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A '''free logic''' is a [[logic]] with fewer [[existential clause|existential]] presuppositions than classical logic. Free logics may allow for [[Term (first-order logic)|terms]] that do not denote any object. Free logics may also allow [[structure (mathematical logic)|models]] that have an [[empty domain]]. A free logic with the latter property is an '''inclusive logic'''.
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you enjoyed this write-up and you would like to get more details relating to [http://www.youtube.com/watch?v=90z1mmiwNS8 Best Dentists in DC] kindly visit our web site.
 
== Explanation ==
 
In [[classical logic]] there are theorems that clearly presuppose that there is something in the [[domain of discourse]]. Consider the following classically valid theorems.
 
:1. <math> \forall xA \rightarrow \exists xA</math>
:2. <math> \forall xA \rightarrow A(r/x)</math> (where r does not occur free for x in A and A(r/x) is the result of substituting r for all free occurrences of x in A)
:3. <math> Ar \rightarrow \exists xAx</math> (where r does not occur free for x in A)
 
A valid scheme in the theory of [[First-order_logic#Equality_and_its_axioms|equality]] which exhibits the same feature is
 
:4. <math> \forall x(Fx \rightarrow Gx) \land \exists xFx \rightarrow \exists x(Fx \land Gx)</math>
 
Informally, if F is '=y', G is 'is Pegasus', and we substitute 'Pegasus' for y, then (4) appears to allow us to infer from 'everything identical with Pegasus is Pegasus' that something is identical with Pegasus. The problem comes from substituting nondesignating constants for variables:  in fact, we cannot do this in standard formulations of [[first-order logic]], since there are no nondesignating constants.  Classically, ∃x(x=y) is deducible from the open equality axiom y=y by particularization (i.e. (3) above).
 
In free logic, (1) is replaced with
 
:1b. <math> \forall xA \land E!t \rightarrow \exists xA</math>, where E! is an existence predicate (in some but not all formulations of free logic, E!t can be defined as &exist;y(y=t))
 
Similar modifications are made to other theorems with existential import (e.g. the Rule of Particularization becomes (Ar → (E!r → ∃xAx)).
 
[[Axiom]]atizations of free-logic are given in [[Jaakko Hintikka|Hintikka]] (1959),<ref>Jaako Hintikka (1959). Existential Presuppositions and Existential Commitments. Journal of Philosophy 56 (3):125-137.</ref> [[Karel Lambert|Lambert]] (1967), [[Theodore Hailperin|Hailperin]] (1957), and [[Richard L. Mendelsohn|Mendelsohn]] (1989).
 
==Interpretation==
 
[[Karel Lambert]] wrote in 1967:<ref>''Free Logic and the Concept of Existence'' by Karel Lambert, Notre Dame Journal of Formal Logic, V.III, numbers 1 and 2, April 1967</ref>
 
"In fact, one may regard free logic... literally as a theory about singular existence, in the sense that it lays down certain minimum conditions for that concept."  The question that concerned the rest of his paper was then a description of the theory, and to inquire whether it gives a necessary and sufficient condition for existence statements.
 
Lambert notes the irony in that [[Willard Van Orman Quine]] so vigorously defended a form of logic that only accommodates his famous dictum, "To be is to be the value of a variable," when the logic is supplemented with [[Bertrand Russell|Russellian]] assumptions of [[Theory of Descriptions|description theory]]. He criticizes this approach because it puts too much ideology into a logic, which is supposed to be philosophically neutral.  Rather, he points out, not only does free logic provide for Quine's criterion—it even proves it!  This is done by brute force, though, since he takes as axioms <math> \exists xFx \rightarrow (\exists x(E!Fx))</math> and <math>Fy \rightarrow (E!y \rightarrow \exists xFx)</math>, which neatly formalizes Quine's dictum. So, Lambert argues, to reject his construction of free logic requires you to reject Quine's philosophy, which requires some argument and also means that whatever logic you develop is always accompanied by the stipulation that you must reject Quine to accept the logic. Likewise, if you reject Quine then you must reject free logic. This amounts to the contribution that free logic makes to ontology.
 
The point of free logic, though, is to have a formalism that implies no particular ontology, but that merely makes an interpretation of Quine both formally possible and simple.  An advantage of this is that formalizing theories of singular existence in free logic brings out their implications for easy analysis. Lambert takes the example of the theory proposed by [[Wesley C. Salmon]] and [[George Nahknikian]],<ref>George Nahknikian and Wesley C. Salmon, "'Exists' as a Predicate" ''Philosophical Review'' Vol. 66: 1957 pp. 535-542</ref> which is that to exist is to be self-identical.
 
==See also==
* [[Square of opposition]]
* [[Table of logic symbols]]
 
==References==
 
{{reflist}}
 
* Lambert, Karel, 2003. ''Free logic: Selected essays.'' Cambridge Univ. Press.
*-------, 2001, "Free Logics," in Goble, Lou, ed., ''The Blackwell Guide to Philosophical Logic''. Blackwell.
* ------, 1997. ''Free logics: Their foundations, character, and some applications thereof.'' Sankt Augustin: Academia.
* ------, ed. 1991. ''Philosophical applications of free logic.'' Oxford Univ. Press.
* Morscher, Edgar, and Hieke, Alexander, 2001. ''New essays in free logic.'' Dordrecht: Kluwer.
 
== External links ==
*{{sep entry|logic-free|Free logic|John Nolt}}
 
{{DEFAULTSORT:Free Logic}}
[[Category:Non-classical logic]]

Latest revision as of 18:16, 30 August 2014

It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.

Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.

At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.

Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.

Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.

Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.

Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.

Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.

In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.

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