# Defining 2 words with respect to each other

I apologize if this is in the wrong forum. I listen to a radio show where the host talks a lot about love & hate. He defines love as 'the absence of hate' and he says that hate is 'the absence of love'.

Is there a formal term for this type of fallacy? I'm sure that within mathematics, it's akin to solving for 2 variables when there is no context for either one of them, or they point to each other, but I can't figure out with respect to logic, the term that explains why this doesn't work. It's like an infinite loop, that's the best way I can describe it.

• It sort of reminds me of yin and yang. Or true and false. I am not sure there is an informal fallacy involved here. – Frank Hubeny Jul 13 '18 at 22:09
• Circular definition? Not really a fallacy though, as there is no reasoning involved. – Bram28 Jul 13 '18 at 22:09
• This is not a real definition. But there are indefinables - words which cannot be defined without relating to each other and their usage cannot be learned from definition, but only from examples. Take whole vs. part. – rus9384 Jul 17 '18 at 8:56

I think I should call this by an established term, 'privative definition'. It defines each concept in terms of the absence or inapplicability of the other.

But that's not quite all. A privative definition can be okay : 'blindness is lack of sight'. What you seem to be calling attention to is circular privative definition. One wouldn't say, 'Blindness is lack of sight and sight is lack of blindness' - sight has far more characteristics than just lack of blindness and these can be specified (the ability visually to judge distance or size, the ability visually to distinguish the hue, saturation and brightness of colours, &c,).

'Love is the absence of hate and hate is the absence of love'. Hate and love can both be - and both need to be - characterised by more than the absence of each from the other. The statement in any case isn't even true; it's a false antithesis. I may have no hatred for X but no love from X either : I may be neutral or indifferent to X. Ditto for love : I may not love Y but not hate Y either since neutrality of indifference may again apply. Love and hate may be mutually exclusive but they are not jointly exhaustive. There are intermediate states.

The meaning of words can adequately be described using Wittgensteins concept of language games. https://en.wikipedia.org/wiki/Language_game_(philosophy)

So while in your example people say that they "define"

• love is 'the absence of hate'
• hate is 'the absence of love

what people really do is creating/changing the meaning of words by using them.

The takeaway is that in general, words derive meaning from their usage alone, not from dictionaries defining meaning. Dictionaries follow and describe the usage of words in a culture. Dictionaries also try to make everyone agree on a meaning, but when in doubt, dictionaries have to be changed when people start using words differently.

Only in certain sciences like those based on maths do words have meanings grounded additionally in numbers instead of only in usage, making their meanings real hard to change (using them wrongly consistently). Only for such words is it useful to even speak about "definitions" of words, many words that we use don't have a "definition", they merely have a "usage guideline".

Else the mental image of meanings of words being something stable is an illusion that comes from the changes being relatively slow. Similar to the illusion that stars, continents or glaciers are non-moving, just because they move so slow.

If these definitions are taken in isolation, they lead to an infinite regress, since each definition is a simple negative reference to the other. As has been pointed out in another question on this forum, this is also a feature of dictionaries, since each word in the dictionary is described in terms of the other words, which are defined in terms of other words, until there is a circularity. (You just have a simpler form here, where you only have two concepts, each defined as the absence of the other.)

Usually this recursive issue in language is resolved by having a set of ostensive definitions (also known as "definition by pointing") of basic concepts that form the base for language, and then we build higher-level concepts on top of these base concepts. If you look up definitions of 'love' and 'hate' in dictionaries, you will see that there is an effort to describe them in terms of lower order concepts. In the case you point out, the problem is that the two definitions tell us nothing about the content of the concepts 'love' and 'hate' other than the fact that they are antipodes. If you didn't already know what these meant, those definitions would not help you.