Paper: Evolutionary Psychology and Feminism (David Michael Buss & David P. Schmitt)

Evolutionary Psychology and Feminism 2011

 

Abstract This article provides a historical context of

evolutionary psychology and feminism, and evaluates the

contributions to this special issue of Sex Roles within that

context. We briefly outline the basic tenets of evolutionary

psychology and articulate its meta-theory of the origins of

gender similarities and differences. The article then evaluates

the specific contributions: Sexual Strategies Theory and the

desire for sexual variety; evolved standards of beauty;

hypothesized adaptations to ovulation; the appeal of risk

taking in human mating; understanding the causes of sexual

victimization; and the role of studies of lesbian mate

preferences in evaluating the framework of evolutionary

psychology. Discussion focuses on the importance of social

and cultural context, human behavioral flexibility, and the

evidentiary status of specific evolutionary psychological

hypotheses. We conclude by examining the potential role of

evolutionary psychology in addressing social problems

identified by feminist agendas.

Keywords Evolutionary psychology . Feminism . Sexual

strategies . Gender differences

 

I came across this study while reading this article, which i think i will comment on later.

 

 

The fact that physical attractiveness is so highly valued

by men in mate selection, and contrary to conventional

social science wisdom is not arbitrarily socially constructed,

does not imply that the emphasis placed on it is not

destructive to women—a point about which many feminists

and evolutionary psychologists agree (e.g., Buss 1996;

Wolf 1991; Vandermassen 2005). Many feminist scholars,

evolutionary psychologists, and evolutionary feminists

concur that the value people place on female beauty is

likely a key cause of eating disorders, body image

problems, and potentially dangerous cosmetic surgery. As

Singh and Singh (2011) and others point out, it can lead to

the objectification of women as sex objects to the relative

neglect of other dimensions along which women vary, such

as talents, abilities, and personality characteristics. Finally,

in the modern environment, it seems clear that men’s

evolved standards of female beauty have contributed to a

kind of destructive run-away female-female competition in

the modern environment to embody the qualities men desire

(Buss, 2003; Schmitt and Buss 1996).

 

In our view, the key point is that feminist stances on the

destructiveness of the importance people place on female

attractiveness need not, and should not, rest on the faulty

assumption that standards of attractiveness are arbitrary

social constructions. Societal change, where change is

desired, is best accomplished by an accurate scientific

understanding of causes. The evolutionary psychological

foundations of attractiveness must be a starting point for

this analysis.

 

indeed, as is (nearly?) always the case: if one wants to change some state of affairs, then actually understanding WHY it is the way it is to begin with is of paramount importance.

 

-

 

Adaptations to Ovulation

Ovulation attains special status within women’s reproduc-

tive biology because it provides the very brief window

(roughly 12–24 h) during women’s menstrual cycle during

which conception is possible. Conventional wisdom in the

field of human sexuality over the past century has been that

ovulation is cryptic or concealed, even from women

themselves (e.g., Symons 1979). Evolutionary psycholo-

gists over the past decade have begun to challenge this

conventional wisdom. The challenges have come in two

forms—hypothesized adaptations in men to detect ovula-

tion and hypothesized adaptations in women to adjust their

mating behavior around ovulation.

 

Ancestral men, in principle, could have benefited (in

reproductive currencies) if they could detect when women

ovulated. An ovulation-detection ability would afford men

the ability to selectively direct their sexual overtures toward

women when they are ovulating, as male chimpanzees do.

And already mated men might increase their mate-guarding

efforts when their partners are ovulating. Both strategies, in

principle, could have evolved in men. The key question is:

Did they?More than 20 years ago, Symons (1987) concluded

that such male adaptations to ovulation had not evolved:

“The most straightforward prediction I could have made,

based on simple reproductive logic and the study of

nonhuman animals, would have been that . . . men will be

able to detect when women are ovulating and will find

ovulating women most sexually attractive. Such adaptations

have been looked for in the human male and have never

been found . . .” (p. 133).

