What is Frege's puzzle? Why did he reject the metalinguistic solution and change to reference and sense? What is his second solution and does it work any better than the first?
and Alex asked:
I'm writing an undergraduate essay about Frege, which is, "Is sense a semantic property of singular terms?" I would greatly appreciate any help on this subject as it is very difficult and I don't understand it!! Thank you.
In his essay, 'On Sense and Reference' ('Uber Sinn und Bedeutung') Frege presents a puzzle about the notion of identity. Identity statements, of the form A=B, can convey factual information about the object designated. To take Frege's example, we now know that the sun we see in the sky is the same object whenever it appears. Once, people did not know this. Or, to quote an example popular with academic philosophers, we all know that Superman is Clark Kent, but Louis Lane does not. If she were to discover Clark Kent's identity, this would be knowledge. But what exactly is this knowledge and how is it represented in the statement, Superman=Clark Kent?
There seem to be just two alternatives:
- A statement of identity describes a relation which every object holds to itself, and does not hold to any other object.
- A statement of identity describes a relation which holds between two names which refer to one and the same object.
On alternative (1), when we say that Superman=Clark Kent, what we actually state is that a certain individual is identical with himself. But this is hardly news! On this reading, there is no difference in informational value between the statement, Superman=Clark Kent and the statement, Superman=Superman.
On alternative (2), when we say that Superman=Clark Kent, what we actually state is that the name 'Superman' designates one and the same individual as the name 'Clark Kent'. This 'meta-linguistic' solution which Frege originally adopted, looks more promising. To know that an object is designated by a particular name is a piece of factual information. For example, I ask what my neighbour's new dog is called and she tells me his name is 'Bruce'. Now I know something I didn't know before.
But Frege rejects this second alternative. Why? This is what he says:
[T]his relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a=b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means.
Philosophical Writings of Gottlob Frege P. Geach and M. Black eds. Blackwell 1970.
As an undergraduate, I remember puzzling over this. What is Frege saying? Of course, I am free to invent my own arbitrary name for Bruce. Suppose my name for Bruce is 'Bonzo'. For me, it is not news that 'Bruce' designates the same entity as 'Bonzo'. For you it might be. Not having a great eye for dogs, you are unaware that the naughty 'Bonzo' I point out tearing up my vegetable patch is the very same well behaved 'Bruce' you were introduced to by my neighbour last week when you were invited over for tea. So what's wrong with this account?
There's nothing wrong with it. It is perfectly all right. The statement that 'Bruce' designates the same entity as 'Bonzo' will convey information to you just in the case when the statement that Bruce=Bonzo conveys information. They are not the same statement, of course. The first statement refers to names while the second statement uses names, but does not refer to them. (You refer to a name when you put it in quotation marks.) However, the two statements do the same job.
But that is precisely the reason why the meta-linguistic analysis doesn't make any contribution to solving the original puzzle. It looks as though the meta-linguistic analysis gets you somewhere, whereas in fact it doesn't. The question, which still hasn't been answered is, What is it that is characteristic of all and only those cases of statements of the form A=B or of the form The object designated by 'A'=the object designated by 'B' which succeed in conveying factual information?
Frege's solution is to propose a distinction between the sense of a name and its reference. The reference of a name is the entity which it designates. The sense of the name, for a given individual or group of individuals who use that name, depends upon now, here comes the difficult bit something (Frege calls it the 'mode of presentation' of the object) which is not the same as the entity itself. In the statements, 'Superman=Clark Kent' or 'Bruce=Bonzo', the names on each side of the '=' sign have the same reference but a different sense.
Objects, as I would put it, have sides. Every object that we are acquainted with, potentially has sides from which that object would be unrecognizable to us. Occasionally, we succeed in connecting two disconnected sides together and recognize that fact by asserting an identity statement.
It is therefore is absurd to claim that the semantic value of names like 'Bruce' or 'Geoffrey' is the object which they refer to. If that were the case, one would have to conclude that we can never know the meaning of any name. If one did know the meaning of a name, then one would have to know the object from every possible side, knowledge to which, as Frege laconically remarks, "we never attain".
