This is a proposition about essence. It is abstract. It exists in thought or as an idea but does not have a physical or concrete existence - meaning or abstract. It is an eternal truth.
Those truths are always called "eternal truths." The gist of the argument is that truths are part of the contents of minds, and that an eternal truth must be part of the content of an eternal mind. There is already an argument not unlike this in Plato where deduces immortality from the eternity of the ideas. But in Leibniz the argument is more developed. He holds that the ultimate reason for contingent truths must be found in necessary truths - The History of Western Philosophy by Bertrand Russell.
When we see two apples we think they have similar qualities, even though each will have a slightly different shape. It cannot be said apple A is exact replica of apple B. In the physical world no two things are the same. Take for instance two hydrogen atoms, they may have different distortions when they strike the container they are in, though these distortions may reduce with time they may not fully disappear for ever. At least at the time the notion 1+1 = 2 appeared in the domains of mathematicians, they were unable to go the the depth of hydrogen atoms but apples are a good example for defining two. Notion of two came about humans seeing similar things. Seeing sheep in a heard, or seeing everyone have two eyes, hands and legs etc build up the concept of two.
Therefore two was not entirely a mental concept. After observing lot of physical things this concept was built in our brains. After the concept was built we do not need the physical things to substantiate it. Like what Wittgenstein said in Tractatus - My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them - as steps - to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright. Then the concept becomes purely mental. The propositions are the ones explaining about similar things, existence of it, it's properties, why we treat certain things as similar things etc. It is an eternal truth.
Construction of the human brain has a special ability to group things. Because of this ability we can separate groups of things which has similar attributes. Here it should be noted that all of the attributes need not match. A percentage is sufficient. This percentage is not a well defined thing. It depends on the brain. Two individuals may differ. Usually, we accept that two things are similar when most of the human brains agree that properties of both are sufficiently same.
Strangely enough 1+1 = 2 concept will not be complete without 3, 4 and 5 so on. This can be explained why an orange and a lemon are not grouped as the same type of fruit. Orange and lemon will have some attributes that are similar, but we won't say they are the same fruit. The reason is when we look at a heap of oranges we know that the attributes shown by the orange is different than a lemon. To make this distinction we will need more than two oranges.
Problems of Quantum theory:
- Two different properties of a particle cannot be measured independently.
- Errors of measuring properties depend on probabilities. Unlike in classical physics where these probabilities only depend on measuring instruments, in Quantum theory they depend on measuring of other properties.
- Measuring of one particle automatically decide the value of other particle.
- Behaves in different ways depending on ability to observer the particle.
- Local Realism - having a preexisting value before a measurement is done.
- Realism - the world is independent of mind.
- Radioactive decay.
No one is worried about 1+1 = 2 not having 100% link to the physical world - people have thrown out the ladder long ago. But worried about quantum theory - people have yet to start throwing out the ladder.
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