As promised in the introduction to this series, we will focus not only on philosophy, but also logic,
and how it emerged and evolved over time to become what it is today. Logic arose as a proper school
of thought with Plato’s pupil Aristotle by the 4th century BCE, but it didn’t simply manifest
overnight. Much like philosophy and science themselves, logic evolved gradually from
persistent attempts to improve discourse toward having more objective, analyzable methods. In this
tutorial, we’ll examine these early steps taken by ancient thinkers, which paved the way for the
establishment of what would become modern logic. As we recall, an argument is composed of premises
which result in a conclusion. The simple example we looked at earlier is a very straightforward
argument, and if we change the nouns into letters we can begin to see how this simple argument can
be equivalent to a formula, with every word having a function. “All” denotes every member
of a category, in this case, YouTubers. “Are” and “is” indicate a connection between the first
category and the second – however not necessarily the opposite, as for example not all mortals are
YouTubers. What we establish with this argument then is a relationship between certain categories
such as “YouTubers” and “mortals”, and how a member of one of those categories, “Dave”,
is therefore a member of the other. Changing these words while maintaining the same format
would still be valid, as with the classic “All men are mortal/Socrates is a man/Socrates is
mortal”. We could even alter these operating words: “All” to “some”, “is” to “is not”,
and so forth, and we would get different kinds of arguments. This basic format is what Aristotle
would call a syllogism, but some of its early elements can be identified millennia before him.
The earliest source we have on formulating some kind of logical operators are the Babylonians,
specifically with the Sumerians and Akkadians in Mesopotamia. Instead of introducing them in
an analysis of discourse, such as philosophy or science, for example, they were developed
as part of their codes of law and jurisprudence, especially the Ur-Nammu (circa 2047–2030 BCE),
the Lipit-Ishtar (circa 1900–1850 BCE), and the Hammurabi (1728–1686 BCE). They would be
publicly written in slabs or walls, and they contained basic operators such as “or”, “and”,
“if… then” – much like premises. When the judges needed to evaluate given facts, then
an inference would occur toward a verdict – or a conclusion. The basic shape would be “If crime,
then punishment (which would be the code of law)/A crime occurred (the fact requiring
judgement)/Then, punishment (the verdict or conclusion)”. These codes directly influenced
the Greek law in which Aristotle lived centuries later, potentially influencing his ideas.
On the other hand, although Confucius preceded Aristotle by a couple centuries,
not much of Chinese philosophy seems to have reached Greece by his time. As we already saw,
Confucius and his predecessors centered their philosophical perspectives around language,
or more specifically, on “names”, or ming, and their relationships with all the things
they designate. In his Analects, when asked what his first priority would be when administrating
the state, he said that it would be to focus on the proper use of names, or “ordering of names”
(cheng ming), as their misuse would generate an incongruity between actions, rituals, songs, law,
and the people, and thus result in chaos and immorality. However, Confucius never delved
further on proper linguistic analysis; this endeavor was only undertaken by the
Mohists some two centuries later. Although their surviving text fragments are limited,
much has been extrapolated to compare their development with Aristotle, and even more modern
notions and concepts. One example is one of their techniques of disputation called “Parallelizing”,
which generated arguments resembling syllogisms, such as: “Dave is a YouTuber;
befriending Dave is befriending a YouTuber.” To assert comparatively if this statement is correct,
more statements would be fashioned in the same shape, such as “YouTube is a website; to visit
YouTube is to visit a website” and so on. Although simple, their logical format and its importance in
evaluating an argument is evident, even though their focus was on the semantic aspect, or its
contents, more so than on the format itself. Near China, Indian logic purportedly began
around the 5th century BCE, but the only written evidence dates from around 300 years later,
with the previously mentioned books focused on argumentation and rhetorical analysis.
The Kathā-vatthu or Points of Controversy, attributed to Moggaliputta Tissa, is interesting,
as an underlying format can be seen in the points of discussion between a defender of
a Buddhist school of thought and an attacker of their values. Adapting the subject to our
current context, this would be an example: “Defender: ‘Is Dave a YouTuber?’/Attacker:
‘Yes.’/Def: ‘Is Dave a YouTuber like any other YouTuber?’/ ‘No.’/‘Acknowledge your refutation/If
Dave is a YouTuber, then he is a YouTuber like any other YouTuber/What you say here is wrong: namely,
that we ought to say that Dave is a YouTuber; but we ought not say that he is a YouTuber like any
other YouTuber. If we deny the latter statement, indeed the former should not be admitted. It is
wrong to affirm the former statement while denying the latter.” Although not explicit,
its shape clearly plays an important role to the validity of their argumentations,
as you can interchange nouns or names and keep its format, as it happens frequently in this work:
“Defender: Is A B?/Attacker: Yes./Is C D?/No./Acknowledge your refutation/If A is B,
then C is D./What you say here is wrong: namely, that/A is B but that C is not D./If C is not D,
then A is not B./It is wrong that A is B and C is not D.”
Further developments in the first five centuries of the Common Era helped improve syllogisms in
India toward more simple and effective formats such as this: “Proposition: X has Y/Reason:
because X has Z./Relation: A relation which possessors of Z bear to possessors of Y.”
This developed especially with the Nyāya-sūtra, or Aphorisms on Logic,
of the Nyāya school and its illustrated successor Caraka-saṃhitā, or Caraka’s collection,
culminating around the 5th century CE with the Buddhist thinker Dignāga and his successors.
Dignāga standardized logical practices for much of posterior Buddhist philosophical inquiry,
ascribing a great deal of importance to parallel examples, as in Chinese logic. One example would
be this: “Proposition: X has Y/Reason: because P has Z./Example: That which has Z has Y,
like D./(where D, distinct from P, has properties Z and Y)”. This is a clear deductive syllogism,
meaning that it is characterized by or based on the inference of particular instances from
a general law, with an explicit focus on its format and method of applicability.
This is in contrast with an accidental use of the syllogistic shape like many of our previous
examples. He also developed advanced notions regarding surrounding concepts, and even a
truth-table. Although these developments were almost a millennium after Aristotle,
nowadays it is recognized that a few Indian elements were more advanced than their Greek
counterparts, having even influenced recent mathematicians and logicians such as George Boole,
creator of Boolean operators in the 19th century. Finally, the presocratics also hinted at some
early logical elements. The Sophists, as well as Diogenes Laertius and Alcidamas,
categorized sentences relative to their argumentative force, while Antisthenes identified
a truthful sentence as corresponding with the real world. An authorless text called Dissoi Logoi,
or Double Arguments, from around 400 BCE, is possibly the earliest fragment on truth
and falsity. Zeno and Socrates, as we saw, were also known for deliberately fallacious methods,
however never explicitly aware of this format. Plato’s formal categorization of this method as
a dialectical argument was also in a manner akin to a prototypical logical analysis. In
the Sophist dialogues, he likewise performs a linguistic analysis of simple statements
and differentiates between their form, or syntax, and their truthfulness, or semantics;
thus, a statement can only be valid when it is successful in specifying a subject and saying
something about it – a crucial separation within logic. Further logical terminology
is developed both in his Euthydemus dialogues and with Eubulides, as they analyze several paradoxes
and fallacies, with Plato further focusing on the differences of valid and invalid arguments.
Most of these early developments, in addition to the ways that proof and deduction were
being developed in Greek mathematics by the 5th century BCE, converged into Aristotle’s “official”
development of logic. In the next tutorial, we will take a look at his general theory,
followed by a more in-depth dive into how he defined logic for millennia to come.