But do names have a semantic value, in Frege's sense? Is there any useful point in looking for the mode of presentation, or sense of a name like 'Bruce', or 'Geoffrey'? Does my neighbour's dog have a 'Bruce' side and a 'Bonzo' side? Only in certain artificially restricted examples. In real life, modes of presentation overlap in exceedingly complex ways. One would have to conclude that Frege's argument for a sense/reference distinction for proper names as a solution to the puzzle about identity statements is totally unconvincing. Names have a fluid and variable currency, not a fixed 'semantic value'.
It can be difficult to understand sense and reference but I think this is just because reference always seemed to be called "meaning" as if sense was irrelevant to semantic theory. However, there are two different aspects to meaning.
Firstly, there is thought and speech. What we refer to is the object or referent. When we "mean" something, we refer to it and, in doing so, we use a particular sense, or a description. You may know John as "the bloke in the pub" and your friend might know him a "the man who works in the bookshop". You can talk about the same person without knowing it, but you are both talking of the same person (you have the same reference), and you may come to both realise it when you come to agree on senses or descriptions under which you know John. Sense is essential to this aspect of meaning. You can't talk about John without a sense, i.e. a description under which you know him, or you wouldn't understand what you were talking about. For Frege, this type of meaning was both sense and reference. It is an account of an individual's understanding of a sentence. Frege called this propositional as opposed to sentential.
The other aspect of "meaning" is the relation between a sentence and the fact in the world. When we use language we use propositions which express our relationship to, or our understanding of, the way the world is. There is what we know of John, but there is also John himself who embodies all facts about himself. The sentence which contains as the referent the word John, picks out John as the individual of whom there are facts which are true or false of him. The sentence "John works in the bookshop" directly refers to a particular person as an objective item and doesn't need to carry sense to have meaning. An ordinary sentence as opposed to a propositional thought is given meaning in terms of its truth conditions, so is directly determined by extra-linguistic facts such as those in the world.
According to Gareth Evans in The Varieties of Reference, Frege did not abandon one semantic theory for another, but recognised that more than an extensional analysis of sentences was needed if a theory of meaning was to encompass an account of what it is to understand a sentence.
His initial theory of meaning was in terms of truth value. The meaning of a sentence is determined by whether or not a description is true or not of the referent. What Frege realised, which is the reason for his sense/reference distinction, was that in many cases we might know an object or person under one description yet not under another. What an individual knows about a referent is its sense, or intension. The sentence relation between sentences and extra-linguistic entities is extensional and doesn't account for what people understand by their language and a theory of meaning should be able to provide some explanation of differences in understanding as well as being able to underpin a theory of communication.
Evans identifies Frege's initial recognition of the problem of understanding in regard to a theory of meaning in an unpublished letter in which Frege gave an example of a mountain discovered from different directions by two explorers. One explorer calls it 'Afla' and discovers it's height to be 5000 metres, the other calls it 'Ateb' but knows nothing of it's height. The second explorer can successfully refer to the mountain as Ateb and might come to discover that Ateb is 5000 metres high. He would thus believe "Ateb is 5000 metres high" but not "Afla is 5000 metres high" because he doesn't know that Ateb is Afla. Therefore, these cannot be the same thought: There are two senses, one referent. It is possible not to know that the mountain is not snow-capped in the summer, so Frege's theory of sense shows how it is possible to informatively communicate with others about objects. Frege's example of Hesperus and Phosphorus (the evening star and the morning star) in 'On Sense and Reference' illustrates the same point. On the extensional analysis, which Frege came to recognise as inadequate, if you believe that "Ateb is 5000 metres high" then you would believe that "Afla is 5000 metres high".
