I understand Longeway's argument as follows. According to Ockham (Summa I.26), there are three kinds of definition. (1) A nominal definition is a way of setting the meaning of the defined term, and so a is true in virtue of the meaning of the term. E.g. 'a bachelor is an unmarried man. (2) Two kinds of real definition. A metaphysical definition indicates genus and difference, for example 'a man is a rational [differentia] animal [genus]'. (3) A natural definition (Spade translates this as physical definition) is one which signifies obliquely essential parts of the thing defined. For example, 'a triangle is a figure contained by three straight lines'.
Ockham argues (Summa II.ii.35, cited in Longeway p. 112) says that any attempted demonstration will depend upon either the nominal definition of the attribute, and so beg the question, or a metaphysical definition, which is essentially inexplicable and provides no scientific assistance, or a natural definition. Only demonstration using natural definition is truly scientific.
Let's flesh this out. The Aristotelian model for scientific demonstration is as follows.
A B is a C
An A is a B
Therefore, an A is a C
To explain why A is C, Aristotle says we must find a 'middle term' B which is common to A and C. But it is clearly not enough for B simply to be synonymous with C, otherwise the syllogism would beg the question. For example
An unmarried man is a bachelor
John is an unmarried man
Therefore, John is a bachelor.
To understand the term 'batchelor' you have to understand that it means 'unmarried man'. Thus the conclusion moves us no further than the minor premiss 'John is an unmarried man' It expresses the same thing in different terms, having the same meaning, and the 'reasoning' is trivial. Nor is a 'metaphysical definition' of any assistance. We can have a direct intellectual grasp of a thing, but only of its genus, as a whole, 'without any insight into its metaphysical structure' (p.114). 'A demonstration rooted in a grasp of metaphysical definition of the primary subject of an attribute can only occur after this life'.
The only case where true demonstration is possible is in the case where the middle term involves a natural definition. And this can only happen where the subject is something composite. Longeway cites (p. 113) the example of a triangle, with spatial parts arranged in such a way that an analysis of its structure will tell us that it has the attribute in question. This is what happens in geometry and mathematics.
This means that there can be no true scientific explanation of things which are essentially simple. Ockham thinks we cannot explain heat, for example, because we cannot explain it in terms of of composition and mathematics. As Longeway explains it "The natural definition of an attribute is of no assistance here for the straightforward reason that a simple quality such as heat has no variety or structure of essential parts, but is rather uniformly alike in every one of its parts. No mechanism by which heat heats is there to uncover. It just heats. And this can only be known from experience" (p. 113)
We can only apply mathematical techniques to things in nature which they are composite, and which can be defined in terms of their material parts. Thus (for Ockham) we cannot have a scientific explanation of substance. Ockham still holds to the Aristotelian view that the causal properties of a substance cannot be explained in terms of the substance's parts. According to Aristotle, substances are essentially simple. Their properties follow from their substantial form (the essence of a substance, corresponding to a species). A substantial form is what is signified by the definiens of a definition. A substantial form is a universal (since only universals are definable - see Metaphysics Z8 1034a6-8). A substantial form is immaterial (because a substance is a combination of material and form). A substantial form is simple (Metaphysics Z12). If the properties of a species could be explained by composition, a substance would not be an essential unity, and so would not be a substance, but a collection of substances.
This is interesting, but doesn't really explain why we should regard Ockham as the founder of European empiricism. As Longeway points out, real progress only began when Descartes and Boyle "insisted on mathematical-mechanical modes of explanation connecting one accident of material substance to another, rather than explanations of the first attributes of material substance". (p.115) One of the essential ingredients of modern science is the rejection of the Aristotelian doctrine of substantial forms. (See Locke about this here, especially section 10). Since Ockham did not reject substantial forms, why should we regard him as the founder of modern science?
Longeway gives no convincing reply to this line of reasoning, except for suggesting that once Ockham has shown the impossibility of scientific explanation using metaphysical definition, it is tempting to look for explanations in terms of natural definition.
we know that early modern scientists were so tempted, and Descartes and othersSince our only tool for understanding why is analysis in terms of material parts and the application of mathematics, it would be natural to be tempted by materialist reductionism in biology.
rejected the assujmption immaterial substantial forms underlying biological
properties precisely because such an assumption did nothing to provide an
understanding why animals and plants have the properties in question. (p 115)
* Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio.