[Wittrs] Re: Games with Logic and Bachelor

  • From: "J D" <ubersicht@xxxxxxxxx>
  • To: wittrsamr@xxxxxxxxxxxxx
  • Date: Mon, 08 Feb 2010 00:18:49 -0000

SW,

Forgive the telephone format, but it was the easiest way to be clear in what I 
am addressing.


>
> First, I want to thank you for that account of "tautology." I thought it was 
> quite good. I'm not all that convinced that all the issue are gone, however. 
> Here's my difficulty. I'm sure you agree that "tautology" has sense. The 
> basic idea in rhetoric seems to be redundancy ("unsolved mystery"). In math, 
> it appears to be the idea of redundancy on both sides of the equals sign. 
> (a=a). I assume this also means 2+2 = 4+1 is tautological? And in logic, it 
> is simply the idea of circularity in premise and conclusion. But here's the 
> problem:

The claim that mathematical equations express tautologies is most associated 
with logicism, the view that mathematics is derivable from logic.  Such a view 
is found in different forms in Russell and in the Tractatus but it is a view 
the later Wittgenstein rejected.  If you want to still say that mathematical 
equations are tautologies - not in the technical sense but in some as yet 
unspecified non-technical sense - there's nothing to stop you.  But it is 
changing the subject (if the subject were logicism) and muddles various issues 
in logic.

And in logic, tautologies (in the technical sense) are compound sentence, not 
arguments, so talk of premises and conclusions is inappropriate.  Now, any 
logical argument can be transformed into a compound sentence, e.g. with a 
conjunction of premises on one side, the conclusion on the other, and material 
implication between them, but not all tautologies exhibit that form.


> 1. People do extend the idea to definitions. 
> http://www.newworldencyclopedia.org/entry/Tautology "Some people consider 
> definitions to be tautologies. For example, 'bachelor' is defined as 
> 'unmarried male.' 'Bachelor' and 'unmarred male' mean the same thing, so, 
> according at least to this understanding of definitions, defining 'bachelor' 
> as 'unmarried male' does not give us any new information; it merely links 
> together two terms that are identical."

Yes.  If you re=read what I wrote, you'll notice that I acknowledged that 
"tautology" is used more widely than its technical sense in various contexts, 
including by some logicians.


> 2. I'm not sure the idea of an "analytic truth" is superior to the term 
> tautology or tautologous if writing for a multidisciplinary audience. (I'm

I wouldn't claim that one could assume that either would be understood by 
various audiences.  Some audiences, e.g. English majors, might assume the 
rhetorical sense of "tautology", and have no acquaintance with the usage in 
logic.  And note that I've already expressed misgivings about the notion of 
"analytic truth" anyway, so I am certainly not insisting you favor one over the 
other.


> writing a manuscript right now, so I bring it up). Here's why. First, 
> tautology has a wider application (wider audience). Second, the basic idea of

Is it an advantage or a disadvantage that people are familiar with a word if 
they are not actually familiar with the particular way it's being used?  Note 
that "tautology" in rhetoric has pejorative connotations.  Not so in logic.  
Just because people have heard a word before doesn't mean they'll understand it 
without you specifying the particular sense in which it is being used.  And if 
you're having to specify that anyway, then the advantage of them having heard 
the word before doesn't seem to amount to much.

>  tautology -- repetition, circularity -- is present in the definition. Note 
> the structure:
>
> bachelor = 1. adult 2 male. 3 unmarried.

I wouldn't object to calling that a tautology, so long as one were not 
confusing this with the technical sense.  Such a non-technical usage does have 
precedent.

My objection is to just calling the word "bachelor" (or any other word taken in 
isolation) a tautology.  Calling the definition of the word a tautology is a 
common and accepted, albeit non-technical (and in some contexts, misleading) 
usage, but calling the word itself a tautology is just plain wrong.  A word 
alone is not repetitious (except perhaps some compound words) or circular.