 

it seems to me that the authors need to learn more logic. the above case seems to be an example of an argument from ignorance, altho in a nonstraightforward way. heres how i interpret it:

 

1) Symons wrote that there is no evidence of such adaptations in humans.

2) thus, Symons thought that there is no evidence of such adaptations in humans.

3) thus, Symons thought that there are no such adaptations in humans.

 

(2) follows given normal conditions, that is, that he wasnt lying etc. it has a hidden premise stating that the conditions are normal, in a kind of default reasoning way.

(3) however attributes an argument from ignorance inference to Symons, which is not warranted. it may be that the adaptations are difficult to find and that science had per 1987 just missed them.

 

Symons might not have held the view the authors attribute to him.

 

-

 

[...] And no other framework suggests that adaptations to

ovulation might have evolved. Whatever the eventual

evidentiary status of the competing hypotheses, it is

reasonable to conclude that the search for adaptations to

ovulation has been a fertile one, yielding fascinating

empirical findings.

 

dat pun

 

-

 

The positive outcome for everyone is that evolutionary

psychological hypotheses, sex role/biosocial theory hy-

potheses, and gender-similarity hypotheses all share the

scientific virtue of making specific empirical predictions.

In this sense, we see this special issue of Sex Roles an

exceptionally positive sign that the discourse is beginning

to move beyond purely ideological stances and toward an

increasingly accurate scientific understanding of gender

psychology.

 

since evo psychs dont hav any ideological stance, this description is exceptionally nice to them. the only ones who need to move past any ideology are the marxist feminists.

 

-

 

 

On being right and avoiding being wrong

The two goals: 1) having true beliefs, 2) not having false beliefs may seem to be equivalent or something like that, but they in fact result in different optimal strats.

Not having false beliefs

If one has only goal (2), the optimal strat is to believe as few things as possible, suspending belief about most things. Even if one meticulously checks the evidence to avoid being wrong, one will make mistakes once in a while perhaps simply because the current best available evidence about the subject is misleading (i.e. indicates that a particular thing is true that is actually false). So, the optimal strat is to believe nothing at all, but it is hardly possible to live like that. Unfortunately acquiring beliefs is more or less automatic in the sense that if one is exposed to evidence one will automatically form the relevant beliefs without making a choice about it.1 So, one needs to avoid exposing oneself to any evidence relevant to things that one does not already believe. Perhaps spending one’s time meditating is the optimal strat here.

Having true beliefs

If one has only goal (1), the optimal strat is to acquire lots of information and believe all sorts of things about it. I’m not entirely sure about the exact optimal strat. Perhaps the optimal strat is to set the evidence requirement for a belief as low as possible becus this makes it possible to form lots of beliefs, even on bad evidence. However, even this takes some time and since one wants to maximize the number of true beliefs, not just any beliefs, one shud probably gather at least some evidence. However, gathering evidence takes time and effort which cud be spend gathering evidence about some other subjects and forming beliefs about them as a result. So, some equilibrium will emerge about the optimal evidence requirement. Gathering evidence about a particular subject is a diminishing returns strat for having true beliefs.

The kind of thing that one shud gather evidence about matters. It is best to stick to areas where there is consensus about the experts and so that one can simply appeal to their authority and be right (most of the time). For subjects where there is much disagreement among experts, one wud need to gather some better evidence oneself to find out what the truth is. This probably means that one shud employ the heuristics mentioned in the previous link and stay away from subjects that fail at one or more of them. So, basically, one shud avoid all the subjects that i like. :P

However, as the number of one’s beliefs keep rising, one will run out of consensus subjects to study, in which case one will need to study non-consensus subjects and form beliefs about them too, even the ‘worst’ and less socially acceptable/politically correct subjects. Perhaps one shud keep these beliefs to oneself.

It is also a good idea to find other people with the same goal so that one can share evidence about things with them to speed up the progress.

Both having true beliefs and avoiding having false beliefs?

