functions and validating values

im working on having php validate negative values, numeric and non numeric and empty values in a value.

i need php to display error message if a value is negative, empty, non-numeric

im also having an issue with not getting values from my html form in $_POST

$first = $_POST['first'];
$second = $_POST['second'];
$operation = $_POST['operation'];

and in my form the names of each value is correctly spelled

for negative values i have

 if ($first or $second < 0)
{
 print("<h2> Error one or more inputs are not negative numbers</h2>");
 echo("<a href="calculator.html"></a>");
}

for empty numbers i have

  if (empty($first) or empty($second) == true)
{
  print("<p> One or more input field is empty </p>");
  echo("<a href="calculator.html"></a>");
 }

and for a value that is not numeric

if (!is_numeric($first) or !is_numeric($second) == false)
{
 print("<h2> Error one or more inputs are not numbers</h2>");
 echo("<a href="calculator.html"></a>");
}

my issue is that every time any number is entered i get error messages if its true or false