And "circular" as applied to definitions, is used pejoratively.  A circular 
definition is one in which the definition includes the word defined or one of 
it's cognates.  That's considered a bad thing.  So if you speak of definitions 
generally exhibiting circularity, you're very likely to be misunderstood.  
Similar considerations apply to calling arguments "circular".

>
> There is nothing in the term that isn't in the definition (in this school-boy 
> sense of the word). So the principle of tautology (or its basic idea) is 
> being used on definitions in the same way it was applied to the logical 
> structure of propositions or used for an equation (or what not). In fact, one 
> might say that the definition above is, in fact, appealing to some sort of 
> logical structure (bachelor = property a b c), from which it finds requisite 
> circularity. Also, I don't think it is a critical part of the family 
> resemblance of "tautology" that circularity in assertion come in the form of 
> sentences or props. That seems to be a sharp boundary that you are observing. 
> (Cf. Marriage is between a husband and wife). My point is that it doesn't 
> seem to stop the use of the ideas.

Whatever one's views on homosexual marriage, polygamy, and so forth, one might 
still have objections to the idea of someone being married to themselves!  A 
definition might not be counted as a sentence and yet might be counted as a 
tautology.  Partly, a definition might be variously called "true" (a connection 
with the technical definition of "tautology" in logic) or at any rate "valid", 
"correct", "accurate", or something similar.  But single words in isolation are 
neither true nor false, neither valid nor invalid, neither correct nor 
incorrect, but only so when they are used.

And using "family resemblance" as an excuse to ignore distinctions that play 
important roles in various discussions suggests that Wittgenstein was 
interested in licensing muddle-headed and misleading talk, a view wholly 
contrary to his life and work.

You've indicated an awareness of the sort of continuous revision to which 
Wittgenstein subjected his work, often replacing one word with another, only 
slightly different, or making a note "not quite right".  He apparently was not 
at all inclined to say, "Well, it's a 'family resemblance' word, so there's 
really nothing wrong with my choice of words here."

>
> When I was in school way back in the 80s, right after the dinosaurs left, I 
> recall quite distinctly hearing tautology in logic and in 'loser contexts." I 
> recall specifically people talking about "bachelor" as both a tautology and 
> an analytic concept. I think I recall professors remarking that Wittgenstein 
> had a peculiar sense of "tautology" as well, but my point here is only to say 
> that other speaking conventions regarding the word seem present.

The definition of the word "bachelor" may be called a tautology.  The word 
itself is not.  A sentence expressing the definition of "bachelor" is commonly 
called an analytic truth.  But again, the word "bachelor" is not.  Perhaps you 
heard people speaking loosely and incorrectly or perhaps your recollection is 
faulty.  The phrase "analytic concept" is sometimes used, e.g. in discussing 
Kant, to discuss a priori categories like space, time, and causality - a topic 
that would take us too far afield.  But if one were to use "analytic concept" 
to characterize any word (or use of a word) that is (or can be) given an 
analytic definition, I see no problem with that.  Except that whether a word 
can be analytically defined is a notoriously open question.  (Actually, any 
word can be given an analytic definition and this may be useful for some 
specific purpose, whether or not - and however much - the analytic definition 
deviates from established usage.)


>
> Lastly, I want to make one thing very clear. The only reason why I used the 
> word "tautology" in prior mails was that I couldn't find the right word for 
> what I meant (and analytic isn't really doing it either). Here's the idea 
> again:

It seems to me that you're talking about words that are analytically defined.

>
> There are some words where their cognition is brain dead. Some words don't 
> actually say anything other than "calculate the definition." Let's call them 
> for right now predicate-calculators. (I'm using predicate instead of 
> definition). The Pope is a "bachelor" only in the sense of a 
> predicate-calculator. A person who has an arterial PH below 7.35 has acidosis 
> only in the sense of a predicate-calculator.


