Aristotle's Rules of Definition


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Please excuse, this is not an objectivist topic. I didn't know where else to post.

I've listened to Branden and Peikoff speak about definitions (Efficient thinking and Intro to logic course). Unfortunately neither quoted their sources. I'm looking for Aristotle's work on the rules for making valid definitions (such as: definitions must express fundamentality, no circularity, rule of negatives, equivalence, etc).

Unfortunately I cannot find it. Can anybody here help me out and point me to the sources?

Thanks a lot.

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mpp,

You can find pretty good discussions here:

Genus–differentia definition (Wikipedia, so this is OK, not great. But some good follow-up sources.)

Aristotle's Metaphysics (Stanford Encyclopedia of Philosophy--with a philosophy geek's dream bibliography at the end.)

Then there are online copies of Aristotle's Metaphysics (Google is your friend), but I can't tell you which translations are best.

When you search on Google, you might want to include an uncommon term like differentia instead of definition. In other words, Google this:

Aristotle differentia

Consider that a start from an interested layman. There are some real-deal brainiacs around here who can point you in directions that are likely better than these. But at least this is a start.

And it will quell any doubt you may have if you ever wondered if Rand came up with the genus-differentia thing. She didn't. She got it from Aristotle. (To people who have read Aristotle, that doubt might seem dumb. But I can say from my own experience, it is real when you have not read much about philosophy except Rand and Rand-related authors. I used to have that doubt myself.)

Michael

EDIT: I forgot, don't forget Chapter 5 of Introduction to Objectivist Epistemology for Rand's own words.

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Please excuse, this is not an objectivist topic. I didn't

know where else to post.

I've listened to Branden and Peikoff speak about definitions (Efficient thinking and Intro to logic course). Unfortunately neither quoted their sources. I'm looking for Aristotle's work on the rules for making valid definitions (such as: definitions must express fundamentality, no circularity, rule of negatives, equivalence, etc).

Unfortunately I cannot find it. Can anybody here help me out and point me to the sources?

Thanks a lot.

Welcome to OL.

I think this is an Objectivist "topic." Heck, he is the only "philosopher" she acknowledges "owing" anything too!

7. Definitions

The definition (horos, horismos) was an important matter for Plato and for the Early Academy. Concern with answering the question “What is so-and-so?” are at the center of the majority of Plato's dialogues, some of which (most elaborately the Sophist) propound methods for finding definitions. External sources (sometimes the satirical remarks of comedians) also reflect this Academic concern with definitions. Aristotle himself traces the quest for definitions back to Socrates.

7.1 Definitions and Essences

For Aristotle, a definition is “an account which signifies what it is to be for something” (logos ho to ti ên einai sêmainei). The phrase “what it is to be” and its variants are crucial: giving a definition is saying, of some existent thing, what it is, not simply specifying the meaning of a word (Aristotle does recognize definitions of the latter sort, but he has little interest in them).

The notion of “what it is to be” for a thing is so pervasive in Aristotle that it becomes formulaic: what a definition expresses is “the what-it-is-to-be” (to ti ên einai). Roman translators, vexed by this odd Greek phrase, devised a word for it, essentia, from which our “essence” descends. So, an Aristotelian definition is an account of the essence of something.

7.2 Species, Genus, and Differentia

Since a definition defines an essence, only what has an essence can be defined. What has an essence, then? That is one of the central questions of Aristotle's metaphysics; once again, we must leave the details to another article. In general, however, it is not individuals but rather species (eidos: the word is one of those Plato uses for “Form”) that have essences. A species is defined by giving its genus (genos) and its differentia (diaphora): the genus is the kind under which the species falls, and the differentia tells what characterizes the species within that genus. As an example, human might be defined as animal (the genus) having the capacity to reason (the differentia).