What about someone who has both goals and perhaps with different importance ratings? Here it is more difficult to give advice about the optimal strat. Perhaps one shud set the evidence requirement pretty high, but not impossibly high so that no amount of evidence is enuf. This shud take care of most of the false beliefs. However, there are more ways to get rid of false beliefs. There are many debunking sites around and lists of common misconceptions about all kinds of stuff. One shud read those to get rid of pesky beliefs that got thru the ‘evidence defense’, perhaps at some time before one was a critical thinker. Beliefs tend to stick around. Here are some good things to read to get rid of misconceptions about various things:

en.wikipedia.org/wiki/List_of_common_misconceptions

en.wikipedia.org/wiki/Misconceptions_about_HIV_and_AIDS

en.wikipedia.org/wiki/List_of_common_false_etymologies

en.wikipedia.org/wiki/Common_English_usage_misconceptions

en.wikipedia.org/wiki/List_of_misconceptions_about_illegal_drugs

en.wikipedia.org/wiki/Common_misunderstandings_of_genetics

en.wikipedia.org/wiki/Snopes.comwww.snopes.com

en.wikipedia.org/wiki/Skeptic%27s_dictionarywww.skepdic.com/

www.amazon.com/Great-Myths-Popular-Psychology-Misconceptions/dp/1405131128/ref=sr_1_1?ie=UTF8&qid=1333843699&sr=8-1

There are plenty more of such skepticism material around which brings me to the next point: One shud study critical thinking and logic with a focus on fallacies so that one can avoid making them and thus acquiring wrong beliefs. It is also a good idea to know about cognitive biases so that one can try to compensate for them. A strong command of mathematics, especially statistics, is also a good idea. This helps assess much of the science as most of that employ statistics now a days.

Then, one shud spend alot of time gathering good quality evidence about subjects. Since it takes time to read stuff, one shud read the highest quality stuff in that it offers the best evidence about the particular subject. This probably means reading science in journals and textbooks to begin with to learn the things about the subject that there is consensus about.

Other relevant literature

soundproofsuite1850.blogspot.com/2007/12/book-review-which-way-western-man.html

ajburger.homestead.com/files/book.htm

Notes

1As a side note, this is why pragmatic arguments for the belief in something are not very useful. One cannot just will oneself to start believing in something that one thinks that there is no evidence for, e.g. the xtian god. See www.infidels.org/library/modern/theodore_drange/sobel.html

What does “begging the question” mean?

Introduction

Abstract

In this essay I attempt to clarify what it means to say that an argument begs the question. One may think that it is a fairly straightforward matter but my analysis reveals that it isn’t so.

Shorthands

“BTQ” means begging the question, or begs the question whichever is grammatically correct on the context.

The phrase “begs the question” in english

The phrase “begs the question” has at least two meanings in english. The first and perhaps most common meaning is that of raising an important question. As it is written on FallacyFiles.org:

The phrase “begs the question” has come to be used to mean “raises the question” or “suggests the question”, as in “that begs the question” followed by the question supposedly begged. The following headlines are examples:

        • Warm Weather Begs the Question:
          To Water or Not to Water Yard Plants

        • Latest Internet Fracas Begs the Question:
          Who’s Driving the Internet Bus?

        • Hot Holiday Begs Big Question:
          Can the Party Continue?

This is a confusing usage which is apparently based upon a literal misreading of the phrase “begs the question”. It should be avoided, and must be distinguished from its use to refer to the fallacy.”1

The second meaning of “beg the question” is in the informal logical fallacy of begging the question. It is this meaning that this essay attempts to clarify.

Proposed definitions

So what does it mean to say that an argument BTQ? There are surprisingly many different answers from good sources. Below I quote many of the different definitions given, some by authorities and some not.