Are you acquainted with the notion of an "operational definition"?  That 
doesn't seem to be too far from what you're talking about and the particular 
word so defined would be called an "operational concept".  Your further remarks 
suggest to me that this may be the expression you're looking for.

And yes, I would agree that the Pope would be counted as a bachelor according 
to what we might call an operational definition of the concept.

>
> However, if one means to say that the person having PH below 7.35 has 
> REQUISITE ACIDITY -- as in, too much acidity in the blood, a value judgment 
> -- as reflected by the measure in service of this idea, the matter is 
> NOT-CIRCULAR (not-tautologous). That is, the person has acidosis NOT AS A 
> PREDICATE-CALCULATOR. Do you see the difference? For the Pope to be a TRUE 
> BACHELOR, we need to see that he is in the service of the same idea that the 
> predicate-calculator is serving. In short, he must be "bacheloristic" in the 
> service of an "adult, unmarried male." Since "adult, unmarried male" does not 
> service his "bacheloristicness," we cannot really apply the 
> predicate-calculator with any meaning here.


I don't think the question of "value judgment" is the issue here and "true 
bachelor" needs unpacking.

But the point you seem to be making is, in the first case, to contrast a test 
whose results satisfy an operational definition and a test whose results 
indicate a medical condition in need of attention.  And in the second case, a 
person who fits an operational definition of a concept and a person who would 
have that concept (not precisified, not operationalized) applied to them by 
everyday language users.

And those two contrasts are both important and legitimate by my lights.  I'm 
not sure if I have you right though.

>
> Did you catch that? If the predicate-calculator isn't in service of the basic 
> idea -- if the predicate-calculator is all alone, so to speak -- there really 
> is no term there at all. Imagine calling the Pope an unmarried male but NOT 
> calling him a "bachelor." If "bachelor"  is a predicate-calculator, that is 
> all that is actually said (when you think about it). For 
> predicate-calculators, the word vanishes.
>

The way you're putting this is muddled and misleading in various ways but if I 
understand you, your point is that the term, once given an operational 
definition, may be used in a given context and for a particular purpose without 
regard to the various concerns, the niceties and nuances, that might arise in 
using the same word in everyday language.

> There are many medical words, I think, that work like this.
>

If I am correct in supposing that the idea your aiming at is that of 
"operational concepts", then that's quite correct.  (You would have better luck 
Googling "operational definition", because "operational concept" is also used 
in a different sense in the military sciences.)

http://en.wikipedia.org/wiki/Operational_definition
http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/res_methd/op_def/op_def_01.html
http://web.utk.edu/~wrobinso/540_lec_opdefs.html
http://www.qualityadvisor.com/sqc/od_what.php

But compare Wittgenstein's remarks on symptoms and criteria in BB and PI.


> "If John is a bachelor, then John is not married."
>
> -- one reply: this is a tautology. A simplified version would be, "If john is 
> not married, then john is not married." No wonder there are no counter 
> examples.

If you are using "tautology in the Tractarian sense, a sense still commonly 
used in logic, then only the properly analyzed sentence is a tautology.  Prior 
to analysis, it is not.  And there's an important reason for heeding this 
distinction.  It enables to be clear about certain things.

Here, the question is whether a particular analysis is correct.  And the point 
of counter-examples is to challenge a proposed analysis.  Assuming that the 
analysis is correct and that therefore the sentence is a tautology and saying, 
"No wonder there are no counter-examples," is blatantly missing the point.

The same sort of "argument" (presupposing the validity of the analysis that is 
in fact being criticized and so presupposing that a given sentence is 
tautologous on that basis) would "disprove" any of the counter-examples one 
might offer.

>
> -- another reply: counter-example is Tiger Woods.