As a theory of meaning the sense/reference account works to an extent, but lies slightly problematically alongside Frege's account of extensional meaning of sentences. Some sentences, about fiction for instance, include names which do not refer to objects. On a logical extensional analysis, this type of sentence would be false because it fails to refer. If a theory of meaning was simply extensional, a person using a sentence about a fictional character would fail to say anything. There would be sense without reference for a class of propositions and sentences. Michael Dummett, the main interpreter of Frege, has held that for these sentences a third, indeterminate truth value should be introduced. Evans holds that Frege took a more Russellian view of fictional sentences.
One specific problem arising from Frege's account is what Susan Haack in Philosophy of Logics refers to as "The morning star paradox". On the extensional analysis, the morning star is the evening star both terms refer to the planet Venus which is an identity relation, and so it is necessary. If the morning star is the evening star then that fact could not be otherwise. However, because there are two senses involved here, it follows that it is contingent. Not everyone knows that the morning star is the evening star. We can easily conceive that they might have been two different stars, given the different senses.
What is the difference between an emotion and a feeling? What are the common or basic emotions?
I don't know of any philosophers who have distinguished between feelings and emotions. However, it would make sense to say emotions are focused feelings, and that all emotions are feelings, but not all feelings are emotions. A few feelings which I would suggest are not emotions because they are not focused are those of calm, anxiety and general happiness or sadness.
Aristotle thought that to be in an emotional state is to be in a certain "frame of mind", e.g. "People who are afflicted by sickness or poverty or love or thirst or any other unsatisfied desires are prone to anger and easily roused". There must also be a cause of the emotion, such as being "slighted" in the case of anger, and each emotion is related to feelings of pleasure and pain. Emotions also guide our thoughts: In the case of anger, Aristotle points out that we are led to thoughts of retaliation.
Aristotle didn't distinguish between feelings and emotions and so analysed feelings such as calm and friendship as emotions. He characterised calm, as a cooling down after anger, which is to continue to respond to an external cause because you calm down in relation to the person who made you angry. However, a person can simply be calm which is a condition rather than an emotion, or simply feel calm for no particular reason, and calmness in these senses would not fall within Aristotle's definition of an emotion.
If we accept that emotions are focused (actually, or as the content of thought) on particular states of affairs outside the body, then feelings can be characterised as unfocused internal states. A paradigm for feeling is the physical feeling of pain. This has a cause inside rather than outside the body. To be calm or happy in this sense, where there is no external cause, can be taken as a feeling and contrasted with emotions. On this distinction, friendship, as directed at another person would be an emotion.
On this analysis, I suppose that the most common emotion is friendship. It is not really possible to talk of common emotions in general, since many emotions, such as jealousy and anger, depend upon one's being of a personality type.
What determines how we use moral rationalization? Example, the person who is released from jail, knows or should know how to stay out of incarceration, yet they have a history of being a repeat offender. The crime does not necessarily have to be the same offense.
This is the problem that was known in Greek philosophy as the problem of akrasia or 'weakness of will'. The problem is acute for any one who believes that we do the action which, in our view, we have the best reason to do.
In your example, the person released from jail knows that they ought to stay out of trouble. It doesn't matter whether one understands this as a moral 'ought' (the offender has learned the error of their ways) or merely the recognition that they are not clever enough to avoid getting caught. Once out, their resolve weakens and they offend again.
I prefer Socrates' solution to this problem to Aristotle's. For Socrates, 'weakness of will' is not the correct description. The failure is a failure of reason and knowledge. If you really knew it was better not offend again, then you wouldn't do it. When you do offend, it is because your knowledge deserts you at the crucial moment. You get distracted from your goal. Aristotle didn't like this explanation. He thought you could know you were doing the wrong thing by your lights, yet do it under the influence of temptation. On such an occasion, your actions are controlled by your passions, not by your reason.
I cannot accept the idea that there are two distinct causes of our actions, our reasons and our passions. Whatever we do, we do for a reason, even if it is a bad reason. The shoplifter who lusts after a pair of designer jeans takes them for a reason which, in other circumstances would be considered perfectly acceptable. I don't see how the desire for designer jeans can be a reason for action on one occasion (when you can afford to pay for them) but not on another occasion. Of course, there are reasons of various kinds for not shoplifting. These have to be taken into consideration. Yet, at the crucial moment, the reasons for staying on the straight and narrow suddenly seem less convincing. Yes, I know it is wrong to steal. But I've got no money and it's wrong that other people are rich and I am poor. And in any case, no-one is really going to suffer as a result of my action. Or, I know I have been caught many times in the past, but practice makes perfect. This time, I am certain I can get away with it!