FallacyFiles.org

In an article entitled “Begging the Question” FallacyFiles.org writes:

“The phrase “begging the question”, or “petitio principii” in Latin, refers to the “question” in a formal debate—that is, the issue being debated. In such a debate, one side may ask the other side to concede certain points in order to speed up the proceedings. To “beg” the question is to ask that the very point at issue be conceded, which is of course illegitimate. “2

And:

“Any form of argument in which the conclusion occurs as one of the premisses, or a chain of arguments in which the final conclusion is a premiss of one of the earlier arguments in the chain. More generally, an argument begs the question when it assumes any controversial point not conceded by the other side.”3

Notice how vague the one mentioned in the first paragraph is. To the defense of FallacyFiles.org, we may note that that paragraph is entitled “Etymology”, and is perhaps not meant to actually explain clearly what it means to BTQ but only to explain how the etymology relates to the meaning of the term.

The second paragraph is entitled “Exposition” and is clearly meant to explain the meaning of the term. However the paragraph features two independent definitions, a strict (which is a disjunction) and a general (or rather, broad) one.

butterfliesandwheels.com

In the article entitled “Bad Moves: Begging the question” butterfliesandwheels.com writes:

“Begging the question – assuming what needs to be argued for [...]”4

skepdic.com aka. The Skeptic’s Dictionary

In an article entitled “begging the question” it is written on skepdic.com:

“Begging the question is what one does in an argument when one assumes what one claims to be proving.”5

And a bit later:

“If one’s premises entail one’s conclusion, and one’s premises are questionable, one is said to beg the question.”6

Notice that these two definitions are not at all identical. Examples will show this later.

Wikipedia.org

In an article entitled “Begging the question” it is written on Wikipedia.org:

“The fallacy of petitio principii, or “begging the question”, is committed “when a proposition which requires proof is assumed without proof.”[3] More specifically, petitio principii refers to arguing for a conclusion that has already been assumed in the premise. The fallacy may be committed in various ways.

When the fallacy of begging the question is committed in a single step, it is sometimes called a hysteron proteron,[4] as in the statement “Opium induces sleep because it has a soporific quality”.[5] Such fallacies may not be immediately obvious in English because the English language has so many synonyms; one way to beg the question is to make a statement first in concrete terms, then in abstract ones, or vice-versa.[5] Another is to “bring forth a proposition expressed in words of Saxon origin, and give as a reason for it the very same proposition stated in words of Norman origin”,[6] as in this example: “To allow every man an unbounded freedom of speech must always be, on the whole advantageous to the State, for it is highly conducive to the interests of the community that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.”[7]

When the fallacy of begging the question is committed in more than one step, it is sometimes referred to as circulus in probando or reasoning in a circle[4] but incorrectly if we look at the definition Aristotle gave us in Prior Analytics.[1]

“Begging the question” can also refer to making an argument in which the premise “is different from the conclusion … but is controversial or questionable for the same reasons that typically might lead someone to question the conclusion.”[8]”7

And:

“In informal situations, the term begging the question is often used in place of circular argument. In the formal context however, begging the question holds a different meaning.[1] In its shortest form, circular reasoning is the basing of two conclusions by means of which there is demonstrated a reversed premise of the first argument. Begging the question does not require any such reversal.

Begging the question is similar to the Fallacy of many questions: a fallacy of technique that results from presenting evidence in support of a conclusion that is less likely to be accepted than merely asserting the conclusion. A specific form of this is reducing an assertion to an instance of a more general assertion which is no more known to be true than the more specific assertion:

* All intentional acts of killing human beings are morally wrong.

* The death penalty is an intentional act of killing a human being.

* Therefore the death penalty is wrong.

If the first premise is accepted as an axiom within some moral system or code, this reasoning is a cogent argument against the death penalty. If not, it is in fact a weaker argument than a mere assertion that the death penalty is wrong, since the first premise is stronger than the conclusion.”8

New York Times

In an article entitled “ON LANGUAGE; Take My Question Please!” it is written in New York Times:

“”This sentence fragment uses ‘begs the question,’ ” he writes, ”in the sense of a question that begs to be asked, usually because it is obvious to all. However, I am plagued by my logic course of some years ago, which taught me that begging the question is nothing of the kind. Rather, begging the question is a logically invalid form of argument that uses the point to be proven as part of the argument for its proof.”

