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1st case Consider two objects made from the same factory without any difference (an ideal scenario). Can we say that the two objects are the same? I would say no because one may be produced earlier and also after being produced they don't have the same position. Can we say that they are identical?

2nd case Consider 5 apples on the table and 5 apples on a chair. We can say that 5 apples = 5 apples but the apples are not the same. I mean the apples on the table could be green and these on the chair red etc. So can we say that the term "same" applies only to mathematical objects?

What is the difference between same, identical and equal?

  • The issues you cite are resolved by distinguishing numerical and qualitative identity, but one can equally well use "sameness" instead of "identity". "Equality" usually refers to identification that explicitly disregards all but selected aspects. – Conifold May 21 at 1:03
  • I think the question here is can the terms identical and equal be misunderstood or confused by someone else namely a listener. People usually speak in some acceptable context to be understood. Culture as well as location make a difference on contexts. Here the CONCEPTS of identity and EQUIVALENCY seem to be expressed. Apple's will always be apples but the details about some apples may make a distinction as on a chair or on a table. Equal does not mean equivalent always. Equal can mean IDENTICAL as in a mirror image of the same attributes with no exceptions. A=A expresses the same attributes. – Logikal May 21 at 1:42
  • Equivalent expresses that the same meaning of a language can be derived in more than one way. 3+3=6 but so does 7-1. These express the same answer or idea but use different symbols or words. Sentences can Express the same thing but be distinct sentences: you are fired and you are terminated express distinct sentences & express the same idea in a context. Identity expresses there is no distinction whatsoever between 2 objects. Any slight distinction means the 2 object are not identical. Essentially object a & b are the same object (perhaps with different names) such as Mark Twain & Sam Clemens. – Logikal May 21 at 1:49
  • We can say the MODEL or TEMPLATE used to create a laptop is the same but each laptop from the same manufacturer would have a distinct serial number for instance. They are not identical but they are equivalent if they are the same model. The word SAME could be either identical or equivalent depending on the context. If basketball player 1 & 2 are on the SAME team does that mean IDENTICAL TEAM or a team equivalent? Most English speaking people would say identical. You & I have the same laptop does not Express we use the exact identical laptop but they are equivalent in make model & attributes – Logikal May 21 at 2:00
  • 5 apples on the table and 5 apples on the chair (simultaneously) are not the same apples. The number of apples on the table is the same that the number of apples on the chair. – Mauro ALLEGRANZA May 21 at 6:09
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A real world factory doesn’t produce identical objects. There are always differences. They are similar. Even a million needles from the same factory won’t contain two identical needles.

When we go down to the nuclear level, atoms are identical. Molecules are identical.

Sameness is strange: Me yesterday, me today, and me tomorrow are the same, but we are different. Not much, but different.

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Same

'... two objects made from the same factory' cannot be one and the same object. Whatever their sameness in the sense that each object has all and only qualities exactly similar to the other's, they are numerically distinct.

Identical

'Identical' is an ambiguous term. It can connnote exact similarity as when each object has all and only qualities exactly similar to another's - or it can mean that X and Y as identical are one and the same object as in Frege's example of the Morning Star and the Evening Star's being identical because they are one and the same object differently referred to, i.e. the planet Venus.

Sameness

This is not confined in its application to mathematical objects. 'The same ...' is incomplete. The same what ? Two automobiles can be of the same model, where there is nothing mathematical about a model (in this sense). Three people can belong to the same family - another non-mathematical object. Mathematics enters necessarily at one point only: countability is implicit in the concept of sameness. Am I the same person that I was yesterday? Yes, I am one and the same person at two different times. If I am in New York and move to LA, have I been in two locations in one and the same country? Yes, of course, the USA.

Equality

'Equality' can mean 'equality in numerical value' as in your apples example but when I say that two models of automobile are of equal utility for your purposes - one's as good, as functional, as the other it's hard to see what strict metric I could use to justify my claim. I just mean, one's as reliable as the other, one's as easy to get serviced or repaired as the other, they equally enhance your image, &c.

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