edibleplastic's New Writeupshttp://everything2.com/?node=New%20Writeups%20Atom%20Feed&foruser=edibleplastic2003-05-13T14:19:56ZThe Metaphysics of Mathematics: Frege vs. Brouwer (idea)http://m.everything2.com/user/edibleplastic/writeups/The+Metaphysics+of+Mathematics%253A+Frege+vs.+Brouweredibleplastichttp://m.everything2.com/user/edibleplastic2003-05-13T14:19:56Z2003-05-13T14:19:56ZIn the modern debate about the <a href="/title/foundations+of+mathematics">foundations of mathematics</a>, <a href="/title/Gottlob+Frege">Gottlob Frege</a> and <a href="/title/Luitzen+E.+J.+Brouwer">L.E.J. Brouwer</a> could be considered the scholars most diametrically opposed to each other. Frege, the developer of modern <a href="/title/logic">logic</a> and patriarch of <a href="/title/Logicism">Logicism</a>, was a staunch <a href="/title/realist">realist</a> when it came to the existence of mathematical objects and truth. They exist objectively and absolutely in the world, and their nature is entirely independent of observer and circumstance. Brouwer, on the other hand, completely rejected the idea of mathematical existence without an observer. He argued for an <a href="/title/embodied">embodied</a> mathematics, <a href="/title/Intuitionism">Intuitionism</a>, that is wholly based on the system it was derived from—the <a href="/title/mind">mind</a>, the <a href="/title/brain">brain</a>, and <a href="/title/conscious">conscious</a> experience. Studying mathematical concepts without somehow implicating the mind would be like studying the notion of property in a world without people.
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The two points on which the two men differ the most seem to be the metaphysical status of mathematics in the world and the…deixis (idea)http://m.everything2.com/user/edibleplastic/writeups/deixisedibleplastichttp://m.everything2.com/user/edibleplastic2002-05-28T20:06:57Z2002-05-28T20:06:57ZAs <a href="/title/tailchaser">tailchaser</a> mentioned, deixis is a type of <a href="/title/reference">reference</a> where the referent can only be understood in the context of the <a href="/title/utterance">utterance</a> because it relies on inherently relative terms. "The <a href="/title/referent">referent</a> is located using the current speech event or one of the participants as <a href="/title/reference+point">reference points</a>" and so in some ways, <a href="/title/you+had+to+be+there">you really had to have been there</a>; otherwise you simply wouldn't be able make the reference.<sup>1</sup>
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Some typical examples of deixis are:
<blockquote>
<a href="/title/I">I</a> don't like it <a href="/title/here">here</a>.<br>
Yeah, Mary was really happy <a href="/title/then">then</a>.<br>
<a href="/title/You">You</a> can return the book over <a href="/title/there">there</a>.
</blockquote>
In each of these cases, the referent of the deictic word would change depending upon where, when, and by whom it was uttered. If the first sentence were uttered by myself in Paris, then 'I' and 'here' would refer to myself and Paris, respectively. It would be different if <a href="/title/Charlie+Brown">Charlie Brown</a> uttered it in the Great Pumpkin Patch. Contrast these sentences with:
<blockquote><!-- close unclosed tag --></blockquote><!-- close unclosed tag --></p>…Hyponymy (idea)http://m.everything2.com/user/edibleplastic/writeups/Hyponymyedibleplastichttp://m.everything2.com/user/edibleplastic2002-05-28T07:50:28Z2002-05-28T07:50:28ZHyponymy is a <a href="/title/sense+relation">sense relation</a> in <a href="/title/semantics">semantics</a> that serves to relate word-concepts in a <a href="/title/hierarchy">hierarchical</a> fashion. Examples are:
<p>
<dd><a href="/title/apple">apple</a>:<a href="/title/fruit">fruit</a></dd>
<dd><a href="/title/car">car</a>:<a href="/title/vehicle">vehicle</a></dd>
<dd><a href="/title/stool">stool</a>:<a href="/title/furntiture">furntiture</a></dd>
<dd><a href="/title/cow">cow</a>:<a href="/title/animal">animal</a></dd>
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The more specific concept is known as the <a href="/title/hyponym">hyponym</a>, and the more general concept is known as the <a href="/title/hypernym">hypernym</a> or <a href="/title/superordinate">superordinate</a>. <em>Apple</em> is the hyponym of <em>fruit</em> and <em>fruit</em> is the superordinate of <em>Apple</em>.