Essential Predication and the Predicables

Underlying Aristotle's concept of a definition is the concept of essential predication (katêgoreisthai en tôi ti esti, predication in the what it is). In any true affirmative predication, the predicate either does or does not “say what the subject is”, i.e., the predicate either is or is not an acceptable answer to the question “What is it?” asked of the subject. Bucephalus is a horse, and a horse is an animal; so, “Bucephalus is a horse” and “Bucephalus is an animal” are essential predications. However, “Bucephalus is brown”, though true, does not state what Bucephalus is but only says something about him.

Since a thing's definition says what it is, definitions are essentially predicated. However, not everything essentially predicated is a definition. Since Bucephalus is a horse, and horses are a kind of mammal, and mammals are a kind of animal, “horse” “mammal” and “animal” are all essential predicates of Bucephalus. Moreover, since what a horse is is a kind of mammal, “mammal” is an essential predicate of horse. When predicate X is an essential predicate of Y but also of other things, then X is a genus (genos) of Y.

A definition of X must not only be essentially predicated of it but must also be predicated only of it: to use a term from Aristotle's Topics, a definition and what it defines must “counterpredicate” (antikatêgoreisthai) with one another. X counterpredicates with Y if X applies to what Y applies to and conversely. Though X's definition must counterpredicate with X, not everything that counterpredicates with X is its definition. “Capable of laughing”, for example, counterpredicates with “human” but fails to be its definition. Such a predicate (non-essential but counterpredicating) is a peculiar property or proprium (idion).

Finally, if X is predicated of Y but is neither essential nor counterpredicates, then X is an accident (sumbebêkos) of Y.

Aristotle sometimes treats genus, peculiar property, definition, and accident as including all possible predications (e.g. Topics I). Later commentators listed these four and the differentia as the five predicables, and as such they were of great importance to late ancient and to medieval philosophy (e.g., Porphyry).

I would start here.

http://plato.stanford.edu/entries/aristotle-logic/#Def

A...

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Thanks everyone for your replies!

I have Copi's book "Introduction to Logic" which was referenced in the wiki article in front of me. Unfortunately, it doesn't contain the sources of the rules.

Metaphysics is a good link, although I think it's primarily concerned with substances and essences and not so much, if at all, with the other more technical rules.

I've read the other links too: no mention of the rules.

Merlin, do you have the book? Can you tell me if Kelley cites any particular passages for definitional guidelines?

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Aristotle's mode of definition is of the form D is a G such that S. Where D is the thing to be defined. G is a genus which contains D and S is a property or condition that specifies a small subset of the genus D. S is the species or special property.

There are other modes of definition which Aristotle never dealt with in detail

One is analogy. Hat is to Head as Shoe is to Foot. so if one side of the analogy is known the other side acquires an analogous meaning. I used this method on my 4 kids and it worked fine It is a handy dandy method to use along with Genus-Species.

The other is the "is-when". Terrible grammar but it produces operational definitions. Phase change of water is when ice melts or water boils or water freezes and steam condenses. Then you can apply the phase change of water analogously to other substances. It works fine as a rough operational definition.

Ba'al Chatzaf

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Aristotle's mode of definition is of the form D is a G such that S. Where D is the thing to be defined. G is a genus which contains D and S is a property or condition that specifies a small subset of the genus D. S is the species or special property.

Miswrite - the bolded "D" should be "G." You can edit it if you notice in time.

Ellen

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Please excuse, this is not an objectivist topic. I didn't know where else to post.

I've listened to Branden and Peikoff speak about definitions (Efficient thinking and Intro to logic course). Unfortunately neither quoted their sources. I'm looking for Aristotle's work on the rules for making valid definitions (such as: definitions must express fundamentality, no circularity, rule of negatives, equivalence, etc).

Unfortunately I cannot find it. Can anybody here help me out and point me to the sources?

Thanks a lot.

As I recall, Aristotle's major discussion of definitions appears in his Posterior Analytics.

Ghs

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Please excuse, this is not an objectivist topic. I didn't know where else to post.

