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Duns Scotus links “immaterial” with “not [spatially] extended” (reminding us of Descartes):

(b) Another way in which this knowledge could be immaterial would be that it is not extended in any way. In this case much more is asserted than the fact that it is not organic. For although everything organic is extended inasmuch as it is received into something extended [viz. the organ], this is not the only reason. It would still be extended if it were received immediately by the composite as a whole, because the composite is itself extended.

– as quoted in Allan B. Wolter: Duns Scotus Philosophical Writings, p. 141

Though Aquinas does claim that

the word ‘body’ is used to denote a genus of substances from the fact of their possessing three dimensions”

– Thomas Aquinas: Summa Theologiae, First Part, Question 18, Article 2)

it seems that for mainstream scholastics being just material (and not also being a body) was not defined by extension and instead by being dependent on prime matter:

For most scholastic authors, in contrast [to Descartes], extension lacks any such significance. Since they tend to be quantity realists (Ch. 14), they are generally committed to the possibility of extensionless material substances (material substances that are, strictly speaking, not bodies [§16.6]).

– Robert Pasnau: Metaphysical Themes 1274–1671, p. 325

Duns Scotus wasn’t a Thomist, but he must have known that most scholastics did have no issues with the notion of unextended material objects (a modern example would be an electron, certainly material, which is speculated to be unextended). If he wanted to show that the soul is not extended, this does not seem to be a very important result, because it does not show the soul to be immaterial.

Did Duns Scotus believe that material things were extended?

If so, why? Did he give any arguments for this proposition?

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He did not. Like the rest of scholastics, he reified geometric points, which, according to Euclid's "definition" (possibly, spurious), "has no part", and hence extension. As for the immateriality of (intellective) soul, he has an independent argument for that, namely that the material is necessarily/essentially individual, and hence can not hold a universal, which intellect can. The non-extension is needed for a different purpose, to rule out forms other than the intellective soul as potential candidates for processing universals. Here is from Duns Scotus and the Problem of Universals by Bates, p.44:

"But why would Scotus mean to say the subject of intellectual cognitive operations cannot itself be something extended and material? If it were material, it could not be indifferent to its singularity; singularity would be necessary to it. That is, inasmuch as it would be material, it would have to be located in space and time and would therefore have to be singular. But if singularity is necessary to it, something that is not singular, like the state of understanding, cannot belong to it. For the state of understanding must be universal. The two could not go together coherently as a whole. It follows that the subject of human intellectual cognition must be an incorporeal entity. As “every other form is extended” in a human being, this immaterial subject “can be nothing other than the intellective soul”."

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