There are a variety of reasons for rejecting such an counter-example, not least 
of which is that if we were to call him a bachelor merely because he was 
behaving like one, we would be completely glossing over the fact that the 
consequences of his actions, if he actually were a bachelor, would be quite 
different.  This is not to say that one could not call married men who don't 
take their vows seriously "bachelors" as a joke.  But while the joke would have 
a point, the point of its being a joke (and not a revision to the definition of 
"bachelor") lies in the fact that it points to how little regard is being shown 
to the very concepts of marriage, of fidelity, of vows.

For it to be more than a joke, all of these other concepts would have to be 
revised as well.  Which is not to say that we coudn't see that happen!  But 
there's a difference between acknowledging the possibility of radical changes 
to our concepts and saying that the standard analysis may not accurately 
reflect our current practices.

The reason the counter-examples of the Pope or men in societies predating the 
institution of marriage cannot be so readily dismissed is that they don't 
obviously conflict with established usage.  While the standard analysis might 
say that cave men are bachelors, that's not actually anything people go around 
saying.  Similarly, people don't go around calling the Pope a bachelor, even 
though the standard analysis (or an operational definition) might support that.

The reasons people would give for objecting to excluding the Pope or men with 
societies without the institution of marriage from being called "bachelors" 
would typically turn on the standard analysis, the dictionary definition.  And 
that's not an unreasonable position: though it is question-begging, the 
boundary between entrenched practice and entrenched definitions isn't 
particularly sharp. And as far as established usage goes, people don't 
typically even consider the question of whether to call cave men or popes 
"bachelors", so there's not a strong precedent either way. The reasons people 
would give for objecting to including Tiger Woods as a bachelor would be much 
more wide-ranging than appeals to dictionary definitions.

Objections to calling Tiger Woods a bachelor would turn on the role this 
concept plays in our lives, our traditions, our moral judgments, our mating 
practices, and so forth.

Incidentally, an alternative to the standard analysis would be to say that a 
bachelor is a male eligible to marry for the first time.  This would already 
address the considerations that lead to adding "adult" and "human" to the 
analysis (small children aren't usually called "bachelors", nor are pets or 
wild animals, though they may be unmarried males), and it would exclude men in 
societies without the institution of marriage, as well as excluding Popes.  It 
also makes clear that a divorcee is not a bachelor (where "unmarried" may or 
may not mean "never married").  Against such an analysis: the expression 
"eligible bachelor" would then be a tautology (in the rhetorical sense, i.e. a 
pleonasm like "unsolved mystery").  But that's not a conclusive argument, since 
we know such pleonasms abound anyway.

>
> The true point is this:
>
> You cannot deploy family resemblance ideas in formal logical statements. What 
> that really says is "If the bearer-John is a sense of "bachelor," then the 
> bearer-John is not a sense of 'married.'  (It doesn't follow). See Tiger.

Wow.  A lot to address here.

1.  You can use words that are subject to vagueness, ambiguity, and so forth in 
the context of formal logic.  You just have to pay attention to what you're 
doing.  That's one reason that, even though the transformations of formal logic 
can be used mechanically, applied logic is an art.
2.  Whether we should use an operational definition/the received analysis of 
"bachelor" was the point under discussion.  Using formal methods might well 
bring out differences between various approaches.
3.  Your objections seem rather hypocritical, given that you raised the use of 
"tautology" and the example of the word "bachelor".
4.  The sentence was hardly a specimen of formal logic anyway.  It was a 
sentence of a form one might find in various informal contexts.
5.  The idea that the sentence "really" says something else is confused.  And 
that it "really" says is something as muddled as what followed...
6.  Equating a bearer with a sense defeats the whole point of the distinction 
between sense and reference.
7.  Calling an instance of a class or an individual to whom a general term is 
applicable and "bearer" runs together the concepts of naming and predication.
8.  The idea that different "bearers" are different senses is utterly confused.
9.  The paraphrase you offerred isn't formal logic.  It isn't plain English 
either.  I don't know what it is and I don't know what possible purpose could 
be served by putting things that way.

JPDeMouy






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