to re-derive their physical laws, therefore, would be no more special than their inability to cut their lawns or edit their databases.

Keep in mind that I'm assuming an evolutionary process rooted on Earth. Contemplating network sentiences based on electrically active algae dispersed through a liquid planet is fun but it is also pure speculation, unrooted in any science we know and not compatible with the apparatus of evolution as we understand it. Even if one did run with such a premise, the resulting thesis would read "Aliens wholly outside of our understanding of life think differently than we do." No kidding :)

Anyway, I think all of this debate falls entirely outside the intended premise of the nodeshell. Such is life when science invades metaphor. It's a mess.

No, it would not.

One starting point (in fact a postulate) of special relativity is that the speed of light in vacuum is the same for every observer, regardless of the motion of them or the source. Sound does not fulfil this requirement for a number of reasons:

• Sound waves need a medium in which to propagate. The speed is different depending on the medium, and there is no sound in space. Even with air it varies according to pressure and humidity, though it is roughly constant for many practical purposes (about 330 m/s).
• The speed of sound is fixed relative to the medium. Therefore, the observed speed depends on the motion of the medium (e.g. wind).

The invariance of the speed of light relates to the lack of a required medium, and it is not unique to light. It applies to all forms of electric and magnetic fields (light being a special case), the strong nuclear force, and supposedly gravitation. However, it is the same c in every case; relativity would collapse if we found something with an invariant speed different from c. It would be interesting, though.

Considering Pender's writeup, I might add that evolution has produced vision several times independently throughout the history of Earth. It is expected to happen in a world dominated by light.

On a final note, you could imagine that the people discover or invent something that is faster than the speed of sound in air. For instance, the strings in m_turner's example may have a rather high speed of sound along them. It is twice the length times the sound frequency, from some very basic wave physics. I believe the people would know this, if they were ready to develop relativity. If you take something like the string in a properly tuned guitar, you get wave speeds in considerable excess of 330 m/s.