What is the difference between equality and logical identity? I'm reading the book Introduction to Logic and to the Methodology of the Deductive Sciences by Alfred Tarski and he states:
"In this book we consider the notion of equality among numbers always as a special case of the general concept of logical identity. One should add, however, that there have been mathematicians who —as opposed to the standpoint adopted here— did not identify the symbol "=" occurring in arithmetic with the symbol of logical identity; they did not consider equal numbers to be necessarily identical, and therefore looked upon the notion of equality among numbers as a specifically arithmetical concept."
So what is the difference between "=" and "logical identity"?

Consider a line segment with endpoints : (0,0) and (3,O) and a line segment with endpoints (0,4) and (3,4). 
You may say that they are " equal". 
But, in fact, they are not " logically equal", for they are not one and the same segment, they count as 2, not as 1 object. 
The two segments are equal ( in length) but not identical. 