Amen. Readers have been protesting this misuse of a term about a concept set down by Aristotle, a student of Plato Cacheris, in his book on logic written about 350 B.C. (Here comes mail on B.C.E.) His Greek term en archei aiteisthai was translated by the Romans as petitio principii, and rendered into English in 1581 as begging the question. In whatever language, it described the fallacy known as ”the assumption at the outset.”

In his 1988 book, ”Thinking Logically,” Prof. James Freeman explains: ”An argument begs the question when the conclusion, in the same or different words, or a statement presupposing the conclusion, is introduced as a premise. The case for the conclusion ultimately depends on accepting the conclusion itself.””9

Notice how it says that it is an invalid form of argument. But surely any argument that commits the strict fallacy of BTQ, that is, the conclusion is identical to a premise, is a valid argument. Why? Valid arguments are precisely those arguments where the premises logically imply the conclusion. Since any proposition implies itself [P⇒P], then any argument that BTQ in the strict sense is valid.

nizkor.org

In an article entitled “Fallacy: Begging the Question” it is written on nizkor.org:

“Begging the Question is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true. This sort of “reasoning” typically has the following form.

1. Premises in which the truth of the conclusion is claimed or the truth of the conclusion is assumed (either directly or indirectly).

2. Claim C (the conclusion) is true.

This sort of “reasoning” is fallacious because simply assuming that the conclusion is true (directly or indirectly) in the premises does not constitute evidence for that conclusion. Obviously, simply assuming a claim is true does not serve as evidence for that claim. This is especially clear in particularly blatant cases: “X is true. The evidence for this claim is that X is true.”

Some cases of question begging are fairly blatant, while others can be extremely subtle.”10

The Cambridge Dictionary of Philosophy

In an article entitled “Circular Reasoning” Robert Audi writes:

“circular reasoning, reasoning that, when traced backward from its conclusion, returns to that starting point, as one returns to a starting point when tracing a circle. The discussion of this topic by Richard Whatley (1787–1863) in his Logic (1826) sets a high standard of clarity and penetration. Logic textbooks often quote the following example from Whatley:

To allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State; for it is highly conducive to the interests of the Community, that each individual should enjoy a liberty perfectly unlimited, of expressing his sentiments.

This passage illustrates how circular reasoning is less obvious in a language, such as English, that, in Whatley’s words, is “abounding in synonymous expressions, which have no resemblance in sound, and no connection in etymology.” The premise and conclusion do not consist of just the same words in the same order, nor can logical or grammatical principles transform one into the other. Rather, they have the same propositional content: they say the same thing in different words. That is why appealing to one of them to provide reason for believing the other amounts to giving something as a reason for itself. Circular reasoning is often said to beg the question. ‘Begging the question’ and petitio principii are translations of a phrase in Aristotle connected with a game of formal disputation played in antiquity but not in recent times. The meanings of ‘question’ and ‘begging’ do not in any clear way determine the meaning of ‘question begging’. There is no simple argument form that all and only circular arguments have. It is not logic, in Whatley’s example above, that determines the identity of content between the premise and the conclusion. Some theorists propose rather more complicated formal or syntactic accounts of circularity. Others believe that any account of circular reasoning must refer to the beliefs of those who reason. Whether or not the following argument about articles in this dictionary is circular depends on why the first premise should be accepted:

(1) The article on inference contains no split infinitives.

(2) The other articles contain no split infinitives.

Therefore, (3) No article contains split infinitives.

Consider two cases. Case I: Although (2) supports (1) inductively, both (1) and (2) have solid outside support independent of any prior acceptance of (3). This reasoning is not circular. Case II: Someone who advances the argument accepts (1) or (2) or both, only because he believes (3). Such reasoning is circular, even though neither premise expresses just the same proposition as the conclusion. The question remains controversial whether, in explaining circularity, we should refer to the beliefs of individual reasoners or only to the surrounding circumstances. One purpose of reasoning is to increase the degree of reasonable confidence that one has in the truth of a conclusion. Presuming the truth of a conclusion in support of a premise thwarts this purpose, because the initial degree of reasonable confidence in the premise cannot then exceed the initial degree of reasonable confidence in the conclusion.”11

What can we gather from this?

