When explaining the distinction between essential and accidental properties bachelors are often used. The idea of essential properties is this:

The distinction between essential versus accidental properties has been characterized in various ways, but it is currently most commonly understood in modal terms along these lines: an essential property of an object is a property that it must have while an accidental property of an object is one that it happens to have but that it could lack. (SEP)

So, bachelors have the essential property of being unmarried. This is because a married bachelor is a contradiction. This is because the concept of being a bachelor implies the concept of being unmarried. Implication with concepts works just as one might intuitively think that it does; very similar to that of propositions (or whatever truth carrier that you like), but see Swartz & Bradley (1979) for a deeper explanation using possible worlds semantics.

So, since we’re good analytics, we shall invoke the power of formalization.

A. For any person, it is impossible that (the person is a bachelor and the person is married).


That’s all fine and dandy. But it seems then that essential properties are just a matter of semantics, of language, and has nothing to do with the bachelor at all. Based on some idea of essential properties and bachelors and so on, we might say that:

B. Bachelors can’t be married.

But then, how do we formalize this?


Going with some very literal interpretation we may get the above, but surely the proposition that that wff expresses is false. Let’s translate it to LAE1

For any person, if that person is a bachelor, then it is not the case that it is possibly the case that the person is married.

So, a bachelor can’t even marry. But this is wrong. Bachelors can and do marry. The only thing is that the concept of being a bachelor and that of being married cannot at the same time be instantiated in the same person. Nothing else. There is no contradiction in saying:

I was a bachelor for many years, but then I married Jane. Gosh she is so wonderful, blahblahblah…

We may reduce this tale to something like:

Bert the Bachelor was a bachelor at time t1, but then later he married and stopped being a bachelor.

Which we may formalize as something like:


1Logically Aided English

It is the mark of an educated mind to be able to entertain a thought without accepting it.

Indeed it is. But I cannot find a source for the quote. It is listed as unsourced on Wikiquote (which is a pretty good indication of it being a misquotation). A google search does not reveal a source but only the usual suspects, that is, sites that spread quotations with no regard for their sources. Kennehtamy thinks that it is Aristotle but I couldn’t find it by searching through neither Politics or Ethics on Gutenberg.


I’m reading Irving Copi’s Introduction to Logic, very boring and not that well written, any suggestions? Just a college level book that gives a comprehensive intro to the topic. Thanks.


“Boring” is not a particularly apt criticism of a text. There are jazzier logic books out there, with bunches of cartoon and jokes (and maybe even recipes for peanut butter and jelly sandwiches) but Copi is a good, solid elementary logic text which has been through more reprints than I can count, and has set the standard for logic texts in English. If you seriously want to learn, you really have to give up the entertainment addiction.

Notice how applicable this is to anything. Simply substitute logic for any serious discipline such as physics, chemistry and sociology.


Some people sometimes mention that deduction conforms to the GIGO principle. I will here show that in a straightforward interpretation of that, it is false.

“Garbage in, garbage out” is a metaphor or sorts. The mental image I form when I hear it is something like a huge machine that, when garbage is put into it, garbage comes out. Perhaps in smaller pieces. How can we apply this to deduction, that is, reasoning with deductively valid arguments? The most straightforward interpretation seems to be this: Deduction is some kind of machine, that when we put in bad data as premises, bad data conclusions comes out. What could bad data mean? The obvious candidate is false data, that is, false premises and false conclusions. What else could it mean? This interpretation thus means: All deductively valid arguments with false premises have false conclusions. This is simply false. Counter-examples are easy to come by and are given in most logic introduction textbooks, here is another:

1. All people that live in France have dark skin.

2. All people with dark skin live in Europe.

Thus, 3. All people that live in France live in Europe.

The premises are both false and the conclusion is true.

The only thing guaranteed by a deductively valid argument is, if the premises are true, then the conclusion is also true. Deductively valid arguments are truth-preserving from the top to the bottom , which is just another way of saying that it is truth-preserving from premises to the conclusion. A deductively valid argument is not falsity preserving from the top to the bottom, however, it is falsity preserving from the bottom to the top, in other words, all deductively valid arguments with a false conclusion has at least one false premise. This is irrelevant to GIGO though.