Vagueness

"Can the world itself, and not just language be vague?"

Yes, the world not only can be vague the current best-models of the world suggest it is vague.

Particle physics suggests at the quantum level particles (such as electrons) exist as a cloud of probability, while others (such as light photons) may behave as both particles and waves depending on circumstances. Relativity explains that time and space are somehow the same such that gravity and speed actually change the rate at which time passes. On cosmological scales time even starts to lose its meaning such that talking about a supernova happening 100 light-years away as happening 100 years ago becomes illogical since nothing travels faster than the speed of light, thus until that light reaches us the supernova has effectively not happened yet.

Biology has revealed the importance of random chance in the expression of genes and the determination of phenotypes. Even in sexually reproducing species the edges between one species and another is often vague, some interbreeding plant varieties for a continuum between two types which cannot interbreed. In most cases species evolve smoothly from one form to another such that there is no first chicken to hatch from the first proverbial egg. Even the edges of what constitutes a single individual is vague in many plant species. Entire groves of aspen may be derived from a single seed and have interconnecting roots beneath the surface. Likewise strawberry and blackberry plants frequently reproduce by sending out new shoots which eventually grow into self-sustaining plants still connected to the parental plant but which continue to thrive when that connection is severed. Similarly Siamese-twins may share a single circulatory system and even share parts of their brain while still having distinct personalities. Other examples of the vagueness of what constitutes an individual are mutualists. Every human being contains in their guts and carries on their skin more bacterial cells than human cells. Lichens are actually made of two separate species one is a plant or photosynthetic bacterium the other a fungus. Similarly corals are a combination of an animal and an algae; and each Portuguese man-of-war 'jellyfish' is actually made of at least three evolutionarily distinct species.

In chemistry, rings of six alternatively double and single bonded carbons (eg. benzene) can switch between two theoretical states and in nature exists somewhere between these two states with electrons forming a constantly shifting cloud around the ring. Chemistry has also discovered states such as super-fluids which are somewhere between liquids and gasses exhibiting properties of both. Similar states exists between solids and liquids under particular conditions. A recent popular example of vagueness in chemistry is the pitch-drop experiment. Pitch is a super dense liquid, it flows so slowly it takes 9 years for a single drop to fall; but hitting pitch with a hammer causes it to crack and shatter like a solid piece of rock.

Thus every major branch of science has uncovered vagueness to the best of our knowledge. Of course the possibility remains that further study will elucidate this vagueness or that these instances simply indicate a failure of human cognition to be able to understand the nature of reality. But, for the moment they provide a compelling case that the world is indeed vague.