PHL246H1 Lecture Notes - Lecture 5: Rudolf Carnap, Formal Language, If And Only If

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13 Apr 2016

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A, b, c, belong to a. sets, propositions. Pr (a), pr (b) belong to r (numbers, probabilities) Assume we have two names, a, b, and one property/predicate symbol: f. State description: in that case, in that formal language, we can use it to define a state description: a maximal description of each object that the language talks about with respect to every property that the language talks about. Our language talks about two objects and one property. It has to tell us whether a has property f and whether b has property f. either both have it, or a has it, or b has it (subsumed under one option) or neither have it. These are the four possible state descriptions and as a rule of thumb, a state description is a conjunction and the # of conjuncts is determined by the number of names/constants (a and b, hence two conjuncts).

Related Questions

Consider three identical spherical conductors. One conductor,labeled A, is given a
charge of 7mC of type Nell. The charge state of the second andthird conductors, B and C, are unknown. The conductors undergo asequence of 3 contacts that occur ONLY between pairs of conductors.After the contacts, the net charge on each conductor is A: (0.25mCof type Nell), B: (1.875mC of type Nell) and C: (1.875mC of typeNell). Letâs make the assumption that the type Paul charge statecorresponds to an excess of electrons.

Because these three spheres are ______________________ the_______________ can be
freely exchanged between any pair of conductors in contact. Sincethese conductive
spheres all have the same size, when the spheres are placed incontact the ______
_____________ will evenly distribute between the two spheres.Because charge is a
property of particles and the particles can not be destroyed ANDthere is no outside
source of charge, the _______________ charge of the ______________must remain
constant at 4mC of type Nell. Based on this information, we candetermine that the
charge of at least one of B or C must be of type_______________.

To determine the order of contacts we must start from the lastcontact and work our way to the first contact. It is important tonote that because we have no initial charge state information forspheres B and C that we have the ability to make an arbitrarydecision about the initial charge state of these two spheres. Inother words, the charge states of sphere B and C areinterchangeable. Third and last Contact: Because spheres ________and _______ have the same charge we can determine that they were______ in contact. If we look at spheres B and C as the system, wefind that the total charge of the sub system consisting of B and Cwas ______________ of type _________.

Second contact: We can safely assume that A touched either B or Cprior to B and C
being brought into contact. Here we can make the arbitrary choicethat B touched A in the second contact. If this is the case, weknow that the charge of B ___________ it touched C must have been______________ of type __________ because it must have the sameamount and type of charge as the final state of _______. Therefore,at this instant we know that the charge on sphere C was________________ of type ____________________ it touched B.

First contact: Now we have an interesting situation. We find thatthe charge state of
sphere C would be consistent with sphere C being initially____________ and being
placed in contact with _______________ since the charge state of Cis exactly
__________ that of ____________ initially. This would mean that thecharge state of
sphere A after contact with ______ would be _____________ of type__________.
However, we already determined that the __________ charge of thesystem containing sphere _______ and sphere _______ in the secondcontact was ____________ of type __________. The only way this ispossible is if sphere B has a charge of __________ of type____________.

Final Results
The initial charge state of sphere Ais:_________________________________________
The initial charge state of sphere Bis:_________________________________________
The initial charge state of sphere Cis:_________________________________________
In the first contact of sphere ___________ to sphere_________________ how many
electrons were transferred from one sphere to the other?
In the second contact of sphere ___________ to sphere_________________ how many
electrons were transferred from one sphere to the other?
In the third contact of sphere ___________ to sphere_________________ how many
electrons were transferred from one sphere to the other?

PHL246H1 Lecture Notes - Lecture 5: Rudolf Carnap, Formal Language, If And Only If

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