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For example, consider two children with identical bicycles engaged in a race while their mother is watching. The two children have the same bicycle in one sense (qualitative identity) and the same mother in another sense (numerical identity). [3] This article is mainly concerned with numerical identity, which is the stricter notion.
Identity is a relation on individuals. It is not a relation between propositions, and is not concerned with the meaning of propositions, nor with equivocation. The law of identity can be expressed as , where x is a variable ranging over the domain of all individuals. In logic, there are various different ways identity can be handled.
Although the theory is that the similarity of elements facilitates transfer, there is a challenge in identifying which specific elements had an effect on the learner at the time of learning. [4] Factors that can affect transfer include: [7] Context and degree of original learning: how well the learner acquired the knowledge.
In philosophy, Occam's razor (also spelled Ockham's razor or Ocham's razor; Latin: novacula Occami) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle of parsimony or the law of parsimony (Latin: lex parsimoniae).
Identity of indiscernibles. The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa. It states that no two distinct things ...
Piaget’s other famous task to test for the conservation of liquid involves showing a child two beakers, A1 and A2, which are identical and which, the child agrees, contain the same amount of colored liquid. Then liquid from Beaker A1 is poured into a taller, thinner glass (B1) and the liquid in A2 is poured into a glass (B2) identical to B1.
Atomism. Atomism (from Greek ἄτομον, atomon, i.e. "uncuttable, indivisible") [1][2][3] is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms. References to the concept of atomism and its atoms appeared in both ancient Greek and ancient Indian philosophical traditions.
A proof by double counting. A combinatorial identity is proven by counting the number of elements of some carefully chosen set in two different ways to obtain the different expressions in the identity. Since those expressions count the same objects, they must be equal to each other and thus the identity is established. A bijective proof.