There is consensus about a strict definition of BTQ which is identical to circular logic. This is defined as: An argument is circular iff one of the premises is identical to the conclusion.

There is no consensus about a broad definition of BTQ. At best this is some intuitive notion. Further analysis could try to find a meaning appropriate for this broad sense. That task I will take up in a forthcoming essay.

Notes

1www.fallacyfiles.org/begquest.html. See also Gary Curtis, “Please Stop Begging that Question You’re Raising”, The Editorial Eye, 2/2007

2Ibid.

3Ibid.

6Ibid.

8Ibid.

9www.nytimes.com/1998/07/26/magazine/on-language-take-my-question-please.html ON LANGUAGE; Take “My Question Please!”, By William Safire, Published: Sunday, July 26, 1998

11Robert Audi, The Cambridge Dictionary of Philosophy, Second edition, p. 177

Fallacy of All objections defeated

This is a common yet relatively unknown fallacy. The typical situation is this: Someone is defending some view or theory. That someone acknowledges the existence of a number of objections to the view/theory that he is defending. He then defeats these objections to his own satisfaction and concludes that there are no good objections. Presuming that the person is rational, this is where he ought to conclude that there are no good objections known to him. He should not conclude that there are none.

Interestingly, I found logician, Graham Priest, that commits this fallacy (oh well, even logicians commit fallacies but hopefully less or less frequently than other people). Graham Priest defends his dialetheism theory in his book In Contradiction. On pages 238-240 he defends a view about the transmission of obligations. He defends that view against some objections and then concludes:

“[...attempting to refute objections...] The principle of the transmission of obligation is, therefore, perfectly acceptable.” (p. 240)

Such a thing does not follow. It is possible and even probable that there are other good objections which render the view not perfectly acceptable.

Some ideas about formalizing questions and answers

Formalization of questions and answers is not a much discussed nor studied topic. Though there is a branch of logic dealing with it, erotetic logics. I admit not to have read much on the issue, in fact, almost nothing. This is because there is almost nothing on the internet about it, and the few books that deal with it are not to find in the danish library system.

The idea is to formalize questions and the answering of such. With formalization we have a framework for understanding when a question has been answered. It seems to me that we only have our intuitions to rely on until a relevant logic has been created, and intuitions are too often not trust worthy.

Formalization of questions

Consider the question:

Q1. Who is credited with discovering the element Uranium?

How should we formalize this? How about:

Q1F. (∃x)(Ux∧x=?)

Ux ≡ is credited with discovering the element Uranium

Though there is a hidden second condition for a correct answer to this question. Note the word “who”. That that word is used implies that the answer refers to a person. So we may add:

Q1F*. (∃x)(Ux∧Px∧x=?)

Ux ≡ is credited with discovering the element Uranium

Px ≡ is a person

Consider a more complex question such as:

Q2. Which scientist is credited with discovering the element Uranium and whose name is Martin and who is german?

Formalization:

Q2F. (∃x)(Ux∧Sx∧Mx∧Gx∧x=?)

Ux ≡ is credited with discovering the element Uranium

Sx ≡ is a scientist

Mx ≡ is named Martin

Gx ≡ is german

Note how we can now formally make sense of/explain complexity of questions. Complexity correlates with the number of predicates in the formalization. But since there are multiple possible formalizations one need to be careful with this correlation. It may be the case that it corresponds perfectly or nearly so with the deepest possible formalization of a question.

Answers to questions

When should we say that an answer has been answered truthfully? Iff substituting the question mark “?” with the answer gives a true formula.1

Consider the correct answer to the first question above:

A1. Martin Heinrich Klaproth

And its formalization:

A1F. m

m ≡ Martin Heinrich Klaproth

Now substituting “?” with “m”:

Q1W. (∃x)(Ux∧x=m)

(Q1W) is true, therefore, the answer is correct.

