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If you consider any two numbers that are not equal in value (2 is not 3), and it is a true statement that they are not. However, it is also true to state that they are the same: both are numbers.

You could apply this in other contexts: an apple and orange they are not the same fruit, but also they are the same because they are both fruits.

How is it that it is true that they are both true statements?

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  • sorry if my edit changed your question
    – user67675
    Nov 17, 2023 at 20:24
  • 4
    It goes back to Aristotle's genus–differentia definitions, genus (fruit) is what they have in common and differentia is what makes them different species within it. How commonalities or "common natures" attach to different species and individuals later became a long-standing philosophical problem, the problem of universals. In modern times, it transformed into theories of similarity.
    – Conifold
    Nov 17, 2023 at 21:42
  • thank you so much this was the asware i was looking for
    – Nopal vol
    Nov 18, 2023 at 8:37

4 Answers 4

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The simple answer is that sameness as you apply it in the two sentences is different in those two contexts. This apparent paradox is resolved by noting the equivocation in your term 'same'. That is actually, there are two senses of the word same: SAME1 (they are the same count) and SAME2 (they are same type of numbers, naturals). Thus:

Two is not the SAME1 as three. (2≠3)
Two is the SAME2 as three. (2,3∈N)

You can see that why we use special symbols in math to avoid these sorts of apparent contradictions. This isn't a deep metaphysical difference; rather, it's just that when you use the word or token 'same' in a sentence, it refers to two closely related, but different meanings.

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  • my emphasis is not on the 'same' but rather on the statements being true both ways, like for example you couldnt tell me which is true if you dont consider any specific characteristics like value of number or features of the fruits
    – Nopal vol
    Nov 17, 2023 at 20:15
  • They're both true at the same time BECAUSE they express different kinds of truths. Same applies to the comparison of ANY property including class membership, size, taste, numerical equality, etc.
    – J D
    Nov 18, 2023 at 15:35
  • For instance, it is true that I am the same as tall and true that I am same as male simultaneously. In your case, they are the same count and the same type of numbers (naturals) at the same time. These properties are therefore independent of each other.
    – J D
    Nov 18, 2023 at 17:57
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Objects and ideas have many properties. Two things may be alike in respect of some properties but not others. For example, since I and the Barbie doll first emerged in 1959, you might say that we are the same age, but we are unalike in terms of our hairstyles. Donald Trump and I are the same species, but unalike as people. Donald Trump and the Barbie doll may be different in terms of height but share the same IQ and hairstyle, and so on. So when you say that two objects are both the same and different, you simply mean that they have some properties in common but not others.

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  • its not accurately considers what i mean in the question, its like we say 3 and 3 are both numbers but i think the other 3 is slightly round and orange
    – Nopal vol
    Nov 17, 2023 at 20:40
  • when there is some sort of equality, the possibility for consideration of any specificity arise and it will make a fog for the problem
    – Nopal vol
    Nov 17, 2023 at 20:46
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The difference is in category. Aristotle called this genus. They are both true statements because they refer to different categories. "Man and the mule are always tame; the leopard and the wolf are invariably wild, and others, as the elephant, are easily tamed." Some animals are always wild, some are always tame, some can be tamed. Men and mules are contained in the category of tame animals. Mules and oxen are contained in the category of beasts of burden. So man is not a beast of burden. Man and mules are both tame. Both of these statements are true. There is no contradiction.

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    +1 but a quote would make your answer authoritative
    – user67675
    Nov 18, 2023 at 14:41
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    See edit for clarification.
    – Meanach
    Nov 18, 2023 at 15:12
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If you consider any two numbers that are not equal in value (2 is not 3), and it is a true statement that they are not. However, it is also true to state that they are the same: both are numbers.

How is it that it is true that they are both true statements?

Because you equivocate: 2 and 3 are the same sort of things, namely, numbers, but there are not the same numbers.

Nobody would argue that a one-hundred-euro bill and a ten-euro bill are the same because both are bills. Nobody does because everybody understands that they are the same sort of things, namely, bills, but not the same bill.

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