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do the following: based on philosophy
The Recipe (Instructions):
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information that can be helpful
Analytical definitions are the definitions most commonly prized by mathematicians and Western philosophers and scientists. The reason is that these definitions state the necessary and sufficient conditions (Links to an external site.) for the definiendum – that is, they do precisely what ostensive definitions inherently fail to do. In the West, their strength has often been thought to be that if you have given a genuine analytical definition of a concept, then by the same token, you guarantee genuine understanding of the definiendum. In other words, to successfully analyze a concept, is (at least by Western standards) to have knowledge of the definiendum. Ask yourself if knowing something is always a matter of “breaking a thing down” into its parts. (For skepticism about this so-called “Western Assumption,” see Australian philosopher Frank Jackson’s article, “The Qualia Problem.”
The weaknesses of such definitions are that they are extraordinarily hard to arrive at, and even if you do, one might wonder how you would know that you had done so! (John Rawls, a well-known political philosopher, tried to give an analysis of justice in his famous book published in 1971, A Theory of Justice (Links to an external site.). Check out the link to see how many pages it took him to do so!)
This idea, or ideal, of analysis is manifest in the general method of science. Those practices attempt to solve problems by “breaking them down” into their constituent parts, and then breaking the constituent parts down into their constituents, and so on and so forth, until no more division is possible. By clearly understanding each “part” (whether abstract or physical in nature), the idea is that if you can isolate precisely what it takes to be such a part, then there is no way of confusing it with any other part, and there is likewise nothing left to say about it in isolation.
This is tantamount to arriving at the essence (Links to an external site.) of the definiendum. A statement of the essence of something answers the question: “What is it that makes this thing the thing that it is, and nothing other than that?” If you know the answer to this question, of any given thing, could you possibly say any more about it, or would that constitute certain knowledge of what that thing is?
Stipulative definitions are definitions that amount either to coinages of new words (called neologisms (Links to an external site.)), or that define familiar words in ways so different from ordinary usage, that they might almost appear to be new words (although strictly speaking, their meaning is what is new, rather than they themselves). Take the word ‘mouse’. Today we associate this word with external devices used to move the cursor to various locations on a computer monitor. A generation or so ago this would have been thought insane (and unmarketable)! The word ‘mouse’, used in this way, was then stipulated (by Steven Jobs?) to refer to this device, sometime in the nineteen-eighties, I believe. In a rather similar vein, in philosophy programs at colleges, we stipulate that ‘validity’ means the property possessed by those arguments in which, if the premises are all assumed to be true, then the conclusion must be true as well. Notice how wildly different this usage of the words ‘valid’ and ‘validity’ is from everyday usage! Now, philosophers don’t regard their definition as stipulative, although it is recognized by them to deviate from general social usage. Therefore, we might say that whether or not a given definition is stipulative, is to some degree a matter determined by the exclusiveness of the group using it.
Does the relative exclusiveness constitute a weakness of stipulative definitions? Actually, it may be both the strength or the weakness of stipulative definitions.
This requires an explanation: On the one hand, by saying exactly how you are using a word, you are assisting your interlocutor (conversation partner) in following along with whatever you are discussing. On the other hand, if your goal is to make a clear case for something by appealing to a special definition you apply to a term, then you aren’t going to be terribly successful making your case in situations where your meaning is highly idiosyncratic.
Ostensive definitions are definitions by example. An example of such definitions that is often used in Introduction to Philosophy courses is a quote from Euthyphro, an acquaintance of Socrates, who said: “Piety is what I am doing, namely prosecuting a wrongdoer.” Notice that this is an example of an intangible or abstract idea – piety. Ostensive definitions are not limited to such contexts, of course: I could very easily explain the meaning of the word ‘cup’ by pointing to a cup, and that too would then be functioning as an ostensive definition. The strength of such definitions is that they give the inquirer a literal example of the definiendum, and one example is usually – but not always – better than none. Moreover, there are contexts in which such a definition is in fact the most desirable kind, since there are some contexts in which knowing quickly what something means, is the surest way of accomplishing the task at hand. Can you think of one such context?
There is a very important weakness associated with ostensive definitions, however: ostensive definitions do not tell us what features of a definiendum are the ones that are relevant for the example’s inclusion in the class of objects (or abstract ideas) being defined. Because of this, it is theoretically possible to include items in the definiendum class, which should be kept out of it; and it is likewise possible to allow into the class, items which should be kept out. Below is an example that illustrates this weakness.
Suppose Xylo [pronounced like “sigh-low,” only with an initial “z” sound] is from the planet Quantum, and Xylo has just recently acquired a fairly good grasp of English and of Earthling cultures. Somehow, however, until today Xylo has never before heard the word ‘cup’. So Xylo asks you, “What is a cup?” and, quite reasonably, you show Xylo a cup and hope he quickly grasps the definition of a cup. The next day, however, Xylo approaches you with a bag and says, “Thank you for teaching me the meaning of the word ‘cup’. I too, now, have a cup. Here is my cup,” and Xylo thereupon holds up his bag for you to inspect. What has gone awry? To complicate matters more, suppose that you point to a cup and Xylo says, “But that cannot be a cup.” Why might Xylo do this? Think hard about the limitation of ostensive definitions in order to answer these two questions. One tidy way of summarizing the weakness of ostensive definitions is to say that they fail to state either the necessary or the sufficient conditions for inclusion in the definiendum class.
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