Are analytic sentences tautologies?

An analytic sentence is one which can be seen to be true by virtue of the meanings of its terms. An example that is often given is:

• A bachelor is an unmarried man.

A widely held view, among academic philosophers, is that analytic sentences are tautologies. I disagree with that assessment. I am not saying that the philosophers are wrong. I am just expressing my disagreement. Maybe we don’t have the same idea as to what “tautology” means.

It is widely agreed that language is conventional. That is to say, there are social conventions that underlay language. That different societies have different languages points to this conventionality.

Among the various conventions, there can be syntactic conventions which set how words should be arranged in sentences. There can also be semantic conventions, which set the meanings of words. And, of course, there can be mixed convention that combine both syntactic and semantic aspects.

To my way of thinking, a tautology is a sentence that is true by virtue of syntactic conventions. But once we bring in dependency on semantic conventions, I don’t think we should use the term “tautology.”

Iowa and Illinois

Here’s an example.

Apparently there is an agreement between the states of Iowa and Illinois, setting the boundary between the two states as the Mississippi river (the center of the Mississippi river). According to that agreement, we can say “Iowa is to the west of the Mississippi.” From my perspective, that sentence looks analytic but I would not consider it to be a tautology.

Mathematics and reality

I have recently posted a couple of comments relating to whether mathematics is real. These were blog comments or forum comments. And, to be clear, these posts were elsewhere (not on this blog). This post will expand on those.

Discovery or invention

A blogger asked whether mathematics is a matter of discovery or invention, and I commented. But I’m not sure where that was. So I am reconstructing and expanding my comment.

My first remark was that mathematics is an invention. I’m reminded that Kronecker famously said “God gave us the natural numbers; all else is the work of man”. But it has long seemed to me that Kronecker gave too much credit to God. It is all the work of man.

I did not want to dispirit the blogger, so I tried to connect invention with discovery.

Nobody doubts that Lego blocks were invented. But give children some Lego blocks, and they will quickly discover all kinds of interesting things that they can do with those blocks. You really cannot separate invention and discovery. If you invented something that was useless and boring, you would quickly forget it. Any important invention involves the discovery that what you invented is useful or interesting or both. We might say that “invention or discovery” is a false dichotomy. They go together hand in hand.

Getting back to mathematics, presumably at some time it was discovered that counting was a useful practice. But maybe the practice had to be invented before you could discover that it was useful. Again, discovery and invention are intertwined.

Numbers are not just counting. For counting, you need a sequence of names to use. But numbers themselves are abstract entities, presumably derived from the practice of counting. So the use of numbers in this way was a separate invention. But again, it was an invention that depended on discovering the usefulness of numbers.

Review of “End this wicked marriage”

UPDATE:

I have added a comment about what apparently happened. And that seems to clear up the puzzle.

END OF UPDATE

This started as a book review. But it has become a puzzle.

Jerry Gramckow is the author of a Kindle book “End this wicked marriage: why Evangelical Christianity needs to divorce itself from the Republican Party”. I learned about the book on Monday, from Jerry’s blog.

But here’s the puzzle. Jerry’s blog has disappeared. It now gives me a 404 (not found) when I try to pull up that page. So I searched for the book title on Amazon, and that too has disappeared.

I still have my copy of the book on my Kindle. I hope that doesn’t disappear, too. Amazon has been known to pull books, though they got many complaints when they last tried this. Perhaps they will let me keep it. I actually have a second Kindle. The one where I read this book is a paperwhite (an e-ink version). My second Kindle is a fire tablet. Checking my library there, the book did show up. And I was still able to download it. So Amazon actually still has the book in its database, but it is hiding that book. It looks as if only people who have already acquired it can access it.

Meandering thoughts on consciousness

This post might wander all over, as I jot down thoughts that seem relevant.

Ding an sich

Kant used the expression “Ding an sich,” which is usually translated as “the thing in itself”. Kant’s idea was that we cannot know the world in itself; we can only know the world as we experience it.

This has turned out to be a controversial view. Many people disagree with Kant about this. However, I am inclined to agree, though perhaps my reasons are different from those of Kant.

In Genesis 1:2, we read “And the earth was without form, and void; and darkness was upon the face of the deep.” I am inclined to see that as a pretty good description of the world in itself, although I doubt that I am using that in the way the author(s) of Genesis intended.

If we attempt to describe the structure or form of the world, we may find ourselves using words such as “texture”, “height”, “color”. We use these words to express human concepts. When we talk of the world in itself, we should limit ourselves to what can be said without depending on human concepts. And there isn’t much at all that can be said.

As for that “darkness” part of the Genesis text, we can reasonably assume that the earth was bathed in electromagnetic waves. But most electromagnetic waves are not visible to us. Our sight depends on a narrow range of wavelengths. That we happen to be able to sense those wavelengths is part of our biology. So we should exclude that as part of what we consider the world in itself.

Kant contrasted this with the world of appearances, or the world that we experience. It seems entirely reasonable to me, that the way we experience the world is very different from the way that an ant experiences the world, or the way that a bird experiences the world or the way that a bat experiences the world. So when we talk of the world in itself, we should consider only what is observer independent. But we cannot know anything apart from observation. Hence my agreement with Kant’s view.