Archive for February, 2014

Illustration of a theme, from Essential Topology by Martin D. Crossley:

Note that, in these examples, there are subsets which are both open and closed, such as the empty set and {0, 1}, and there are subsets which are neither open nor closed, such as {0} in the first example. So, just as with R, the terms “open” and “closed” are not opposite to each other, and we can only know if a subset is closed or not by looking at its complement.

To most people, it would seem obvious that “open” and “closed” are contraries – both cannot be true, although certainly both could be false, or perhaps just inapplicable to a certain situation. In any case, if a door is open, it’s not also closed. And, to most people, the contrary meanings of the words should carry over into any context – “open” and “closed” are so unambiguously opposite to each other that any context into which these words could be imported cannot help but to import their contrary nature. So, either topology should not allow a space to be both open and closed, or it should not use these words at all.

Yet the quoted text refutes that commonsense notion.

And now to come to the point of this post – “subjective” and “objective” have the same relation as “open” and “closed” – not always contrary, in other words.

Now, dictionary definitions are not arguments, but they are useful starting points for discussing the meaning of words; whoever wrote the definition thinks that other people actually do, or ought to, regard that word as having that meaning. That said:

1. existing in the mind; belonging to the thinking subject rather than to the object of thought (opposed to objective ).
2. pertaining to or characteristic of an individual; personal; individual: a subjective evaluation.
3. placing excessive emphasis on one’s own moods, attitudes, opinions, etc.; unduly egocentric.
4. Philosophy. relating to or of the nature of an object as it is known in the mind as distinct from a thing in itself.
5. relating to properties or specific conditions of the mind as distinguished from general or universal experience.

subjective. (n.d.). Dictionary.com Unabridged. Retrieved February 14, 2014, from Dictionary.com website: http://dictionary.reference.com/browse/subjective

4. being the object or goal of one’s efforts or actions.
5. not influenced by personal feelings, interpretations, or prejudice; based on facts; unbiased: an objective opinion.
6. intent upon or dealing with things external to the mind rather than with thoughts or feelings, as a person or a book.
7. being the object of perception or thought; belonging to the object of thought rather than to the thinking subject (opposed to subjective ).
8. of or pertaining to something that can be known, or to something that is an object or a part of an object; existing independent of thought or an observer as part of reality.

objective. (n.d.). Dictionary.com Unabridged. Retrieved February 14, 2014, from Dictionary.com website: http://dictionary.reference.com/browse/objective

Note that definition 1 of “subjective” and definition 5 of “objective” certainly aren’t contrary to each other: the example used for the latter, an opinion, has to be the opinion of someone, of some thinking subject. So, ipso facto, that “objective opinion” is also subjective. I think the supporter of the idea that the two terms are contrary would not be satisfied with this. I’m not either.

How about definition 1 of “subjective” and definition 7 of “objective”? After all, each definition says it is “opposed” to the other. Well, the supposed opposition is not as strong as it appears. Take an example. I am thinking right now about a book I’ve bought and that’s being shipped to me (I hope!) within the next few days. The book itself has a certain weight, a certain appearance, a certain texture to the paper, etc. My thoughts about it include the anticipation of receiving it, the hope that I can understand it without too much trouble, and, of course, various thoughts about the objective qualities mentioned above. “weighs 1.2 pounds” is a fact about the object of this thought (although I suppose it applied to me a very long time ago, before birth…considered as an object, that is, as it makes little sense to say that I, as subject, weigh anything…but that’s another discussion). “is wondering when to read the thing that weighs 1.2 pounds” is a fact about the subject of this thought. These facts are not in any sense contrary to each other; indeed, they have to work together to complete the experience. I think about an object, making it an object of my thought; the subjective directing of my attention toward the object, and the object’s being its objective self, combine to create the experience. The two aspects are opposed to each other, but in no way that generates contradiction.

Imagine two football players, one a wide receiver, the other a cornerback. The receiver runs a route; the corner, in man coverage, shadows the receiver’s movement. The point of the receiver’s movement, which might include fakes or adjustments that are not strictly provided for in the prescribed route, is to get open. The point of the cornerback’s movement is not to allow the receiver to get open. So the two aspects are opposed, but they create one event, which we might name “the coverage of WR by CB during play N of drive M”, and I think the name has gone long enough – you can see the point.

The point of this example isn’t to be a perfect image of the subjective/objective mix making up the experience; it’s merely to show that being opposed is not sufficient to generate contrariety or contradiction. Indeed, imagine another person asks me what I’m thinking about, and I tell him. Then, “thinking about that book” is a subjective fact insofar as it’s considered from my point of view, but an objective fact when considered from the point of view of my inquisitor. I can extend the insight, too. “I am anxious about my first year of college” is subjective from my point of view, but objective from the point of view of a therapist. One might call it a psychological fact. And if a hundred thousand such subjective-but-also-objective facts are considered together, they might make up a sociological fact. But the names aren’t important; what is important is that the duality of aspect of the thought(s) makes them both subjective and objective by necessity.