What I think Aristotle is absolutely right about is the crucial importance of habit. However, this can be shoe horned neatly into the Socratic account. The ability to keep ones eyes fixed on an objective and resisting the distractions of momentary temptation is something that can be strengthened or weakened by habit. Thinking is an action just as much as doing. It would be absurd to claim that I perform the mental action of choosing to consider a particular reason, only because I consciously think about the reason for considering that reason. The result would be a vicious regress. In order to consciously think about the reason for considering the first reason, I would have to think about the reason for thinking about the second reason for considering the first reason, and so on.
The knowledge in which moral or prudential virtue in Socrates' sense consists, involves, above all, a certain capacity for memory. It is memory that determines the reasons that occur to us at this or that time, and how we respond to those perceived reasons. The greatest curse of human beings, as Max von Sydow's Merlin remarks, is that they forget!
I study electronic engineering in a foreign country. We have been asked to make an essay:
Le savoir est-il ce qui peut s'enseigner?
I understand that question to mean: Is it possible to teach all forms of knowledge?
I think for Plato knowledge is what has a precise content, we can give a definition. I refer to the dialogue Meno which is about a problematic definition of virtue. According to Plato, if something for example, virtue is knowledge, then it can be taught.
But if we consider knowledge acquired from experience, and not from a professor, in this case, is it possible to teach this knowledge? Personally, I learnt a lot of things during my work experience that I think someone else couldn't teach me.
Plato thought that we acquire practical 'knowledge' by means of the mere transfer of information, examples being flute-playing and medicine. Real knowledge, for Plato, had to be of the abstract and eternal and when we apply concepts for which we don't have a definition such as virtue to the empirical world, we are using beliefs and opinions
Real knowledge is acquired by the "tethering" of right opinion which is appropriate for geometrical problems where repeated working out of problems is needed before you can claim to know. It involves "reasoning out the explanation" which is needed for conceptual knowledge such as the definition of "virtue", or knowledge of properties in the empirical world. To tether or reason out the explanation is to fully understand. We can only know certain things. Plato thought that the world was subject to change and flux and could not be an object of knowledge, so real knowledge is that which is attained through reasoning.
Today it is thought sufficient that we know what something means just so long as we can use the concept this is so for knowledge of the empirical world, at least. "Virtue" is a more difficult concept because it is evaluative, so although we have beliefs about what virtue is, real knowledge can only be achieved by understanding which requires reasoning. We can inform others of our beliefs about virtue, but if we don't actually know what it is we cannot really teach others because we would not pass on knowledge.
I don't know what it is that you have learnt from experience which you feel someone else couldn't teach you. If you have learnt from observation, supposedly you could have been shown. Of course, this would not amount to knowledge according to Plato, and couldn't be taught.
Basically, on teaching, practical knowledge (for Plato and everyone else) can be taught. For abstract knowledge (maths and conceptual definitions), Plato would not allow that this can be taught, because you can only come to know something on your own, having reasoned out the explanation, or having understood. You can only "prompt" (i.e. question) others to acquire a proper understanding for themselves. Philosophers other than Plato might characterise prompts as teaching. For difficult concepts such as "virtue" we do not have definitions, and so on Plato's view and most other people's, we can only transfer information. Where we don't have undisputed explanations, we only have beliefs, and these are what cannot be taught on anyone's account, only conveyed or passed on. This may be characterised as "being taught", by non-Platonists, but it is not the acquisition of knowledge on anyone's account.
I don't know anything about electronic engineering, but perhaps you can achieve a deep understanding as opposed to just following instructions or rules. Understanding is something you do on your own.
I've though about this question loads and I'm really confused: Is it possible that all the world just exists in our heads?
