Truth, mathematical figures, and immutable principles

Use in the book

Truth cannot be corporeal, Ficino argues, since God, angels and numbers are true without being bodies. He then makes the stronger claim that truth is not properly in bodies: matter supplies no determinate species, and form in matter has its power impaired by admixture and extraneous conditions. Mathematical exactness offers his example. A true circle on a true plane is said to roll continuously because it touches at an indivisible point. That historical physical inference should not be mistaken for a modern mechanics result; its local function is to contrast exact intelligible figures with sensed bodies.

A further argument separates the account of quantity from quantitative extent. The entire account of circle applies to a small circle as to a large one; the entire account of length applies to a short line as to a long one. Thus an account of an extended thing is not itself extended in the same manner. Universal principles are also described as immutable, whereas bodies change. Knowledge directed toward those principles and the truth it possesses are consequently classed as incorporeal.

Reason, rather than a particular sense, judges what truth is and what stands nearer to it. This does not imply that the chapter's sensory examples disappear; it assigns them a limited evidential role. The subsequent description of truth as food depends on this argument about the character of its object.

Places to read

1. VIII.2.7God, angels, numbers, exact geometry and universal accounts supply distinct arguments for incorporeal truth.
2. VIII.2.8Reason judges truth and the soul is said to feed upon its incorruptibility.
3. VIII.4.11Truth is defined through correspondence of things and minds.

Translation in this edition

Spiritibus at VIII.2.7 means incorporeal spirits, unlike spiritus at VIII.2.3. The qualifying forte and saltem quantum spectat ad sensum accompany the claim about geometrical principles in bodies. They should not be omitted to create a stronger unqualified statement.

longitudo / latitudo / profunditas

longitudo / latitudo / profunditas. Printed forms: latitudine; latitudinis; lineae; longitudine; longitudinem; longitudinis; longitudo; profunditate; profunditatis; superficies.

Length, breadth and depth as dimensions whose accounts are separable in thought. An exact point lacks length, a line breadth, a surface depth; the corresponding intelligible principles are not themselves measured bodily spans. References: VIII.2.7, VIII.4.2, VIII.5.2, VIII.10.2. See Truth, mathematical figures, and immutable principles.

mathematici / circulus / planum

mathematici / circulus / planum. Printed forms: circuli; circulus; mathematici; plano; planum.

Mathematicians, an exact circle and an exact plane. Their ideal figures support the contrast between intelligible exactness and sensed material shapes; the rolling claim is historical reasoning, not current mechanics. References: VIII.2.7. See Truth, mathematical figures, and immutable principles.

mutabilis / immutabilis

mutabilis / immutabilis. Printed forms: immutabiles; mutabilia.

Capable or incapable of change in the relevant nature or account. Universal principles are said to be unable to be otherwise, whereas bodily instances are subject to alteration. References: VIII.2.7. See Truth, mathematical figures, and immutable principles.

mutatio / mutare

mutatio / mutare. Printed forms: mutatio; mutationem; mutet; permutatur; variatur.

Change or alteration of state, distinguished from stable intelligible content. Bodily conditions alter sensory appetite, while reason's immutable accounts are used to establish a different mode of cognitive being. References: VIII.2.6, VIII.4.3, VIII.13.2. See Truth, mathematical figures, and immutable principles.

quantitas

quantitas. Printed forms: quantitas; quantitate; quantitatem; quantitati; quantitatis.

Quantity, the bodily extension through which parts and division arise. Matter precedes quantity in the order of dependence, and soul lacks the quantitative parts whose dissolution could destroy a body. References: V.3.1, V.4.5, V.4.6, V.5.9. See Prime matter and enduring support.

Quantity or measured extent, different from an intelligible account and from intensity of perfection. The soul does not become larger through virtue; the account of quantity itself is whole in different amounts and is not another extended quantity. References: VIII.2.4, VIII.2.7, VIII.3.7, VIII.4.6, VIII.4.12, VIII.6.1, VIII.9.1. See Truth, mathematical figures, and immutable principles.

ratio (account or principle)

ratio (account or principle). Printed forms: Ratio; ratio; rationem; rationes; Rationes; rationibus.

An intelligible account, defining principle or explanatory structure of a thing. The common account of humanity and the complete account of a circle are not extended like particular humans or circles. References: VIII.1.1, VIII.1.2, VIII.2.7, VIII.16.3. See Truth, mathematical figures, and immutable principles.

ratio (additional inflections)

ratio (additional inflections). Printed forms: ratione; rationibus; rationis.

Reason, account or intelligible principle according to its governing construction. A reasoned proof, a universal object's account and the phrase 'insofar as' are not interchangeable senses; the local syntax decides. References: VIII.2.1, VIII.2.7, VIII.2.8, VIII.3.8, VIII.4.2, VIII.4.4, VIII.4.10, VIII.4.13, VIII.15.1, VIII.16.3. See Truth, mathematical figures, and immutable principles.

veritas / verum

veritas / verum. Printed forms: vera; veram; verior; veriora; Veritas; veritas; veritate; veritatem; veritatis; verius; verum.

Truth or genuine intelligible integrity, not only a sentence's correctness. It is the soul's food and the stable object of knowledge; genuine figures and unchanging accounts contrast with materially restricted instances. References: VIII.2.5, VIII.2.7, VIII.2.8, VIII.4.5, VIII.4.11, VIII.13.1, VIII.16.4. See Truth, mathematical figures, and immutable principles.