I've listened to Branden and Peikoff speak about definitions (Efficient thinking and Intro to logic course). Unfortunately neither quoted their sources. I'm looking for Aristotle's work on the rules for making valid definitions (such as: definitions must express fundamentality, no circularity, rule of negatives, equivalence, etc).

Unfortunately I cannot find it. Can anybody here help me out and point me to the sources?

Thanks a lot.

As I recall, Aristotle's major discussion of definitions appears in his Posterior Analytics.

Ghs

A 'basic truth' in a demonstration is an immediate proposition. An immediate proposition is one which has no other proposition prior to it. A proposition is either part of an enunciation, i.e. it predicates a single attribute of a single subject. If a proposition is dialectical, it assumes either part indifferently; if it is demonstrative, it lays down one part to the definite exclusion of the other because that part is true. The term 'enunciation' denotes either part of a contradiction indifferently. A contradiction is an opposition which of its own nature excludes a middle. The part of a contradiction which conjoins a predicate with a subject is an affirmation; the part disjoining them is a negation. I call an immediate basic truth of syllogism a 'thesis' when, though it is not susceptible of proof by the teacher, yet ignorance of it does not constitute a total bar to progress on the part of the pupil: one which the pupil must know if he is to learn anything whatever is an axiom. I call it an axiom because there are such truths and we give them the name of axioms par excellence. If a thesis assumes one part or the other of an enunciation, i.e. asserts either the existence or the non-existence of a subject, it is a hypothesis; if it does not so assert, it is a definition. Definition is a 'thesis' or a 'laying something down', since the arithmetician lays it down that to be a unit is to be quantitatively indivisible; but it is not a hypothesis, for to define what a unit is is not the same as to affirm its existence.

http://classics.mit.edu/Aristotle/posterior.1.i.html

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The entry for Definition in the Index to the Complete Works of Aristotle (Jonathan Barnes, editor) lists about fifty places scattered through Aristotle’s texts, notably, in Posterior Analytics, Topics, On the Soul, and Metaphysics, but in others as well. A great collection of essays, including much on Aristotle, is Definition in Greek Philosophy (David Charles, editor); one of the essays on Aristotle is by James Lennox, who is one of the directors of the Ayn Rand Society.

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Merlin, do you have the book? Can you tell me if Kelley cites any particular passages for definitional guidelines?

Yes, the first edition. It presents the same 6 rules as here. Their elaboration is 8 pages.

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Merlin, do you have the book? Can you tell me if Kelley cites any particular passages for definitional guidelines?

Yes, the first edition. It presents the same 6 rules as here. Their elaboration is 8 pages.

Some of those items in the tutorial fail the -definition- of definition but are reasonably good descriptors which if used in conjunction with good definitions can give a better idea of what the things defined are.

Ba'al Chatzaf

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Some of those items in the tutorial fail the -definition- of definition....

We/I invite your elaboration.

1 and 4 do not cut the Kelley mustard, but are true statements which in conjunction with proper definitions and other statements could be useful

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1 and 4 do not cut the Kelley mustard, but are true statements which in conjunction with proper definitions and other statements could be useful

Just looking at 3-4 dictionaries (link), the genus was statement. That or genus = explanation seems to satisfy both 1 and 4.

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Thanks again to everyone who's contributed.

I've followed every lead and I've found Aristotle wrote explicitly about the rules (topoi) of definition in Topics, VI.

Although vague and short on the rule of equivalence and fundamentals, the others are addressed there.

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Please excuse, this is not an objectivist topic. I didn't know where else to post.

I've listened to Branden and Peikoff speak about definitions (Efficient thinking and Intro to logic course). Unfortunately neither quoted their sources. I'm looking for Aristotle's work on the rules for making valid definitions (such as: definitions must express fundamentality, no circularity, rule of negatives, equivalence, etc).

Unfortunately I cannot find it. Can anybody here help me out and point me to the sources?

Thanks a lot.