If all the things in the world exist in our heads, and our heads are in the world, then our heads exist in our heads. Now that is really confusing!
I suppose what you mean is, Is it possible that all the world exists in our minds, where the existence of a mind does not require the existence of a material object, such as a brain or a skull bone.
The first thing to point out is if I really thought it was possible that there were no material things, and that everything 'external' I see around me is nothing more than a kind of projection of something within my own mind, then I would seriously question whether you exist, as a separate subject with a mind. All I know of you are words on this computer screen! But then I might go on to question whether my wife and children exist. Everything I know of them, just as everything I know of you, is based on experiences in my own mind. Our own experiences are all that any of us ultimately has to go on.
Having got that far, there is still more to doubt. All I know of my past experiences is what I can remember of them now. So my past experiences might be nothing more than a projection of experiences currently occurring in my mind. I could have come into existence one minute ago with all my apparent 'memories' as they are now, and I would never know.
Even if, armed with a good dose of common sense, all these speculations seem to us highly improbable are then still possible? Do they make logical sense? Do I have to remind myself every so often that this wide, wonderful world and all the people in it might, just possibly, be nothing more than a momentary bubble of experience that calls itself 'I'? A mere illusion of a 'world' which appeared out of nowhere and will disappear the next moment into the nothingness from whence it came?
So far as nothing is absolutely certain in philosophy, I have to concede though I don't like it that what I have just said is possible.
That's not the question we should be asking. The real question is whether it is possible that we might be persuaded, by the philosophical argument of a Berkeley, or a Leibniz or a Kant, to embrace one or other version of the theory that what we call 'the physical world' is not real in itself, but rather something woven together out of the strands of experience.
Kant's theory is in some ways the most attractive of the three. He held that reality is something apart from the things that appear in our experienced 'worlds'. Berkeley, Leibniz and Kant are all agreed that there cannot be appearances without something behind those appearances, their ultimate source. Kant was the only philosopher out of the three to realize that this 'something' would have to be totally outside all human knowledge and experience.
What would be the consequences for a society without religion?
The consequences for a society which is not completely religious are available to see in all ages. It is rare for religion to be all-pervasive, and today, in Britain, Australia, America, at least, there are multiple religions as well as a vast amount of atheism. I think that religion is useful for laying moral foundations within a society. As the world is, most people who have no commitment to religion are still exposed to religious teaching, but if a society had no history of religion at all, morality would still have an impact.
Morality might be grounded in "rational bargaining" which is a recognition of the rights and freedoms of others, aiming at a peacefully run society, or it may be grounded in utilitarianism. Utilitarianism aims, simplistically, for the greatest happiness of the greatest number, and would rule against bad deeds as not conducive to happiness. However, such societies would be simply rule or pleasure governed but there is another element of morality which may be based upon religious teachings, such as forgiveness. Deep moral feeling such as remorse and forgiveness come from the subject rather than some form of organised social rules. If the wrong doer, in committing an immoral act does not suffer himself in terms of remorse then morality really has no inner, subjective, hold and a society without religion might well differ very much from a religious society.
However, without religion there remains the natural feeling people have for one another. This may seem an inadequate thing to rely upon, but I don't believe that people perform charitable acts, or are just good, simply for religious reasons. We all behave well to people we love, just because we love them and where there is love, there is forgiveness and remorse. These moral feelings are easily extended beyond relationships based on the close tie of love. So morality with a deep subjective aspect would exist without religion because religion doesn't necessarily provide us with these feelings if there is also a source in love and the recognition of common humanity.
There will always be natural human fellowship, as well as individual and organised charity. Every human being has a cause which touches him. Each organised charity brings in people with particular interests and sympathies.
I believe that people are capable of living in peace with each other and performing good deeds without religion.
In fact, religious differences often cause social division.
Do you have suggestions for someone who feels caught between the ethics of Apollo and Dionysus? I know Nietzsche fell firmly in the Dionysus camp, but I don't feel like he had it all figured out. I think Aristotle's Golden Mean is more of my kind of ethic. Anyway, I'd be interested in any further readings on the topic.
