The law of identity (or how to not say foolish things)

Sometimes the things people say or the ideas they express just don’t make sense. We’ve all encountered this, and often on some level (perhaps intuitively) we know that what’s being said is in some way an untruth. Seeing as philosophy (which means love of knowledge) often involves the search for truth, it makes sense to outline some basic rules to help us find what is true and steer clear of what is fallacious.

One of Aristotle’s most important contributions to philosophy was his development of formal logic, and the principles he outlined are still in use today. There are three basic laws from which the other rules of formal logic are derived.

1. The Law of Identity

The law of identity is quite simple: it states that an object is the same as itself, or A = A. Aristotle says:

Now “why a thing is itself” is a meaningless inquiry (for—to give meaning to the question ‘why’—the fact or the existence of the thing must already be evident—e.g., that the moon is eclipsed—but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical, unless one were to answer, ‘because each thing is inseparable from itself, and its being one just meant this.’ This, however, is common to all things and is a short and easy way with the question.) – Metaphysics, Book VII, Part 17

It is important to understand exactly what Aristotle was saying. Whenever we identify a thing we are creating a dichotomy between that thing and the rest of the universe (symbolically, let’s say A and not-A). The next two laws follow from the law of identity (and they are not separate laws per se, but rather affirmations of what is implicit in the law of identity).

2. The Law of Non-Contradiction

Following logically from the identification of object A and the creation of two subsets (that is A and not-A) that is implicit in the Law of Identity, it is impossible for A to be both A and not-A at the same time and in the same relationship.

e.g. Consider the statement “Socrates is mortal and immortal.” The Law of Non-Contradiction states that Socrates cannot be both mortal and immortal.

3. The Law of the Excluded Middle

Again, following logically from the two subsets created by the Law of Identity, it is impossible for the object to be neither A nor not-A.

e.g. Consider the statement “Socrates is mortal or not mortal.” According to the Law of the Excluded Middle the “middle position” that Socrates is neither mortal nor not-moral cannot be true.

So the next time someone says something silly like “the only absolute truth is that there is no absolute truth” remind them to stop contradicting themselves and start making sense!

The consequences of ideas: Aristotle, unity and the conquests of Alexander the Great

One may study Aristotle for only the briefest of time and yet become aware of his obsession with unity. Desiring a connection between Plato’s eternal and unchanging world of the forms and the natural philosophy of a perpetually changing physical world, he unified the two by locating the form within the substance. The body and mind of a man is made one through it’s form. And ultimately, the universe itself is unified by the Prime Mover. In reading Aristotle’s works, many more examples like the aforementioned can be found.

Alexander the Great was a student of Aristotle. For brevity I quote from wikipedia:

Alexander III of Macedon (20/21 July 356 – 10/11 June 323 BC), commonly known as Alexander the Great (Greek: Ἀλέξανδρος ὁ Μέγας, Aléxandros o Mégas^iii[›]), was a Greek king of Macedon, a state in northern ancient Greece. Born in Pella in 356 BC, Alexander was tutored by Aristotle until the age of 16. By the age of thirty, he had created one of the largest empires of the ancient world, stretching from the Ionian Sea to the Himalayas. He was undefeated in battle and is considered one of history’s most successful commanders.

Prior to the space race, the most expensive and largest scientific campaign undertaken was the collection of samples performed by Alexander’s army on behalf of Aristotle. Aristotle’s influence on his pupil is undeniable.

Inheriting his tutor’s obsession with unity, Alexander undertook a project historians call Hellenisation. In short, his aim was to homogenise the population of Europe and Asia using Greek culture. As Alexander conquered a region, he replaced the local officials with a ruling class of Greeks and brought with his army Hellenic settlers to help diffuse Greek culture. While he was moderately successful, the most common result was a hybridisation of the local and imported Greek cultures.

Alexander’s aim was to reach “the ends of the world and the Great Outer Sea.” One can imagine how different the world would be had he done so. He died in Babylon at the age of 32. After his death, his empire was divided by civil war.

What is goodness?

In Plato’s dialogue Euthyphro, Socrates poses Euthyphro the following dilemma:

Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?

This dilemma can be modified to: does God command it because it is good or is it good because God commands it? I will attempt to answer this dilemma using Aristotelian metaphysics and the God of Aristotle (when I mention God below I am referring to the God of Aristotle).

Firstly, we must make note of Aristotle’s distinction between natural substances and artifacts. A natural thing possesses intrinsic causes which we call its nature. In contrast, artificial things have no intrinsic but rather extrinsic causes. For example, the final cause of living things resides inside them while the final cause of an artifact (such as a house for example) resides in the mind of the artificer. What follows from this is that what is good or bad for a natural substance is determined by the final causes intrinsic to it.

