UPDATE Place Holders don't appear to be the solution.
Page 221 of Programming the Perl DBI:

     "SELECT name,age FROM ?" # wrong will probably fail.

With most drivers, placeholders can't be used for any element of a sta
+tement that would prevent the database server from validating the sta
+tement and creating a query execution plan for it.
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Comment out or replace read_log(shift) with get_table_list(shift) in the first listing and add the following subroutine. It is supposed to print the table name then dump the table for every table in the database.

sub get_table_list ($) {
    my $log = shift;
    my $dbobject = DBI->connect("DBI:XBase:".$basedir.$logdir)
        or die $DBI::errstr;
    my @tables = $dbobject->tables;
    print "Database contains the following tables:\n__________________
+______\n";
    foreach my $table (@tables) {
        print "$table\n";
        read_log($table);
    }
    print"\n\n";
        $dbobject->disconnect;
}
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Placeholders and $dbi->quote don't work with table and field names. They only work for data elements.

For identifiers, each database has its own quoting mechanism. The ANSI standard is double quotes:

SELECT foo FROM "$bar"
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SQL Server uses square brackets:

SELECT foo FROM [$bar]
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New versions of DBI have the $dbi->quote_identifier method. It can be used the same as $dbi->quote

my $quoted_log = $dbi->quote_identifier($log)
my $sql = "SELECT foo FROM $quoted_log";
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This may be new enough that DBD::XBase does not support. Then you will have to find out what quoting mechanism it uses and use that.

Neither quoting mechanism nor the quote_identifier method worked. I also attempted low-level access directly through ::XBase which resulted in an 'invalid argument' for long file names. Any one know of an alternative to DBD::XBASE or ::XBase to read/write .dbf files? Specifically Foxpro files?

Thanks for the information. Unfortunately none of the methods of quoting worked for me. So ... I suppose this means that DBD::XBASE may be broken. I am going to go dive into that now and see if it has some weird quote mechanism or not.