The real question is how far a belief furthers and supports life, maintains and disciplines a species Beyond Good and Evil.
Nietzsche's celebrated distinction between the Apollonian and the Dionysian can be found in his first book The Birth of Tragedy. If you are interested specifically in ethics, rather than the metaphysical and aesthetic strands of the idea, I think the question to ask is how strong are Nietzsche's arguments against moral realism and what exactly is the outcome of his position. Perhaps thinking about this will help you feel less trapped; Walter Kaufmann's book on Nietzsche is excellent.
Here is my take: Nietzsche claims that we are psychologically prone to error through our desires to conform and to avoid pain (pain in the sense of the terror that seeing the world as nauseatingly absurd can induce in us) Descriptions of moral 'facts' are merely descriptions of a moral attitude. There are no moral phenomena, only moralistic interpretations of them.
This is a specialisation of his general metaphysical view there are no facts and no order (hence no moral order) at all. In most need of re-evaluation are thus our meta-ethical beliefs concerning the possibility of justifying the ethical beliefs we hold. His is a kind of 'error theory' about how we arrive morally realist conclusions and is essentially a rejection of the correspondence theory of truth. In this sense it is somewhat similar to J.L. Mackie's arguments for subjectivism in his book Ethics which I recommend. Nietzsche also offers us a psychological explanation for why this error persists what is the non-moral provenance of moral interpreting and what is its function in human life (see the quote at the top!)
A good question to consider is whether Nietzsche smuggles in some kind of moral realism with this talk of what is 'life-enhancing'; it sounds like a normative notion based on his interpretation of Darwin. Our nature is x, so we ought to do things to enhance it. His lengthy and bitter criticisms of Christianity (see Anti-Christ) often focus on the thought that Christianity could never be life-enhancing and is indeed inimical to happiness when practised because of the lack of value he sees it as placing on existence in this world.
On a purely personal reading of Nietzsche, I thus think that his moral criticisms of Christianity are actually very much along the lines of Greek virtue theory. So you are right to be thinking of Aristotle and the Golden Mean as a possible alternative to some of the more gloomy aspects of what he says elsewhere. Golden Means (e.g. courage is a mean between cowardice and irrascibility) encourage us to function in the right way they help us to survive and be happy. If you think Nietzsche gets it wrong with the Apollonian and Dionysian aesthetic (roughly, hide from the absurdity in the first case, glorify it and love it in the second), there is still something powerful in the 'virtue theory' aspects of his thought a virtue is to fulfill your nature as a human.
Nietzsche also speaks of the relativity of moral values however. Whether this sits a little more difficultly with virtue theory is something I often wonder. As Zarathustra puts it:
Much that one people calls 'good' another calls 'shame' and 'disgrace'. So I found. I found much that we here name evil and there decked in purple...a table of values hangs over every people.
Note that this is not a good argument for 'irrealism' and does not mean that we should abandon ethical realism altogether. Bernard Williams claims that we cannot engage with the ethics of a Medieval Teutonic knight (say) not because his moral beliefs were necessarily false but simply because those beliefs are too remote. Modern realists like David Wiggins and John McDowell would agree with Nietzsche that if you gave up your language and conceptual scheme you would end up in chaos; but does Nietzsche (and Mackie for that matter) make the right moves? Perhaps it is the standard for realism that needs to be weakened, and that abandoning ethical realism completely is not the move to make.
Mathematicians have tried to find certainty in the world through proofs and logic. Along the way Kurt Gödel proved that mathematics would never be completely certain.
I thought one could not prove a negative. How did he do that?
'Mathematicians have tried to find certainty in the world through proofs and logic.'