Philosopher Richard Robinson has several pages of interesting discussion about this topic in his book "Definition"

starting at page 140:

http://www.amazon.com/Definition-Richard-Robinson/dp/0198241607

You may be able to read this for free at

http://www.questia.com/library/1503699/definition

"There are are certain traditional "rules of definition", four or five or six in number, originally

collected from scattered remarks in Aristotle's Topics, and repeated with minor variations in

textbook after textbook or logic, down at least to the nineteen-thirties."

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NBI Book Service used to carry two books on logic: Lionel Robbins, Logic: An Introduction; and H.W.B. Joseph, An Introduction to Logic. The latter book, which I have admired since my college days, is anything but an "introduction" in the modern sense. Both books contain discussions of definitions, of course.

That these two volumes remain in good standing among O'ist types may be seen in Binswanger's comments here .

Also, don't forget Rand's own discussion of definitions in her Introduction to Objectivist Epistemology.

Ghs

Later edit: Joseph's book contains an excellent account of the "agency" theory of causation, which links causal necessity to the Law of Identity. This became standard fare among O'ist types. That approach was also defended by Brand Blanshard in The Nature of Thought.

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A side point if you're looking into Aristotle is that his vocabulary doesn't match up one-to-one with ours. His word logos gets translated variously as definition, word, expression, sentence, formula or account, so an occurrence of definition is some translator's judgement as to which of these applies.

I suspect that Joseph's book gave Rand her mistaken impression that Aristotle said "A is A" and that he formulated a "law of identity." Joseph didn't write as a historian and didn't always distinguish between Aristotle and his tradition. Thus one might infer that anything he says is what Aristotle says.

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A side point if you're looking into Aristotle is that his vocabulary doesn't match up one-to-one with ours. His word logos gets translated variously as definition, word, expression, sentence, formula or account, so an occurrence of definition is some translator's judgement as to which of these applies.

I suspect that Joseph's book gave Rand her mistaken impression that Aristotle said "A is A" and that he formulated a "law of identity." Joseph didn't write as a historian and didn't always distinguish between Aristotle and his tradition. Thus one might infer that anything he says is what Aristotle says.

Excellent point.

Various translations of most great works are subject to battles over definitions which unfortunately spill real red blood on real battlefields.

I remember hearing a presentation of a particular word in the original biblical work. The presenter argued that the Aremaic translation of "Jesus walked by/on the water..." relied on markings above certain "letters" that had not survived the ravages of time.

The presenter basically then took a leap of stupidity and inferred that we should not trust that entire translation.

A...

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  • 2 weeks later...

Bill / Eva / Andie / Tom / et al. is back, semiliterate in philosophy (#21 reads as if somebody had written an Aristotle plugin for the Postmodernism Generator), illiterate in classics ("esse" is an infinitive, not an indicative; "is" would be "est" in Latin or εστι in Greek) and excessively fond of "rather".

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Pete,

I'm just going to take care of this one without ceremony. I'm sick of this crap.

Just saying. So the reader understands you were criticizing a post that is no longer there.

EDIT: Done.

btw - This wasn't done just on the basis of your observation, although that is definitely in the mix.

Michael

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btw - This wasn't done just on the basis of your observation, although that is definitely in the mix.

Rather than show backroom stuff and tip my hand to the trolls, this particular troll doesn't need too much time to fuck up. Check out this post out on RoR by Steve Wolfer. He is addressing the same person I deleted here:

You asked who "suggested that [you're] a former female poster?" You want to know who Eva Matthews is? Really?

Here is a post, under your member name: http://rebirthofreason.com/Forum/Dissent/0273.shtml#12

But the funny thing is that it is signed "Eva." Why were signing your post with her name?

Heh.

:)

I would bet any amount this troll often gets high and/or drunk when posting.

Michael

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Michael:

Is it possible that the poster "Harraway" just carelessly copied "Eva's" post #11 into "his" post #12 and accidentally posted it and forgot to go back and edit the post #12?

A...

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