Articles outline topic sentence and closing

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Articles outline topic sentence and closing

Q from 3 and 4 The consequence is outrageous. That is why the paradox is a serious problem. An appropriate reaction to any paradox is to look for some unacceptable assumption made in the apparently convincing argument or else to look for a faulty step in the reasoning. Only very reluctantly would one want to learn to live with the contradiction being true, or ignore the contradiction altogether.

By the way, what this article calls "paradoxes" are called "antinomies" by Quine, Tarski, and some other authors.

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We naturally want our theory of truth not to allow paradoxes. Aristotle offered what most philosophers consider to be a correct, necessary condition for any adequate theory of truth.

A sentence is true if, and only if, what it says is so. In his article, "The Concept of Truth in formalized Languages," Tarski rephrased the idea this way: A true sentence is one which says that the state of affairs is so and so, and the state of affairs indeed is so and so. Before we can say more about the trouble with our theories of truth and reference, it will be helpful to describe the use-mention distinction.

This is the distinction between using a term or sentence and mentioning it. Lassie is a helpful dog, but "Lassie" is a name, not a dog. Placing pairs of quotation marks around a term serves to name or mention it. The use-mention distinction applies to sentences as well as terms.

Similarly, if the same sentence about snow were named not with quotation marks but with the numeral 88 inside a pair of parentheses, then 88 would be true just in case snow is white.

There is still another way to refer to sentences, namely via self-reference.

Articles outline topic sentence and closing

If I say, "This sentence is written in English, and not Italian," then the phrase "This sentence" refers to that sentence. This is all straightforward, and is a well-accepted way of doing naming and referring.

There is another important point to make about the use of quotation marks. It is a remark about sentences. If we have two names with the same denotation, then usually one name can be substituted for the other in a sentence without the newly-produced sentence changing its truth-value.

There are well known exceptions to this substitution principle. For example, suppose this is true: John said, "Mark Twain was not a famous 21st century U. So, in substituting we need to be careful about substituting inside a quoted phrase.

All these remarks about truth, reference, and substitution seem to be straightforward and not troublesome.

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Unfortunately, together they do lead to trouble, and the resolution of the difficulty is still an open problem in philosophical logic. Here is what Tarski is requiring. If we want to build a theory of truth for English, and we want to state the theory using English, then the theory must entail the specific T-sentence: If we want instead to build a theory of truth for German and use English to state the theory, then the theory should, among other things, at least entail the T-sentence: A great many philosophers believe Tarski is correct when he claims his Convention T is a necessary condition on any successful theory of truth for any language.

However, do we want all the T-sentences to be entailed and thus come out true? Probably not the T-sentence for the Liar Sentence. Substituting the latter for L on the right of the above biconditional yields the contradiction: That is the argument of the Liar Paradox, very briefly.

The proof requires the following additional assumptions. Here we quote from Tarski We have implicitly assumed that the language in which the antinomy is constructed contains, in addition to its expressions, also the names of these expressions, as well as semantic terms such as the term "true" referring to sentences of this language; we have also assumed that all sentences which determine the adequate usage of this term can be asserted in the language.

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A language with these properties will be called "semantically closed. We have assumed that in this language the ordinary laws of logic hold. But if so, then one can eventually deduce a contradiction.

This deduction by Tarski is a formal analog of the informal argument of the Liar Paradox. The contradictory result tells us that the argument began with a false assumption.How to use this in a sentence. Example sentences with the word this. this example sentences.

Articles outline topic sentence and closing

Liar Paradox. The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The Classical Liar Sentence is the self-referential sentence. The outline of your paper involves breaking your topic down into an essay introduction, the body paragraphs and the conclusion.

More on this in the next section. When creating the outline, identify the topic sentence for each paragraph, and add the supporting statements, evidence, and your own experiences or reactions to the subject underneath.

The conclusion wraps up your essay, serving as the other bookend in stating and proving your thesis statement. The topic sentence in the example lets the reader know that the paragraph will talk about the expenses of going to college. Immediately following the topic sentence is the first supporting sentence (underlined) and two detail/example sentences.

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