On Conservativeness and Incompleteness

8 03 2005

Field addresses many of the points raised in my previous post in his essay by this title (reprinted in “Realism, Mathematics, and Modality”) and I realize that I should have had an idea of what he would do anyway, having read the introduction to that book. He believes in a primitive modal notion of logical consequence that may in fact be quite powerful, to which both the syntactic and semantic consequence relations described by proof theorists and model theorists are approximations. The fact that one is an upper bound and the other is a lower bound, and that in some languages they coincide, is evidence that these approximations are exact for those languages. However, these results (and even the theories themselves) only really make sense from a platonist perspective, because they discuss abstract entities like deductions and models.

Advertisements

Actions

Information

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s




%d bloggers like this: