As a neophyte lingual/semanticist, I may be deep enough in my cups to throw a line or two to start the discussion.

1) Yes, perhaps not loss so much as a conditioned pruning of temporal, cultural and sociological 'richness' embedded in the L2 destination word or symbolic abstraction so that the L2 meaning fits within the context of the L1 user's metaphor.

2) Some might consider the normalized(standardized?) set of grunts and whistles formed with the human respiration apparatus, phonemes, as the basic unit of language with the lexeme as simply a storage container to transport information. As storage, the container is shaped (no generative grammar here!) at the convenience of the sender and which hopefully can be re-rendered into information by the receiver.

Yes, on legacy thought leaders and encyclopedias, but words and phrases are just containers. Sometimes, multi-colored lego blocks that fit nicely, sometimes Russian dolls, and sometimes a categorization (vegetable) is used as a singleton (Eat your vegetables[peas]!). Due to the mobility (migration, adaptation and TV) of language we also have the evil twins, polysemy and cognate.

Maybe, on the mappers of common neural activity. The fMRI activists have quite a bit to say about P600 and N400 signals. Certainly coarse and not 1:1, but perhaps syntactically translingual.

3) Yes [qualified], "nobody believes" is strongly worded. Perhaps, "there is little empirical evidence from experiments or measures that can have been taken from available subjects". Popularist linguists may suggest one or more, adaptive, general function cognition organs that quickly become specialized near-natal.

4) Yes. The grey(gray) area of boundary-value distinction. Real Numbers has "the greatest value less than". Calculus has "approximations" and "limits" to the area under the curve, and Bayesian decision choices have Posterior Likelyhood Distributions.

Survey responses are not precise but may be measured sufficiently close (%error?) to the clustered centroid of a collection to be considered as represented by that centroid value. That don't make it right, distinct or discrete. 

The mistake is to think of the items on a Likert scale as precise mappers. In reality, each maps to the underlying construct in a different way (depending on the strength of the construct they measure and in the subjective distances between the item response categories involved). What gives the scale its strength (rather like what gives neurons their ability to reason) is that as you sum responses into a Likert scale, the categories tend to take on a smooth distribution which, if the scale is constructed well, will not show evidence of censoring at either extremity (floor and ceiling effects). 

So scale items are a classic case of assembling faillible (and, indeed, flawed) elements into a more robust whole. 

Dear Todd Morris:

Thanks for the reply!

Some comments:

"

1) Yes, perhaps not loss so much as a conditioned pruning of temporal, cultural and sociological 'richness' embedded in the L2 destination word or symbolic abstraction so that the L2 meaning fits within the context of the L1 user's metaphor."

it's been a long, long time since I studied applied linguistics and second-language acquisition, so I could be misremembering, but aren't such notations used to indicate...well, second language acquisition (or was it secondary language in for those raised as bilingual in an environment in which L1 is the dominant language?)? In any event, I'm not sure how it applies. For example, there are no native speakers of most of the languages I read, and haven't been for hundreds or thousands of years. Also, typological research (Greenberg, Comrie, Haiman, etc.) and the rather dismal failure of generative linguistics suffices to show that such mappings are an intrinsic property of language. And if we think otherwise, we need only go to a dictionary to see how words are defined in one language by other words, and how there is no 1-to-1 mapping from such definitions from one language to another.

"2) Some might consider the normalized(standardized?) set of grunts and whistles formed with the human respiration apparatus, phonemes, as the basic unit of language with the lexeme as simply a storage container to transport information"

Sure, one can consider the physiological constraints on phonemic production as boundary conditions for the possibility of units; not, however, semantic/conceptual units. Phonemes do not, in general, encode information. There are lots of exceptions, but these are never relevant for Likert-type response data, as responses to such items (however they are delivered- paper, online survey, verbally, etc.) require the simultaneous conceptualization of the continuum as well as and inexorably bound with the individual possible responses. We are well beyond phonemes here.

"3) Yes [qualified], "nobody believes" is strongly worded. Perhaps, "there is little empirical evidence from experiments or measures that can have been taken from available subjects". Popularist linguists may suggest one or more, adaptive, general function cognition organs that quickly become specialized near-natal."

Linguists don't conduct neuroscience experiments. Nor do they work with computational neuronal modelling, neuroimaging data (except as it is presented in more general cognitive science research), etc. True, we neuroscientists don't work with language in the ways that linguists do and are at a disadvantage here (Jackendoff's rather thorough critiques of my first PI demonstrate this nicely). However, Chomsky, Pinker, Jackendoff, Sag, Pollard, and all of those who have posited a language module, language faculty, organ, etc., are neither talking about a single brain area (they disagree with the domain-general linguists, but not in thinking the brain contains some neuroanatomical region that is responsible for only and for all language processing, production etc.). Also, both "grandmother neurons" and "concept neurons" are quite literally intended to refer to SINGLE NEURONS. Hence, even were the language faculty a clearly identifiable brain region, it wouldn't matter in the slightest.

"4) Yes. The grey(gray) area of boundary-value distinction. Real Numbers has "the greatest value less than". Calculus has "approximations" and "limits" to the area under the curve, and Bayesian decision choices have Posterior Likelyhood Distributions."

Calculus doesn't deal with approximations. That's one of the most fundamental aspects of it: we deal with limits at infinity because we deal with infinite precision. A convergent series equals the value it converges to, precisely because we take infinitely many terms. A definite integral gives the exact "amount" of some "spatial region" (usually in Rn but obviously integration extend both to the complex plane and to non-Euclidean spaces). Also, Bayesians don't have anything without calculus, nor do frequentists. Distributions are "areas under curves", defined (usually) over a normed interval. But I don't see how the ways in which curves in some dimensional space will behave locally linear providing that one "zooms in" close enough, or the use of decision theory (Bayesian or no) has to do with treating semantic content as a single, infinitely precise value utterly devoid of the very semantic content it is intended to be a measure of.

"Survey responses are not precise but may be measured sufficiently close (%error?) ..."

Here you cut to the heart of the matter. Most of the statistical methods used in Likert-type response data were developed to deal with measurement error. That is, we use some instrument like a scale or radar and we know that our measurement will be off. We've been dealing with this since before Kepler developed his laws using an ad hoc approach to measurement error. When we treat linguistic responses as corresponding to some value, what can we even begin to say about the "error"? Nothing. Every individual who responds is forced to select a value that is treated purely formally but is quintessentially functional/semantic. There's no "error", because there's no measurement. Measures always involve error. What makes them measures is that we are able to deal with this error because we can quantify it in some way. Here, we don't quantify it- we multiply it via combining the individually (unknown) error/information loss per item per participant into one giant summation of errors we treat as infinitely precise.

Thanks again!

-Andrew

The following article reviews the literature concerning equivalence of scales between source and target language.

Spector, P. E., Liu, C., and Sanchez, J. I. (2015). Methodological and substantive issues in conducting multinational and cross-cultural research. Annual Review of Organizational Psychology and Organizational Behavior, 2, 101-131.

The problem is that it isn't really just an issue of a problem between source and target language. It is quite literally a problem of fundamental error/information loss for every item for every participant, because there is no way of approximating the quantification of measurement error when one forces a conceptual response to be utterly devoid of semantic content. I've quite literally scrolled through the scans from an fMRI study in progress (before the fancy statistical image processing produces what is supposed to indicate significant activation is added in) and seen participants neural responses differ when it comes to the same question within half hour and hour blocks.

So, again, what is the theoretical justification for pretending that a theory of measurement (which we have largely abandoned in terms of the original justification; hence "Likert-type" and the general lack of research justifying Likert over Thurstone, let alone any general theoretical bases for treating conceptual responses as purely formal) actually measures what it is claimed to? All measurements are imperfect. That's a given. What's important is the capacity to quantify error. We don't have the capacity to approach the nature of "error" in this case, so instead we simply pretend our "measurement" is infinitely precise and all statistical analyses performed are essentially summations of unknown quantities of error for every item from every participant. Unless, of course, we have some theoretical justification. Hence my question. But referring to the potential to vaguely map source constructions to target constructions in translation isn't, so far as I can tell, anything remotely resembling theoretical justification. 

     I don't have the expertise in linguistics or even measurement theory to answer your question in the terms it was framed in, but as a behavioral scientist, I have long thought that measures with vague verbal labels for response options produce results that include a huge amount of error from the variation in meaning that individuals attribute to the labels.  This is especially true in clinical psychology (my field), because we are often asking questions about the relative severity of symptoms, and it may be  unclear to many whether the question is about severity relative to one's own experience or severity relative to the entire range of the experience for all. 

    For example, in a measure that is widely used to study and follow patients with PTSD, respondents are asked to answer "how bothered" they have been during the past month by symptoms such as "Repeated, disturbing, and unwanted memories of the stressful experience?" with response options of not at all, a little bit, moderately, quite a bit, and extremely.  Setting aside for the moment that the average person cannot accurately recall emotional experiences up to a month in the past, that the average person does not think about their distress in terms such as "moderately" and "extremely", and that the degree of being bothered by a symptom is a muddy way to quantify severity, it is not at all clear what the referent is for the labels.  Is the "being bothered" moderate or extreme relative to one's usual experience?  Relative to others' experience?  If individuals interpret the question differently, then they aren't referring to the same construct.  They may also be inaccurate in observing and evaluating their own typical emotional experience or others' typical emotional experience. 

     None of these problems are the result of the Likert scale itself, I think.  It is possible to use anchors for the response options that are anchored with terms that are clear, unambiguous as to referents, and understood the same way by virtually all.  For symptoms, labels that refer to frequency grounded in time seem to meet those criteria, e.g., "Once in the past week" "once every day" "more than once a day".  Typically, though, Likert scales use vague verbal labels that create the kinds of problems described above.

Hmmm, I used L1 and L2 to identify the Source and Destination languages of the translation problem. Language1 may or may not be native.

A.Messing, a point to consider regarding generalizations; many of the foundational mathematical "truths" (sins of the father) for dealing with large numbers were discovered/invented BY HAND, 5-600 years ago.

Dear Eve Carison:

Thanks for the thoughtful and thought-provoking response! There is one thing you mentioned I feel is important to respond to::

"None of these problems are the result of the Likert scale itself, I think"

I agree completely. So much so, in fact, that despite restrictive approach I'm taking to the treatment of linguistic or semantic information using numbers (namely, I'm only considering scales), I've opted for idiomatic nomenclature: Instead of referring to Likert-scales or even Likert-type scales, I define what I call "Likert-Like" response data.

I do this not only because some of the measures/scales I consider might not be called Likert-scales (or Likert-type scales), but also to better identify certain causes underlying the kind of issues you raised. Because a central component of my argument is that we can't generally hope to capture conceptual/semantic responses by treating them as numbers (even if we do so in terms of frequencies), the only way I could provide a formal/mathematical demonstration that this is so is by proving myself wrong (if I can demonstrate, mathematically, an unacceptable level of error inherent in such treatments, then I've demonstrated that the uncertainty in the data is quantifiable; as quantifying error is the heart of measurement theory and much of the sciences in general, if I could do this I'd be doing it rather than saying it can't be done). So I am relying on several different lines of evidence instead of a purely mathematical one.

One such line of evidence comes from comparing the results of studies using Likert-like response data and analyses of questionnaires/diagnostic tools relying on these. In particular, there are "Likert-like" response data that actually address empirical phenomena. For example, several diagnostic tools used in the medical sciences use instruments that require patients to indicate the frequency of some (theoretically) objective phenomenon (e.g., number of stomach aches, difficulty maintaining or attaining an erection, etc.). Then there are scales/instruments/etc., that use Likert-like items to measure subjective experiences, but experiences that can be at least to some extent investigated/tested empirically. For example, pain intensity scales, scales in sensory research, etc. It can be shown that across sciences Likert-like response data that can be empirically tested becomes increasingly problematic in numerous ways as responses involve increasingly greater subjective. So, for example, it's well-established in fields from marketing to augmented cognition

that ratings of sensory data

1) vary by modality

2) vary by intensity (i.e., participants don't rate higher sensory stimuli the way they do low)

3) clearly are not ratio or interval data (or, to the extent papers like "Nominal, Ordinal, Interval, and Ratio Typologies are Misleading" are correct, clearly can't be treated using the kinds of statistical tests generally associated with such data types)

&

4) vary in how an individual's response to the same question/item itself varies (i.e., some people are more consistent than others when rating the same experience or some aspect of it).

I've long felt that the dominance psychiatrists have over clinical psychologists or even neurologists when it comes to everything from prescribing medications to determining by what criteria which mental disorders are defined by. In fact, before the DSM-III, there wasn't anything remotely regarded as a universal manual of mental disorders and their symptoms, and one of the reasons for the emergence of the DSM-III as such a work was to justify the superior competency of psychiatrists by defining mental disorders as discrete pathologies requiring medical expertise (I started my undergrad career with the intent of becoming a clinical psychologist).

Yet, 30 years later, the research that was supposed to reveal a physiological basis for this assumption of discrete pathologies has, instead, shown an incredible degree of overlap in terms of comorbidity, neural correlates, and even the efficacy of medical treatments that "shouldn't" work because they don't treat the hypothesized pathology (which, apparently, doesn't provide evidence for a more nuanced understanding of mental disorders than the biomedical model so long as one calls such treatments "atypical").

However, while even hallucinations and other phenomena one would imagine can't be related to/caused by something like sociological variables (although this is in fact not true), mental disorders are rarely if ever simply constructs defined into existence wholly by their inclusion in a diagnostic manual (MPD/DID is the only partial exception I can think of). The fact that it is normative in certain cultures to experience visual and/or auditory hallucinations of recently deceased loved ones doesn't make hallucinations in general a socio-cultural construct, and regardless of whether or not experiences of depression are diagnosed with X mood disorder as opposed to Y, depressive symptoms remain more easily defined than do e.g., measures of religiosity or many other nebulous constructs investigated in the social & behavioral sciences.

Thus in general, the more we have defined into existence the very constructs we seek to measure, the easier it becomes to develop and "validate" some way of measuring them that renders impossible any method of determining WHAT we are actually measuring, let alone quantifying the error involves in the means by which we do so.

Dear Todd Morris:

"many of the foundational mathematical "truths" (sins of the father) for dealing with large numbers were discovered/invented BY HAND, 5-600 years ago."

One of the reasons this project has taken longer than it should is due to my tendency to include within any treatment of some topic an unnecessarily involved, overly detailed description of its history. When I started my first draft of the paper, I had to stop because I'd written a dozen or more pages and had yet to get past Galton, Pearson, & Edgeworth. When I started my second draft, I got as far as Kepler (who died long before Galton). And when I say draft, I do mean draft (I included notes to myself and incomplete in-text citations for my use). This is probably as close as I will get to being able to justify the time wasted on such matters, so forgive my leaping upon this as an opportunity to do just that by quoting from my second incomplete “draft” and my current third draft.

From the current draft:

“It is worth recalling a remark that Poincaré attributed to his friend Gabriel Lippmann, concerning the “law of errors” (“loi des erreurs”):

‘Elle ne s'obtient pas par des déductions rigoureuses; plus d'une démonstration qu'on a voulu en donner est grossière, entre autres celle qui s'appuie sur l'affirmation que la probabilité des écarts est proportionnelle aux écarts. Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s'imaginent que c'est un théorème de mathématiques, et les mathématiciens que c'est un fait expérimental.' (Poincaré, 1912)

This was long before a series of papers starting with Box (1954) and becoming increasingly more devastating by showing problems that could result even from sampling from normal distributions, how arbitrarily small departures from normality could seriously bias all the most commonly used statistical methods, etc. (Wilcox, 2010; Wilcox, 2012).”

Poincaré’s quip about the circular reasoning by scientists/experimenters, who believed in the normal law of errors because they “believed it to be a mathematical theorem”, and mathematicians, who thought “it [to be] an experimental fact”, is hardly over a century old, yet it post-dates the development of both the central limit theorem and least-squares method developed in particular by Laplace, Legendre, Gauss, Poisson, & Dirichlet. Copernicus, Kepler, Galileo, Newton, etc., didn’t have any of the foundational truths for dealing with large numbers, or if they did then we have very different understandings of what the various “laws” of large numbers are.

From the second draft:

"It is true that, despite the relatively advanced mathematics and fledgling statistics employed by natural philosophers from the Greeks to Kepler nonetheless lacked any sort of coherent probabilistic error theory (Hald, 2003). Yet the novel (if ad hoc) methods employed by Tycho Brahe, Kepler, Galileo Galilei were not merely mathematical advancements but scientific. For the Greeks and their Roman-Hellenistic intellectual descendants, both geometry and the planetary bodies were intricately tied to cultic practice, mysticism, and a variety of elements from religious life in antiquity. And in many a text on mathematics or mathematics and “science” in antiquity, too often are the mystical and magical elements purged from the accounts of the heights of classical learning. Pythagoras, the legendary Greek mathematician, was widely regarded as a mystic, even a magician (Dickie, 2001). Indeed, the very word for mathematician in Classical and Hellenistic Greek, μαθηματικός, also meant “astrologer” or “astronomer”, even “magician” (LSJ; see also Dickie, 2003). Tacitus (Annals 12.51) tells us that the senate expelled astrologers, or mathematici, from Italy. Suetonius’ report is worse: he informs us that the emperor Vitellius executed mathematici on accusation alone, for “nullis tamen infensior quam uernaculis et mathematicis”. Even among the learned, it seems that the mathematici were not regarded as the scientists and mathematicians some rather Romantic modern accounts (see esp. Carrier, 2008) seem to think they were. Sextus Empiricus, for example, often held up as an exemplar of scientific learning during the Roman Empire, composed the polemical work Against the Mathemticians (Adversus Mathematicos). From the Pythagoreans and Pre-Socratics to the Neo-Platonists and Neo-Pythagoreans, astronomy was heavily religious and indistinguishable from astrology, geometry was sacred, and mathematics was a craft of mystics and sorcerers (Collins, 2008; Dickie, 2003; Thomas, 2004; Eitrem, 1991; Phillips, 1991; Riemer, 2007). An interesting partial exception to the mystic astronomer/mathematician is Aristotle, whose account of the heavens is no less religious but unlike those who contributed to ancient astronomy, Aristotle’s essential belief about the celestial sphere is that it is beyond our knowledge (Falcon, 2005)…

Nor were early modern astronomers immune to mysticism: Kepler’s polemical responses to Fludd’s mystical writings contained no small amount of a superiority based upon a superior mystical understanding of the cosmos (Westman, 1984). Yet there is an essential difference, and one which is most important of all astronomical research of this period. The source for Kepler’s whole corpus Harmonicae was not mere pictorial representations and various borrowings from Classical and Hellenistic mysticism: “in extremis planetarum motibus proprijs, secundum certas ab Astronomia demonstratus mensuras inesse demonstravi.”

Thanks to Brahe’s help, vast amount of observational data, and no small amount of novel mathematical methods to account for variance from measurement error, Kepler had at his disposal all the “measurements” he could wish for. Yet rather than force the data to fit his various religious and mystical/philosophical biases, he put first and foremost a sound basis for any and all hypotheses regarding astronomy, and chided any would-be astronomer who would take excessive liberties, hypothesizing beyond what was allowed by probable causes and scientifically established principles: “Non enim mera debet esse licentia Astronomis, fingendi quidlibet sine ratione; quin oportet ut etiam causas reddere possis probabiles Hypothesium tuarum, quas pro veris Apparentiarum causis venditas, et sic Astronomiae tuae principia prius in altiori scientia.'"

5-600 years ago we knew almost nothing about probability or anything that could be called a kind of statistics: “What is widely regarded as the first printed work in probability theory was a fifteen-page tract in Latin by Christian Huygens, appended to a mathematics text published by Frans van Schooten in Leiden in 1657" (p. 39 of Stigler's Statistics on the Table: The History of Statistical Concepts and Methods). Outside of astronomy, probability was almost entirely rather scattered work on chances involved in games and gambling (by Cardano, Pascal, etc.), and as Hald points out (A History of Probability and their Applications before 1750), “[b]efore the Renaissance, probability was nonmathematical.” It wasn’t until the 1700s that we begin to find “laws” of “large numbers” such as those of James Bernoulli, and not until Gauss that we have something resembling a law of errors such that someone like Poincaré even COULD make a comment like that quoted above.

A. Messing;

Ah, the brief but brilliant European polymath era of Liebniz, et al. Something of a candle in a cave for periods of enlightenment, very much a punctuated equilibria. I was thinking of the earlier geometric roots[sic] of the Mean Value Theorem and other infinite series approximation methods contributed by Parameshvara and his cohorts of the Kerala school. ( Has anyone found or contributed work on temporal and spatial tracing of causal factors for these aberrant breakouts of intellect?) 

If my wanderings could be said to have had a point it would be, the basis for current handling of large groups of numbers, and terminal factors of individual small (infinitely small?) measures, is founded upon manual methods developed to annotate 'things which we know must be, but are really too tedious to describe.' 

That, unfortunately, sounds to me like a belief system.

http://www.blackwellpublishing.com/ridley/classictexts/eldredge.pdf

In response to your response... as a behavioral scientist who studies responses to trauma, I'm not sure I'd agree that an experience like pain is very much more rooted in "something objective" or can be studied empirically any better than something like the symptoms of DID.  In fact, pain can be extremely subjective, and if you use a measure such as the duration of tolerance for holding one's hand in ice water, people's experience of what is painful and what is unbearably painful varies greatly.  I have not looked closely at the literature, but I imagine that pain experience is greatly affected by emotions, so that negative emotions and pain are synergistic.  In contrast, while a very superficial conceptualization of DID may make it seem as if it is wholly constructed, there is increasing evidence that dissociative states experienced by people diagnosed with DID can be measured "objectively".  E.g., see attached link

While some things are certainly MUCH harder to measure than others (and I'd say both pain and dissociative states are hard to measure), the bottom line is that we NEED to measure some things in order to treat them.  That brings us back to Likert scales with vague, verbal labels.  The precision of measurement of a variable like pain is going to be greatly compromised by use of vague verbal response options labels such as "moderately" or "extremely," and we ought to use other options whenever possible.

Article Opposite brain emotion-regulation patterns in identity state...

Dear Eve Carison:

"In response to your response... as a behavioral scientist who studies responses to trauma, I'm not sure I'd agree that an experience like pain is very much more rooted in "something objective" or can be studied empirically any better than something like the symptoms of DID."

In your statement you refer to 'the symptoms of DID". Pain is a symptom. Doesn't it logically hold that measures for such a symptom would be more easily measured than diagnoses which required the assessment of multiple such diagnoses (if one assumes that "pain" is the kind of symptom that one must assess to diagnose a mental disorder, rather than in general far more easily assessed, rather than that even the assessment of most diagnoses involved in mental disorders are even harder to measure)?

Pain is a subjective experience. DID is a diagnoses, and by definition cannot be measured (one is either is diagnosed with DID and properly so, or not). To the extent there exists a diagnosis DID apart from a psychiatric & psychosocial construct, it is a diagnoses, and therefore requires measures in order to determine whether it applies; it cannot be measured as such or it isn't a diagnosis.

Dare I dilute this interchange with questions instead of answers? I suppose it falls under "any and all input," and I cannot think of a more esteemed readily available audience -- particularly Mr. Messing himself.

On the typical issues related to Likert or Likert-esque data (e.g. ordinal values treated as interval, lexical transferability, etc.), I offer no constructive input. However, I feel it is important to bring up the issue of central tendency.

That is, not central tendency bias/error -- where respondents are inclined towards centralized responses -- but the concept that mean values expressed on Likert-type response data tend to be centralized due to the issue of truncated variables (i.e. 5 or 7 points with no continuum).

For example, if you administer a 5-point scale to two respondents, the possible number of combinations for them arriving at a combined mean score of 1 or 5 is one. However, the possible number of combinations for them arriving at a combined mean score of 3 is five.

Obviously, if you increase the respondents to three, four, five, etc. the possible number of combinations to reach a combined mean score of 3 grows exponentially; a plethora of combinations is possible with even a few dozen respondents. Yet, the possible number of combinations for arriving at a mean score of 1 or 5 remains stagnant at one.

How do you approach this dilemma when analyzing data? How can you associate a degree of 2 or 4 with more "oneness" and "fiveness" respectively to account for the central tendency of respondents? Forced distribution seems feasible, but the practice of imposing a hypothetical normal distribution curve on data seems to me a sub-optimal and outdated practice.

Obviously, scholars could formulate their scales to account for this dilemma beforehand (e.g. administering Likert-esque questionnaires using fuzzy sets theory), but what about data that has already been retrieved? Entropy?

I hope these questions prove fruitful in encouraging thoughtful debate in this discussion board. I equally hope they do not appear to detract from its purpose.