Up@dawn 2.0

Sunday, January 15, 2017

Chapter Two Summary of Stephen Mumford's Metaphysics

       In chapter two of Metaphysics: A Very Short Introduction, Stephen Mumford poses another question similar to his start in chapter one. What is a circle? Not to be confused with the mathematical definition of a circle, Mumford challenges the reader to seek a deeper meaning as to what a circle is.
If we continue our thought process from chapter one of properties and particulars, we can say that circularity is a property in many different things, i.e.. a coin, a wheel, the circumference of a ball, the rim of a cup, as Mumford points out on page 14. A property can be thought of as a feature or quality of a particular. For example, a pen is a pen, a particular pen. It may be owned by someone, located on that persons desk at a certain time. Circularity, however, appears many places at many different times. “The fact that circularity appears in one place at one time does not stop it appearing in other places and times.” (p.15). Thus, there are two ‘entities’ as Mumford defines, particulars (ie. pens, tables, sheep, etc.) and properties or universals (ie. circularity, tallness, redness, etc.).
Now, suppose there was a way to eliminate all things that had a certain property. Mumford continues to use circularity as an example in his text. If all things circular were destroyed, smashed, bent, broken, etc. would that in turn destroy circularity? Or just the existing cases of it? We could argue that even if this were possible, circularity would still ‘exist’. So where then? Plato seems to have an answer for us. Plato believes all the “Instances of which we are acquainted are all imperfect copies of the true versions” (p.17) and that the true versions of properties and relations (ie. redness, tallness, circularity, taller than, harder than, etc.) reside in a heavenly realm. This realm cannot be seen or touched, but reached only through ‘pure intellect’. Due to their perfect nature, Plato called these true versions of properties and relations Forms. Now, because in his theory there is a division between what we see in the world v. what resides in this heavenly realm, there has to be some sort of relation between the two in order for there to be a difference between them (worldly circles are imperfect in relation to the Form circle). Yet, relations belong in the heavenly realm according to Plato, thus creating an infinite regress, a never ending resemblance causing a problem with his theory which Plato is never really able to solve.
Next, Mumford introduces us to a theory where the idea of things being split into two entities, properties and particulars, is rejected. The argument here is that if these two are separated, then at some point they have to be brought together. For example, in his text Mumford points out, “We would have to get roundness and greens, as properties, united with the physical things in the world, such as an apple. But that is when we have to start speaking of the apple…” (p.19). Instead for there being two entities of properties and particulars, the theory of only particulars existing is presented. This particulars-only view, or nominalism, shows how we feel we can be sure about the existence of things, like a table or a coin, where as we are less sure about abstract ideas like circularity existing outside of our perceived world. Nominalist would say circularity is just a word to describe a group of particulars, i.e.. a coin, a wheel, a ball. Particulars are groups of things that resemble each other in this view. Te issue with this view is if the objects listed have another thing in common, for example not only are they all circular but they are all made out of metal, these things now have two resemblances bringing back the fact that being circular and metal are different which implies properties. This problem also does not seem to ever get resolved.
In an opposing view, Mumford explains the Aristotelian view where properties exist here with us. Circularity exists in all things circular, regardless of whether they are perfect or imperfect and regardless of the time they existed in (the present, the past, the future) thus including all circular things that will ever be.

It is here Mumford leaves us hanging a bit as he transitions into the next chapter titled Are wholes just the sums of parts? where I hope he explores these topics from chapter two more.


  1. "Good job summarizing chapters 1 & 2, Sarah. "What is a table?" & "What is a circle?" are really questions about what we understand by things and concepts. My view: things are re-experiencable items of use, concepts are extrapolations thereof. A concept without application to things, actual or possible, is of little use.

    I'm reminded also of Eddington's famous two tables, that of everyday experience (possessed of solidity and utility) and that of higher-order descriptive physics (accurate to a theoretical degree, but of litle practical value). Both are real, in their appropriate respective domains, and neither is absolutely prior or superior.

    But the interesting question, metaphysically, is whether the stuff of practical experience doesn't in fact merit priority - if only because it's so darned practical (i.e., useful) in ordinary contexts of living.

    What is a circle? A transcenden t platonic form, or an approximation to previous earthly instances of encounter?

    Bottom line, for me: reality, what's real, must always connect with what's met in everyday experience.

    But isn't it interesting that we seem to have an inborn drive to discover what's real, and to distinguish it from what's illusory? (Not that we always, or even often, succeed in making that discovery and drawing that distinction...)

    1. So our sense need to be our tools for reality, or distinguishing what is real to us ... which causes us to priorities stuff of practical experience over abstract notions? Meaning, we can see, feel, encounter a table or something circular... and by engaging our sense in this evaluation we can process it as existing in our reality. When contemplating a transcendent circle, we can not see it, touch it, hold it, but merely imagine it... therefore it is 'less real' in our brains? Neither is a higher priority over the other, but because we can engage our bodies and process the information in our brains into the assessment of the 'thing' and not just our abstract thoughts, we tend to have more of a bond perhaps, or maybe recognition is a better term, thus creating a higher priority to the 'thing' in our reality as opposed to an abstract notion like a transcendent circle? Just thinking out loud here.