Granting Aristotle’s essentialist metaphysics, logically there are things that are necessarily bad for a natural substance that even God could not change (seeing as its powers cannot cause a contradiction). For example, God could not command a human being to go on a murderous rampage because given our nature there is no conceivable way in which that kind of activity could be good for us. This eliminates the second horn of the dilemma: that is to say that things cannot be good simply because God commands them.

Remember again that Aristotle’s God is pure actuality. This means that God is actually goodness, or in other terms goodness itself. Because that which is a mixture of actuality and potentiality (i.e. created things) cannot exist independently of that which is pure actuality (i.e. God) it follows logically that the ends which are contingent upon goodness itself must also be good. Thus is the first horn eliminated: God does not command from a standard that is external to him, but rather internal.

In short, according to Aristotle the dilemma is a false one. To understand this dilemma more fully, one must realise the differences between Platonic and Aristotelian realism. For the Platonic realist, universals are external to things; following from this the gods must of course love the pious because it is pious, as the Form of Goodness can in no way be internal to them.

Actuality and potentiality

Aristotle’s concept of actuality and potentiality is striking for two reasons; its disarming simplicity, and following that its place as a fundamental to understanding many of his other theories. Act and potency follows logically from Aristotle’s thoughts on causation.

Act and potency are dichotomous and parasitic in nature. That is to say, if something possess the potential to be X, its potentiality to be X is reduced as it actually becomes X. In this way pure potentiality is really nothing at all – until it is actualised.

In terms of Aristotle’s causality, matter (or material cause) is potentiality while form (or formal cause) is actuality. When a change occurs to produce X, X’s matter undergoes the change into X and is constant throughout the process. For example, consider bronze: the matter of bronze has the potential to be many things such as a cube or statue. When a bronze cube is changed in a statue, the matter of the bronze remains the same throughout the change.

If a bronze cube’s matter is bronze, then the cubeness is its form. In other words, bronze is always potentially a cube (among other things) and only becomes a cube when it receives the form of cubeness.

Act and potency are related to Aristotle’s empirical epistemology, whereby knowledge is formed through sensation of the forms present in the external world. These forms do not need to be only shapes, they can also be sweetness, blueness, etc. During sensation, the intellect takes on the form of the sensed object without becoming the thing of the sort of form it is sensing.

The God of Aristotle is pure form, or pure actuality. It is perfection in the sense that it has no potentiality, and thus cannot be greater in any way. Logically, there are attributes that follow from being pure actuality: immateriality (as materiality is potentiality), immutability (as change requires potentiality), eternal (as becoming would require change) and etc.

Aristotle’s ideas of act and potency are related to his discussion of goodness, which I will elaborate upon in my next post.

A further note on Democritus and the intelligibility of the cosmos

About two weeks ago I posted on Democritus’s atomism and the nature of truth.

Following a quote of Democritus’ paradox I wrote:

The problem is thus: if atomism is true then the intellect logically must affirm the subjective nature of sensation (as the Socratic tradition also affirms) which at the same time provide the evidential basis for the atomic theory. Accordingly, atomism is a relativistic philosophy whereby truth is relational (if it exists at all). It is not known if Democritus attempted to provide an answer to this problem.

I realise that I have made the mistake of reading Democritus’ (and possibly his followers) ideas through the colour of my own glasses. Democritus may have never attempted to solve this problem because he did not believe it to be a problem at all.

Typically, the Socratic tradition (i.e. Platonic and Aristotelian philosophies) hold that the world is thoroughly intelligible in of itself; that is to say there is a sufficient explanation for why the world exists the way it does. Following that, the Socratic tradition is typically mildly skeptical (or moderately rational if you like) in regards to man’s ability to completely understand the cosmos; though we can of course fathom things like formal and final causality through the application of reason.

As I have described previously, the atomistic tradition relies on mechanistic and necessitarian explanations of cause and effect. Thus while the laws of nature render parts of the world intelligible, they themselves remain necessary and cannot be made intelligible (or brute facts to use a cruder modern terminology).  Therefore, under the atomistic worldview the cosmos can only be partially intelligible both in of itself and to any observer.

It is obvious why Democritus may not have considered his paradox to have truly been a problem when one understands that the belief in the partial intelligibilty (and thus partial un-intelligibility) of the cosmos follows logically when one fully embraces the atomistic philosophy. Of course, anybody who believes that the world is thoroughly intelligible in of itself will ultimately be forced to reject Democritus.

As stated previously, one may find the similarities between Democritus’ atomism and the modern philosophies of mechanism and scientism striking.