This is true even if I’m lying. After all, take the claim “It is 40 degrees Fahrenheit at time t and location x” and let “t” and “x” be sufficiently precise for the relevant purpose. One wouldn’t call this an objective fact if it was actually 38 degrees, but by being untrue, it doesn’t stop being objective. So if I’m lying, nothing changes about the objectivity of “a hundred thousand people in the US are currently anxious about their first year of college.”

But again, I think the analysis focuses on the wrong definitions, and thus misses the mark. It’s true that I’ve shown that “subjective” and “objective” are not always contrary, but then I can’t see that anyone but a straw man was arguing that those senses of the words were the ones that never worked together.

So enough just reading off definitions; what is a person saying who says “opinions are subjective and nothing subjective can be objective,” or some such thing? I suppose that begs the question that that’s a clear and accurate presentation of the view of the person who makes the distinction. Let’s take what I think will qualify as a good example of a subjective judgment, in the sense in which such people take the word: “I like Led Zeppelin.” As before, whether this is true or not, it’s an objective fact that a person does or does not like the band, so when someone is expressing a “subjective” preference in such a manner, there is still objective content to it; it’s true or not, and surely it makes no sense to say that the truth of the fact depends on the subjective judgment of each person! I can sense the reader objecting: “But ‘I like Led Zeppelin’ is true for you but not for me, so of course it’s subjective-and-not-objective!” Imprecision of language, I say! To make “I like Led Zeppelin” into a neat logical sentence, suitable for receiving a truth value in plain old extensional logic, I need to name “I”. The speaker gets a name, let’s just say “c” (for “constant”, see how creative that was?), and now “c likes Led Zeppelin” does not depend on the subject uttering it or thinking it at all.

I think perhaps I haven’t been fair again. So let’s try two more claims:

“Led Zeppelin songs are enjoyable”


“Led Zeppelin is better than Pink Floyd”

If both are prefixed with something like “I find that” then my treatment immediately above should deal with the two. But that’s too easy. I see no reason to think that I should prefix them so.

I don’t know exactly what the first means. If it means “Led Zeppelin songs are enjoyed in some possible world” or “at least one person enjoys Led Zeppelin songs,” there’s an objective fact (again, true or false!) being stated. I think a trickier rendering is “although I lack concrete information about the tastes of most people, I enjoy Led Zeppelin songs, so most people must also,” which certainly seems objectionable. Perhaps worse, take it to mean “everyone ought to enjoy Led Zeppelin songs.” I think this hits upon the sense in which “subjective” and “objective” exclude each other – a subjective preference is only illegitimately hypostasized into an objective fact about all other subjects’ preferences.

So, “this is enjoyable” is subjective. And, sure, it’s subjective in a way that isn’t objective, or at least not in every sense – sure, it’s an objective fact that someone enjoys something, but not that the enjoyment is an inherent part of the object rather than the subject. And yet…I wonder about something. I wonder if there is a sense in which the duality of aspects appears again. If the majority of people do enjoy Zeppelin, there may be something in the object that triggers the same subjective preference in many people. Now, we have no reason to doubt that those who don’t enjoy the songs don’t enjoy them, nor should we ascribe bad taste to those who don’t enjoy them; therefore, the preference has to be called “subjective” for two reasons: it deals with the subject aspect of subject-experiencing-object, and it is a matter of that varies from subject to subject – it involves taste, opinion, or whatever. Yet there’s an objective element, if the same objective facts about the object cause the experience to be similar even in its “subjective-and-not-also-objective” elements.

And then there’s a normative statement like at least one meaning of “you should like Led Zeppelin songs.”

I think I’ve proved too much, or, really, claimed that “subjective” and “objective” are more compatible than they really are, and certainly more compatible than I’ve proved. So let’s return to the central issue. Now is probably the right time to explain the “XOR” in the title. I think the claim “judgments are either subjective or objective” is taken to involve exclusive disjunction. I’ve tried to argue that it need not. The strongest evidence for an exclusive reading is a judgment about preferences of taste. However, I think a few things need to be kept in mind. First, often “a subjective judgment can’t also be objective” merely begs the question. If “subjective” is defined to exclude objectivity, then the claim is tautological but simply ignores what the words actually mean in many contexts. I’ve demonstrated that above. Second, a focus on the subjective aspect of experience should not be taken to mean that the objective aspect doesn’t exist. Finally, and this is the most important point here, it should be recognized that there may be a basis in the object even for a subjective preference. So a subjectivity that excludes objectivity, even when legitimate, should not be extended beyond its proper limits; a person’s preference for a thing should not be construed to ignore some basis in the object, and thus an objective aspect, to the preference.


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Forcing oneself to think rigorously is difficult, especially outside a certain kind of academic environment. And since I am outside any kind of academic environment, I am also outside a certain kind.

This blog will document the struggle against such difficulties. Logic is fundamental. However the world fundamentally works, it has to be thought of and spoken of for any sense to be made of it. This fact helps to explain why it’s so interesting, but the fact is more important than the reason.

Logic is a constant source of wonder. It’s really very thrilling to explore it.

Let’s see where this goes.

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