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Saul Kripke provides us with a clear way of how we understand and use names in Naming and Necessity. While this solves the problem of how we attribute and understand proper names an interesting question arises when we look to examine scientific units of measure such as meter, mile kilometer and rates. We can now ask ourselves what is in a measure just as Kripke had asked what is in a name. Is a unit of measure synonymous with all definitions for a unit of measure and how do we understand units of measure when the unit is represented is not one we are familiar with.

". . . using this definition not to give the meaning of what he called the ‘meter’, but to fix the reference. (For such an abstract thing as a unit of length, the notion of reference may be unclear. But let’s suppose it’s clear enough for the present purposes). He uses it to fix a reference.There is a certain length which he wants to mark out. He marks it out by an accidental property, namely that there is a stick of that length."(Kripke, S (1980) Naming And Necessity, Oxford.)

While this provides us with a better understanding of how a meter is fixed to a reference it seems apparently strange that in everyday conversations we are able to so interchangeably use and comprehend large non fixed units of measure. It seems as though the we can interchangeably switch and comprehend large and maybe even previously unknown units of measure in everyday conversation. For example we not be familiar with the unit of length in terms of meter but we may be able to use this effectively in a conversation if we have a reference not to the abstract length of a meter but of a known entity such that a football field is 100 meters long. The question now that we can asked is how do we address the use of measure in everyday language as the use of such seems to go beyond the fixed reference posed by Kripke?

As mentioned, Kripke touches upon this in Naming and Necessity, and Wittgenstein does in Philosophical Investigations. This is also touched upon in the article Wittgenstein on the Standard Metre by W.J. Pollock.

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    The standard of length comes first, then the length of the football field. And by the way, football fields in the USA are one-hundred yards long, not counting the two end zones, which are are each ten yards long. Given that the end zones are part of the field of play, on kickoffs and pass plays, for example, there's a case to be made that football fields are 120 yards long. Note that this example brings up the issue of different sets of units, and therefore the need for unit conversions. – Richard Kayser Aug 14 '16 at 20:31
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    Because of the importance of being able to trace measurement results to standards of measurement, and to be able to intercompare such measurement results across national boundaries for the purposes of trade, research, etc., a great deal of thought and effort has been devoted to developing an internationally-accepted system of units of measurement. See en.wikipedia.org/wiki/International_System_of_Units – Richard Kayser Aug 14 '16 at 22:15
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Unfortunately, we do not have a satisfactory theory of meaning (semantics) of natural languages, i.e. of understanding words, or even of using them (pragmatics). Kripke's causal theory of reference for proper names comes closest to a consensus, but only if it is narrowly restricted to proper names, and even then it is not too close. The alternative theory, that we pick out referents by definite descriptions, still has many supporters, and recent experiments to test folk intuitions on this score were inconclusive. Moreover, the two theories have complementary problems, see Kripke's Revenge by Sider:

Over 100 years ago Frege (1952/1892) pointed out the problem with Millianism: sentences containing co-referential names seem semantically inequivalent... Within the propositionalist tradition, the natural alternative to Millianism is that the semantic content of a name is the same as that of an identifying definite description... But, new linguistic data suggested, knowledge of identifying descriptions is not required for linguistic competence. Moreover, definite descriptions do not fix the referents of names, nor do names behave like descriptions in the scope of modal operators. The data of Kripke et al. is genuinely puzzling. It in no way undermines the old Fregean arguments against Millianism; it simply is new, conflicting data. Thus, many recent theories seek reconciliation, accommodation of both Kripkean and Fregean data.

Kripke's and Putnam's attempts to extend the causal theory to natural kinds (like wood, red, bee, etc.) remain controversial, see e.g. Ben-Yami's Semantics of Kind Terms, and even they did not attempt it for artificial kinds. Scientific units seem to involve aspects common to names, and both kinds.

With old units that predate modern science, like foot or meter, one can imagine some ancient baptism and chains of transmission that led to their adoption and spread before the French Convent ordered physical prototypes to be made. New units however, like joule or ampere, were exclusively specified by definite descriptions, and even with the old ones the Bureau of Weights and Measures consistently moved away from physical prototypes. The meter was not tied to the Paris prototype since 1927, so even Wittgenstein's discussion of it was already moot, let alone Kripke's, and the current description adopted in 1983 is "the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second”.

Definite descriptions allow for more uniformity and precision, and so are preferred in science in "official" capacity. But does it mean that in practice scientists measure distances traveled by light in vacuum when they need to use a meter? Surely not. They use imperfect prototypes produced using perhaps less imperfect prototypes, which may or may not ultimately link to the official standard (this is similar to causal chains but not connecting to a baptism). Casual speakers' connection to the official description is even more tenuous.