Similarly with the second question:

Q2W. (∃x)(Ux∧Sx∧Mx∧Gx∧x=m)

Again this is true.

Translating to Logic English

Logic English (LE) being the language where to formalizations are translated, as with propositional logic and predicate logic. This is a precise language that corresponds perfectly with logic. (Another thing that I am working on.)

Consider again the first question unanswered and answered:

Q1F. (∃x)(Ux∧x=?)

Q1W. (∃x)(Ux∧x=m)

I propose this translation to LE:

There exists one x such that x is credited with discovering the element Uranium and x is identical with who?

There exists one x such that x is credited with discovering the element Uranium and x is identical with Martin Heinrich Klaproth.

Questions as expressing propositions

It is clear from my chosen formalization and translation that I think questions express propositions. So they can express something that is true or false like other sentences. This should not be too surprising. Consider the loaded question fallacy. That happens exactly when one asks a question that expresses a false proposition. A proposition expressed by the question is false iff it is not the case that there exists an x such that [predicates]. The clause with the “x=?” is ignored when evaluating truth values.

So, by accepting that some questions express propositions we can make sense of the loaded question fallacy.

Multiple correct answers

It is possible formalize the multiple correct answers aspect of questions. Consider the question:

Q3. What is x identical with in the equation x2=4?

Formally:

Q3F. (∃x)(x2=4∧x=?)

There are two correct answers to this question:

A3a. 2

A3b. -2

Substituting “?” with the answers produces:

Q3Wa. (∃x)(x2=4∧x=2)

Q3Wb. (∃x)(x2=4∧x=-2)

Which are both true formula. So, there are more than one true answer. We could formalize this as (with help from set theory):

Q3F*. (∃x)(x2=4)∧((∀y)(y2=4⇒y∈A∧MA>1))∧(x=?)

MS ≡ the number of members of S

A ≡ (the set of) answers

We can also translate this to LE:

There exists an x such that x2=4, and for all y, that y2=4 logically implies that y is a member of A and the number of members of A is more than 1, and x is identical with what?

It seems to me to be best to always have the question clause “x=?” at the end of a formula. Otherwise a translation of the formula into LE would produce a sentence that has a question mark in the middle of it. That would be grammatically incorrect. I strive to make LE grammatically correct or close to. The goal being that LE is readable by people that can read english.

An idea is to get rid of the first part of (Q3F*) and only keep the part with the universal quantifier (∀x), but that would produce problems with the question clause at the end. Like this:

Q3F**. (∀y)(y2=4⇒y∈A∧MA>1)∧(x=?)

x” is not mentioned at all before the question clause at the end.

Notes

1More precisely, a formula that when interpreted with the supplied interpretation keys expresses a true proposition.

Careful with that equivocation, Eugene!

ACB:

1. S knows that every statement in his geography textbook is correct. (His well-qualified geography teacher has told him: “I have checked this book carefully, and everything in it is correct”. The teacher is right, and S believes him.)

2. One of the statements in the textbook is that Quito is the capital of Ecuador.

3. Therefore, S knows that Quito is the capital of Ecuador, even if he has never heard of Quito or Ecuador.

This doesn’t seem right to me. What do you think?

Emil:

Hmm. Formalization may help.

1. (∀P)(TP→K(P))
For all propositions, that a proposition is expressed in the textbook (TP) materially implies that S knows that P.
2. TA
(proposition) A is expressed in the textbook.
⊢, 3. K(A)
Thus, S knows that A.

This is valid. But I don’t think that is the argument expressed above. The argument expressed above relies on confusion/equivocation on premise 1. The difficulty is formalizing what the other thing that is meant by that phrase is. Hmm.

My (1) above is not a correct formulation of what if meant by the premise phrase in the natural language. What about:

1′. K((∀P)(TA→A))

S knows that for all propositions, that a proposition is expressed in the textbook (TP) materially implies that P.

That seems to capture what is meant. The equivocation has been explained to my satisfaction. (1′) and (2) does not logically imply the conclusion, so that argument is invalid.

Source.