# What is the Difference between Vagueness and Indeterminacy?

Is "There will be a sea battle tomorrow" a borderline case of vagueness? Or, is it a case of modal indeterminacy? Or both? Where do we draw the line between the two? And ,what about "There is a sea battle?" Does it qualify as a borderline case of vagueness or not?

• About the "sea battle" see Problem of future contingents : it seems a modal issue and not about vagueness ... – Mauro ALLEGRANZA Jun 20 '14 at 17:56
• About Vagueness and indeterminacy : a case of synonimy ? – Mauro ALLEGRANZA Jun 20 '14 at 17:58
• Welcome, Everest! Can you include any background information that you found that seems relevant? Are there any sources you checked? – James Kingsbery Jun 20 '14 at 21:52
• "There will be a sea battle tomorrow" is typically taken as a modal issue. However, if there is no agreement between two experts on whether "There is a sea battle" because of differences of opinion as to what constitutes a "sea battle" then it would appear to be a vagueness issue, no? – Everest Jun 21 '14 at 0:43
• This seems to be mostly a matter of English definitions... vagueness = a statement that is imprecise, i.e. it is not clear what is being stated. indeterminacy = a statement which has an unknown truth value, i.e. it is not known or possibly not knowable whether a statement is true. – virmaior Jun 21 '14 at 1:12

Aristotle invented the statement "There will be a sea battle tomorrow" to question his own assumption that all propositions have a definite, time independent truthvalue (De interpretatione IX). According to propositional logic the following disjunction is true:

“There will be a sea battle tomorrow or there will be no sea battle tomorrow.”

If each proposition has a well-determined, time independent – but possibly unknown – truthvalue , then already today is determined what will happen tomorrow. The example shows that propositional logic supports determinism.

If you want to avoid such determinism you can employ modal logic and introduce the new operator "possibly". The refined statements are "Possibly there is a sea battle tomorrow" and “Possibly there is no sea battle tomorrow”. The refined disjunction now reads

“Possibly there will be a sea battle tomorrow or possibly there will be no sea battle tomorrow.”

This is a weak statement which does not support determinism.

Anyhow, I do not see how this example from logic relates to the concepts of vagueness or indeterminacy.

As others have noted, vagueness concerns meaning while indeterminacy can concern either the reference of a term or the truth-value of a sentence.

Adopting modern semantic, one could say that a term is vague if it is not defined clearly, which entails that it has no determinate reference in the world (the term might refer to one thing or the other), which can in turn entail truth-indeterminacy when the term is employed in a sentence, but not necessary so. For example, "all penguin-like animals are birds" could be definitely true even if "penguin-like" is vague.

Conversely there can be truth-indeterminacy even when all terms have a precise meaning. Aristotle's example purports to be such an example. So the answer to your question is: this is a case of truth-indeterminacy, not vagueness.

We could then distinguish between two kinds of truth-indeterminacy: epistemic (we lack sufficient information) or metaphysic (e.g. in certain interpretations of physics, when a property doesn't objectively have a precise value). Aristotle's example can be interpreted as one or the other, depending if determinism is true or not.

However indeterminacy might also refer, in some contexts, to indeterminacy of the reference which is more easily confused with vagueness, albeit distinct. Then the distinction is more subtle: vagueness is when a term is not clearly defined, indeterminacy is when there is no determinate reference. Vagueness entails indeterminacy but not the converse: all terms can be clearly defined relatively to each other, yet the reference of the terms might still not be determinate because of a fundamental underdetermination (this is Quine's thesis).

If one adopts Frege's theses that the reference of a proposition is its truth value, then reference-indeterminacy and what I called truth-determinacy are one and the same concept, either applied to terms or propositions.