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Typically in semantics we can view things from two points of view, either from the <a href="/title/Extensional">Extensional</a> viewpoint (relating the meanings of words to the outside world) or from the <a href="/title/Intensional">Intensional</a> viewpoint, (relating word <a href="/title/meaning">meaning</a> to <a href="/title/mental">mental</a> concepts). From an extensional view, the superordinate is the <a href="/title/class">class</a> of items that includes the class of hyponyms. If one is the <a href="/title/subset">subset</a> of the other, then they are in a hyponymical relation. By this thinking, if the class of flowers contains the class of daisies then they are in the<!-- close unclosed tag --></p><!-- close unclosed tag --></p><!-- close unclosed tag --></p>…Synonymy (idea)http://m.everything2.com/user/edibleplastic/writeups/Synonymyedibleplastichttp://m.everything2.com/user/edibleplastic2002-05-27T20:17:40Z2002-05-27T20:17:40ZSynonymy is the semantic relation of <a href="/title/sameness">sameness</a>. When two words have the same <a href="/title/meaning">meaning</a>s, we say that they are <a href="/title/synonymous">synonymous</a>. While this is true, simply defining synonymy as sameness is rather unenlightening. Many <a href="/title/linguist">linguist</a>s prefer instead to define it as being "words whose similarities are greater than their differences". While this is a much looser definition, it serves to highlight the fact that it is the <a href="/title/difference">difference</a>s in similar words that makes them interesting. How different can two words be and still be synonymous? Are there types of difference that break synonymy? Are there different kinds of synonymous pairings?
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In general, we can break synonymy down into three <a href="/title/category">categories</a>, varying by <a href="/title/degree">degree</a>.
<p>
<ul>
<li><strong>Absolute Synonymy</strong>
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Two words are defined as being <a href="/title/absolute">absolutely</a> synonymous if they are are <a href="/title/equinormal">equinormal</a> for all <a href="/title/context">contexts</a>. This means that for every context where Word A is perfectly acceptable, Word B is as well. Similarly, whenever<!-- close unclosed tag --></li><!-- close unclosed tag --></ul><!-- close unclosed tag --></p><!-- close unclosed tag --></p>…Meronymy (idea)http://m.everything2.com/user/edibleplastic/writeups/Meronymyedibleplastichttp://m.everything2.com/user/edibleplastic2002-05-27T16:36:33Z2002-05-27T16:36:33ZMeronymy, derived from the root <em>mer-</em> meaning "<a href="/title/part">part</a>" (see <a href="/title/mereology">mereology</a>), is a relation in <a href="/title/semantics">semantics</a> that expresses the <a href="/title/part-whole+relation">part-whole relation</a> that lexical items may have. Examples of this are:
<p>
<dd><a href="/title/finger">finger</a>:<a href="/title/hand">hand</a></dd>
<dd><a href="/title/wall">wall</a>:<a href="/title/house">house</a></dd>
<dd><a href="/title/sleeve">sleeve</a>:<a href="/title/shirt">shirt</a></dd>
<p>
In this relation, the part is known as the <a href="/title/meronym">meronym</a> and the whole is called the <a href="/title/holonym">holonym</a>.
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In theory, the meronymic relation is <a href="/title/transitive">transitive</a>, meaning that if an item is a part of a part, then that first item is part of the larger <a href="/title/whole">whole</a>. For example if John has a <a href="/title/scar">scar</a> on his <a href="/title/elbow">elbow</a>, we know that John has a scar on his <a href="/title/arm">arm</a>. While this holds for many situations, it is certainly not perfect, as we can see in the following example:
<p>There is a wasp on the steering wheel, there is a wasp on the car.
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<p>In this case, the wasp is <em>in</em> car, rather than on it. Meronymy doesn't make any <a href="/title/ontology">ontological</a> claims as to the real transitivity or precision of this relation. We are only concerned<!-- close unclosed tag --></p><!-- close unclosed tag --></p><!-- close unclosed tag --></p><!-- close unclosed tag --></p><!-- close unclosed tag --></p>…Lexical decomposition (idea)http://m.everything2.com/user/edibleplastic/writeups/Lexical+decompositionedibleplastichttp://m.everything2.com/user/edibleplastic2002-05-24T16:00:54Z2002-05-24T16:00:54ZLexical decomposition is the belief that word meanings can be built up compositionally from the meanings of simpler words. In the same way that every number can be expressed as the <a href="/title/Fundamental+theorem+of+arithmetic">sum of several primes</a>, each word in the <a href="/title/lexicon">lexicon</a> would be the result of combining the senses of several <a href="/title/semantic+primes">semantic primes</a>. A word could then be decomposed to reveal its semantic ancestry.
<p>
For example: <a href="/title/Stallion">Stallion</a> = <a href="/title/Horse">Horse</a> + <a href="/title/Male">Male</a>
<p>
In this case, 'stallion' is built up from the more primitive concepts 'horse' and 'male'. The motivation for pursuing lexical decomposition as a means of understanding word <a href="/title/sense">sense</a> has historically been based on the fact that no matter how many different sound combinations we find in a language, it is possible to trace them all back to a <a href="/title/finite">finite</a> and usually small set of <a href="/title/phoneme">phoneme</a>s. In <a href="/title/English">English</a>, for instance, there are approximately 30-50 phonemes which combine to produce every single word in the English language. If we can produce the sound of every<!-- close unclosed tag --></p><!-- close unclosed tag --></p>…