Words are mental paintbrush handles. Saying "triangular lightbulb" paints a picture with words.

The point of communication is to transmit a message. But the message is not the words. The message is the picture, the mental model inside your head.
So the message is reduced to words, which are then used by the recipient to construct a new mental model, with possible errors.

Interpreting words is a complex task. Words do not always have literal, well-defined meanings (if they did, machine translation would be a much easier problem to solve).
Words and words clusters activate patterns in our brain, some patterns subtler than others.

So the actual meaning of a word, a sentence, a communique could be considered to be how it is interpreted by the recipient's brain, what kind of mental model or mental image is created.

Communication is imprecise. We might want to know how imprecise.
The words, the sentences you use are only an approximation to the mental image in your head. But some approximations are better then others.

Pi could be approximated as 3, 3.14, 3.1415, etc, depending on what task you are doing.
The shape of Earth could be approximated as a sphere, an oblate spheroid or a topographical map.

If you are doing calculations by hand, it's probably a waste of time to use a value of pi with 15 decimals.
If you want a satellite to stay in low orbit around the Moon, you'll want to know the precise nature of the lunar gravitational field including any anomalies, not just an approximation which assumes the field is uniform.

Use appropriate precision for the task at hand. Use higher precision to lower errors. Use lower precision to save time and resources.

In order to communicate in higher precision, it helps to pay attention to the what information is transmitted beside the literal meaning of the words.
This is less important for "precise" topics such as math and science, and more important for "sensitive" topics such as emotions, conflict resolution, politics and gender equality.

Pay attention to the "tone" of the conversation.
Not just what someone is saying, but what does expressing it the way they do imply?
What patterns are activated in my brain when processing this information?
The more precise your perception is, the subtler patterns you notice in yourself when processing information.
The more precisely you communicate, the more accurately you control what patterns are activated in the listener's brain, including more subtle ones. 

The non-central fallacy relies on transmitting a message, on sneaking in connontations through non-literal meaning of words.

Is it wrong to say "Martin Luther King is a criminal"? Is it inaccurate? Is it imprecise?

Remember: you are trying to communicate a mental model. 

When I consider the words "Martin Luther King is a criminal", I feel a sense of unease.

When I ask myself "what does it imply to phrase it that way", I think it implies that:

  • Martin Luther King is a bad person
  • Anyone who commits any crime is as bad as a stereotypical criminal
  • Martin Luther King has commited serious crimes

If the person saying that then clarifies "Martin Luther King was in the course of his civil rights work arrested several times for acts of civil disobedience, such as ignoring a police order, loitering, and parading without a permit", my internal reaction would be "Oh, is that all? I thought you said he was a criminal"

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Dan Dennet has an excellent section on a very similar subject in his book 'freedom evolves'. To use a computer science analogy true telepathy would be the ability for 2+ machines with different instruction set architectures being able to cross compile to code that is binary compatible with the other ISA and transmit the blob to the other machine. We have to serialise to a poorly defined standard and then read from the resulting file with with a library that is only a best guess at and implementation of the de facto spec.

It's not just knowledge that we telepathize with language. With declarative sentences, we transfer whole multimodal scenes from one mind to another. With interrogative sentences, we initiate database queries (memory retrieval) in other minds. And with imperative sentences, we copy over behavioral programs into the minds of other agents for execution.