Mathematicians not only have tried to 'find certainty', they have found it. Mathematicians are free to use 'proofs' and 'logic,' i.e., formal reasoning, in deriving one mathematical proposition from another and in deriving propositions from theorems. There is absolutely nothing wrong with the 'proof' that 2 + 2 = 4; 137 x 59 = 8083; that the empty set is a subset of every set; that if a load bearing surface will support a weight of 5 kg. per square cm., it will support a weight of 1kg. per square cm. And so on. Gödel's two theorems do not impinge on the possibility of such proofs and demonstrations; indeed, Gödel himself makes use of logic in arguing for his first incompleteness theorem, of which the second is a corollary. How could he not use logic here?
'Along the way Kurt Gödel proved that mathematics would never be completely certain.'
Gödel really did no such thing. Try convincing a shopkeeper that you ātdon really owe her 25 pence if you've given her 75 pence for an item that costs a Pound, or try convincing a physicist that the speed of light is not the limiting velocity in the universe because of anything Gödel 'proved.' All that Gödel proved is that for formal systems there will always be sentences whose truth is not decidable within that system. There will always be some sentence, P, such that if a system, S, is complete, the truth or falsity of P will be as a matter of logic undecidable within S. 'You can't prove me either true or false,' P might be imagined as saying. 'And if you do try, you will generate another equally undecidable sentence, P-prime and so on.' Gödel's results were damaging for Hilbert's dream of completely formalizing mathematics.
'I thought one could not prove a negative. How did he do that?'
I think that what you have in mind here is something like proving that the Abominable Snowman doesn't exist, which has nothing to do with mathematics or with Gödel. It is often said that such a 'negative' cannot be proved because there is always the chance that someday we might find such a creature. Certainly our failure to have found the Yeti so far is not a logical demonstration that Yetis don't exist, but this is a failure not of mathematics or of logic, but of exploration and discovery, if it is a failure at all.
When Leverrier 'discovered' the planet Vulcan and used it to explain the perturbations in the orbit of Neptune, he warned that it would always be unobservable because it was, from an earthly viewpoint, always behind the sun. So, how can we prove that (as we now know) Vulcan does not exist? Simply because Vulcan, the sun, and the earth, would have constituted a straight-line solution to the three-body problem, a solution that is demonstrably unstable.
Do not look for ramifications of Gödel's results where there are none.
How did the legal system in England recently come to a conclusion which gave doctors the legal right to proceed in the separation of the conjoined twins, Mary and Jody?
If this is what you'd consider a righteous moral decision, then how would one be morally aligned in any argument to refute any further influx of abortion and euthanasia requests?
In consideration of the judge's remark that "Right to life does not include the right to be parasitic upon nor malignant to the life of another"; in more realistic terms, What form of life upon this planet is not either parasitic or malignant to another? And even better, What does mutation now become if the claims of Darwin are correct in relation to it being the paramount process in evolution?
I gather from the newspaper that it would be medical negligence to deny the twin who would be able to survive as an individual a chance of life. The other twin, the "parasite" (a horrible way to describe a potential individual!), would not have survived alone and would have caused the death of the one with a chance of survival. If nothing had been done, both would have died and this would mean that the doctors who could have allowed one to survive would have been negligent. It is not the case that there were two individuals involved, since the parasitic twin could not have survived alone. Given that the parasitic twin was not an individual because she could not survive alone, it is questionable whether this was killing her rather than protecting the stronger twin who is an individual in the sense that she can survive alone.
The legal decision isn't a "righteous moral decision". It is practical and protects the interests of those concerned, and those concerned are individuals; i.e. the twin who as an individual can survive alone, and the doctors' professional interests (the doctors, if they did nothing, would have allowed the death of an individual). The parasitic twin did not have interests which could be taken into account. If there was "righteousness" in this case it was on the part of the parents and religious objectors who saw this as murder. In the eyes of the law, you cannot murder a thing that is not an individual, not a person.
This has nothing to do with abortion and euthanasia because in both these cases the death of the individual is involved.
Surely, Darwin believed in the survival of the fittest. In the case of the Siamese twins the fittest one would not have survived without medical intervention! Siamese twins, in their duality, are not fit. There is a distinction between positive mutation and its converse. In evolutionary terms, Siamese twins are not a positive mutation with survival expectations. But at least some survival is possible due to medical science.