Reference-fixing

The field- and time-dependent cluster operator is defined as T t, ) = nd HF) is the SCF wavefunction of the unperturbed molecule. By keeping the Hartree-Fock reference fixed in the presence of the external perturbation, a two step approach, which would introduce into the coupled cluster wavefunction an artificial pole structure form the response of the Hartree Fock orbitals, is circumvented. The quasienergy W and the time-dependent coupled cluster equations are determined by projecting the time-dependent Schrodinger equation onto the Hartree-Fock reference and onto the bra states (HF f[[exp(—T) ... 

In general, a thermometer is called primary if a theoretical reliable relation exists between a measured quantity (e.g. p in constant volume gas thermometer) and the temperature T. The realization and use of a primary thermometer are extremely difficult tasks reserved to metrological institutes. These difficulties have led to the definition of a practical temperature scale, mainly based on reference fixed points, which mimics, as well as possible, the thermodynamic temperature scale, but is easier to realize and disseminate. The main characteristics of a practical temperature scale are both a good reproducibility and a deviation from the thermodynamic temperature T which can be represented by a smooth function of T. In fact, if the deviation function is not smooth, the use of the practical scale would produce steps in the measured quantities as function of T, using the practical scale. The latter is based on ... 

The idea that certain physical states could reproduce always the same temperature rises in the second half of seventeenth century (Hooke, 1664 Renaldini, 1694, see e.g. ref. [8]). Intuitions of this idea can be also found in Aristotele and Galeno. Nowadays, the importance of the control of the thermometric calibration is underestimated and the use of reference fixed points is usually limited to metrological laboratories. 

In 1968, an international agreement was reached about the definition of an official (practical) scale of temperature for T> 14 K. This temperature scale IPTS-68, corrected in 1975 [11], was defined by reference fixed points given by transitions of pure substances. To extend the low-temperature range of IPTS-68, the EPT 76 [12-13] gave nine reference temperatures defined by phase transition of pure substances in particular the superconductive transition (between 0.5 and 9K) of five pure metals was introduced. Moreover,... 

It is worth remarking that, in fact, such devices do not supply true reference fixed points as explained in Section 8.2, since these devices were calibrated one by one against primary thermometers. Their accuracy is 0.1-0.2 mK. 

Last, we wish to remind that thermal cycling may spoil the thermometer calibration. The frequent check of the calibration by means of reference fixed points (see Section 8.5) is advisable. 

The diffusion coefficient in Eq. 5.50 actually is a composite of diffusion tensor elements defined in a frame of reference fixed in the solvent phase (i.e., water). For a discussion of the ways in which the diffusion coefficient can be defined, see J. B. Brady, Reference frames and diffusion coefficients, Am. J. Sci. 275 954 (1975). 

InfaUibilism is not particularly popular these days. It is important to warn therefore that this infallibilism is very restricted. First, it holds only for the reference-fixing sentences, which is a very narrow class. Second, it is formulated with respect to justification conditions rather than justifications. As I noted in the previous chapter, the justification procedures may be improperly executed. As a result, our judgements whether an infallible justification condition is satisfied are themselves fallible. A daltonian knows very well what procedures he has to use decide whether something is red or green. But his condition prevents him from... 

We have finally arrived at Step 1, the selection of the reference-fixing sentences. Two quick remarks before we face the main question. One, all of these remarks are about sentence types, not about tokens. The properties of sentence tokens which do not result from belonging to a particular type have no bearing on reference. Two, we should not make much of the distinction between sentence and sentences. If reference is fixed by a complicated conjunctive justification condition, we are free to treat it either as the justification condition of one long conjunctive reference-fixing sentence, or the conjunction of the justification conditions of several separate sentences. 

The unclarity of the reference-fixing mechanism of some concepts is probably an unavoidable consequence of the way conceptual systems develop. We often encounter new things for which the current system has no nice niche. It would be uneconomical to completely redesign the system whenever this happens. So we just tinker a bit. We decide which concept to apply, ignoring that this will complicate the reference-fixing mechanism. After a long series of ad hoc decisions we get patched-... 

It follows from this rudimentary account that we can have analytic sentences only in so far as the reference-fixing justification conditions are clear. If there are many sentences in which a word occurs, but it is unclear the justification conditions of which sentences bear on the reference of a word, we cannot say any more which sentences containing the word are analytic. Consider electron . This word occurs in a vast number of sentences. Some of them have to do with the experimental techniques which make electrons observable, like cloud-chambers. Most of them are highly theoretical sentences, some of which contradict one another - for physicists have said contradictory things about electrons. It is difficult to pinpoint the sentences whose justification conditions play a part in the fixation of the reference... 

We may now compare this account with the accounts of reference implicit in the major theories of truth. First of all, this account is verificationist. As far as the fixation of reference is concerned, it does not really differ from a verificationist view like Dummetf s. Dummett would probably require though that the reference-fixing justification conditions be fully operational. The major difference concerns what happens after the fixation of reference. Whereas I will use reference to construct genuine, i.e. possibly verification-transcendent truth conditions, a fully-fledged verificationist semantics would construct verification conditions, instead. 

The deflationist would find some points objectionable, but the account can be easily adapted to her needs. The first point is that Step 2 accepts a substantial notion of truth for certain sentences. But this step may be reformulated in this way take the justification conditions of the reference-fixing sentences . In this way the notion of truth can be kept as a thin notion. The second point is that in the disquotation formulae of Step 3 the notion of truth shows up in the parentheses, so truth seems to play an explanatory role in the fixation of reference. A deflationist would refuse that truth can explain anything. Notice, however, that the disquotation formulae do their job even if the parentheses, in which truth is mentioned, are cut off. So the machinery works even if one does not accept a verificationist conception of truth for these sentences and refuses to attribute any role to truth in the determination of reference. If you wish, the internal realist has a choice to be deflationist about truth. Naturally, this does not mean that after these changes the deflationists will automatically subscribe to the present account. They may reject the idea of reference-fixing sentences, or they may reject that for these sentences truth coincides with justification, or they may favor an account of our linguistic ability that does not mention justification at all. 

To understand this, we must first see in more detail how the reference-fixing justification conditions depend on the features of the human mind. Remember the operationality constraint mentioned couple of pages back a reference-fixing justification condition is either operational, or if it is not, there must be operational... 

This is important, because it is in virtue of this that the Tarskian mechanism yields truth conditions which may go beyond verification conditions. Let us see an example of how this happens. Suppose a physicist derives from his theory that a certain elementary particle p has a certain property Q. Suppose further that the justification condition which fixes the reference of includes the description of an elaborate experimental set-up. Suppose that the reference-fixing justification condition for g includes the description of a completely different sort of... 

It becomes clear now why my account is neither circular nor incoherent. It would be circular only if the truth conditions used in Step 2 were the same as the ones which result from Step 4, if Step 2 presupposed Step 4. But this not the case. First, because Step 2 deals with the truth conditions of a small set of sentences, the reference-fixing sentences, whereas Step 4 applies to all sentences. Second, Step 2 identifies the truth conditions it mentions with justification conditions, which renders this use of truth condition independent of the one resulting from Step 4. 

In a frame of reference fixed with respect to an oblique shock, let ip be the angle between the approach velocity and the shock plane and 3 be the deflection angle of the flow upon passage through the shock, as illustrated in Figure 6.9 for the wave labeled incident shock. For an ideal gas with constant specific heats, it is then readily shown [94] that in the adopted frame,... 

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