Propositional semantic theories, like Frege's or Kripke's, may be looking for theoretical unity where none is to be had. Linguistic practice is heterogenous, with multiple ways to pick up usage. Kids may learn to use "meter" in sentences correctly by mimicking and inferring, without bothering to know what it "looks" like. Another problem is that propositional theories seek to assign meaning and reference to expressions in isolation, whereas indications are that linguistic use is holistic, in addition to opportunistic and eclectic. The use of words is learned from how they combine with other words and/or used in pragmatic situations, not so much from their propositional meaning and/or reference. Some of this is addressed in inferential semantics.

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I haven't read Kripke's Naming & Neccessity, however the linked article quotes Wittgenstein from his Philosophical Investigations:

There is one thing of which one can say neither that it is a metre, and nor that it is not a metre - and that is the standard metre kept in Paris. But this of course is not to ascribe some extraordinary property to it, but only to mark its peculiar role in the language game of of measuring with a metre rule.

It's interesting to see here that Wittgenstein is playing the language game of paradox - neither it is, and nor it is not - but given that Wittgenstein immediately says there is nothing extraordinary in this, we must looking for the obvious.

In this world there is no notion of an absolute length; a length has to be picked out - or named - and we name it as the reference or standard; once this baptism has been done we can go on and measure, or name other lengths as equivalent to this length; one naming begets other names, but these new names are referred to the original naming; though these are new names, they are not new in the originary sense - they are dependents.

Thus, the length of the platinum rod is not metre, because it is the reference metre; any other length will have done.

But having named it the metre, we can go on with this game to measure other lengths; one thing we do not do is measure the reference metre; for obviously it cannot be other than what length it is, the length of the standard metre, what it is identically. It cannot, not be a metre, it is neccessarily a metre.

A different angle to take, is to understand all measures as a form of extension, this goes back to Spinoza, and from him to Descartes. There is a submerged sense of this in physics proper when we consider that in classical mechanics units are called dimensions (ie dimensional analysis), the basic dimensions being mass, length & time; dimension of course is evocative of length, ie extension.

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A little background on metrology (the science of measurement, not weather prediction) first.

Because of the importance of being able to trace measurement results to standards of measurement, and to be able to intercompare such measurement results within and across national boundaries for the purposes of commerce, trade, research, technological advancement, etc., a great deal of time and effort has gone into establishing an internationally-accepted system of units of measurement. See en.wikipedia.org/wiki/International_System_of_Units (SI units) and http://physics.nist.gov/cuu/Units/units.html.

The base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity; the corresponding SI base units are meter, kilogram, second, ampere, kelvin, mole, and candela.

The SI base units are proper names / rigid designators by Kripke’s definition: each base unit refers to the named object in every possible world in which the object exists. For example:

  • The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

  • The kilogram is the mass of the international prototype of the kilogram (IPK), which is made of a platinum-iridium alloy machined into a right-circular cylinder (height = diameter) of 39.17 mm to minimize its surface area. The IPK is stored at the International Bureau of Weights and Measures on the outskirts of Paris.

  • The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom at 0 K.

The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed.

Values of physical quantities are determined by comparing the objects to physical standards (e.g., atomic clocks in the case of time) that have been developed by national metrology institutes around the world to realize the SI base units.

Values of physical quantities are not proper names: the results of measurements of these values differ from laboratory to laboratory in our world, not to mention what might happen in every possible world in which the relevant objects exist.

With regard to other aspects of the question:

  • While the length of a football field is not the SI base unit of length, someone, using a relatively inaccurate (but deemed adequate for the purpose) realization of the meter -- such as a calibrated tape measure -- at some point staked out a field nominally 100 meters long (nominally because all measurement results have associated uncertainties).

  • No one needs to be familiar with the meter, as I have presented it, to comprehend, through experience, the length of a football field. Is it really strange that people are able to interchangeably use and comprehend “non fixed units” of measure in everyday conversations under circumstances such as these?

A few final thoughts on "comprehension" of “non fixed units”:

  • The values of physical quantities can range over many orders of magnitude. For example, the diameter of a proton is 1.75 x 10-15 m while the diameter of the observable universe is 8.8 x 1026 m. That’s more than 41 orders of magnitude!

  • It’s not obvious that anyone, lacking direct experience, can comprehend such small and large lengths. Even so, people who work with such lengths on a regular basis can readily converse because they share a common vocabulary. And as part of that, it certainly helps, as you say in your question, that they are not thinking in terms of abstract lengths, but in terms of “known entities” such as protons and observable universes.

  • note the anthropocentric origin of the entire set of language. like even the unit: "orders of magnitude". the logarithmic quality makes more universal sense, but who says that 'orders of magnitude' be the base 10 logarithm? why not base 2? or base e? maybe it should be 140 orders of magnitude difference 2<sup>-50</sup> and 2<sup>90</sup>. – robert bristow-johnson Sep 23 '16 at 6:19

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