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John asked:

Precisely what is wrong with Zeno’s Achilles and the Tortoise argument?

Answer by Craig Skinner

Only some 200 words of Zeno survive. We rely on later commentators such as Aristotle and Simplicius. The latter first called Achilles’ opponent the Tortoise.

Zeno was a pupil of Parmenides, and the 4 paradoxes of motion (Achilles, Dichotomy, Arrow, Stadium) attempt to show that motion is impossible in line with the nothing-changes view taught by the great man.

Since motion clearly is possible, indeed actual, there must be something wrong with the arguments as you suggest.

I will briefly outline the Achilles and the Dichotomy, which are logically equivalent, and then suggest how they might be refuted.

The Achilles:

Achilles (A) is a good runner. He sportingly gives his slower rival, the Tortoise (T), a start. The race begins. By the time A reaches T’s start point, T has moved on to a new point. By the time A reaches that new point, T has moves again to a further point. By the time A reaches that further point, T has again moved ahead, and so on endlessly. A can never catch T.

The Dichotomy:

Version 1: To travel any distance, I must first reach the halfway point. Then I must reach the halfway point of the remainder, then the halfway point of the new remainder, and so on endlessly. I can never complete the journey.

Version 2: To travel any distance, I must first cover half the distance. To do this I first have to travel half of that half (first 1/4 ). Before that, half of that quarter (first 1/8), before that, 1/16, and so on endlessly. I can never start the journey.

The paradox is not that we must travel an infinite distance, or for infinite time. Clearly, knowing the speeds of A and T, and the length of T’s start we can easily calculate where/ when A catches T, or when the Dichotomy runner completes the run. The paradox is that an infinite number of actions (tasks) seems necessary — A has to pass every one of the unending sequence of points where T once was.

What’s wrong?

To refute the argument we must deny at least one of its 3 presuppositions, which are:

  1. In travelling a distance we must cross each and all of the intervening points.
  2. A line consists of an infinity of points.
  3. It is impossible to complete an infinite series of actions (tasks).

Aristotle denied 1., saying a line can’t consist of points, they have no size, whereas a line has. A point is potential, becoming actual only if we divide the line there. The paradox invites us to repeatedly divide the line at an infinity of potential points, but A does not have to touch an infinity of actual points to catch T.

Others deny 2., saying a line doesn’t consist of an infinity of points, rather space is not continuous but consists of tiny discrete units (quantized). In covering a distance we traverse a finite number of  space quanta. Motion is jerky but this is undetectable due to the fantastically tiny size of the quanta.

Yet others deny 3., saying that an infinity of tasks is possible. This is a subtle business, bringing in Aristotle and Dedekind cuts, and dealing with it would make this answer too long (ask me if you’re interested).

After 2500 years there is still debate, and no closure, especially about 2. and 3.

Some modern mathematicians offer as a solution that that the time/ distance till A catches T is the (finite) limit of an infinite convergent series (1/2 +1/4 +1/8 + etc). But this simply tells us what Zeno already said, that the distance is finite, just infinitely divisible, and doesn’t explain how we complete the task.

I hope this helps.

Andrew asked:

When, if ever, should a terminal patient’s right to be told the truth about their condition — that they are dying — be overridden?

Answer by Craig Skinner

I dont think a patient of sound mind who asks for the truth should be lied to.

As a medic, I would say medical ethics revolves around 4 principles:

  • beneficence (do good)
  • non-maleficence (do no harm)
  • autonomy (patient’s right to truth and to decide)
  • justice (fair sharing of limited resources)

Your question relates to autonomy. Relatives often say the patient shouldn’t know the truth because she couldn’t cope with it — she would give up, wouldn’t fight any more. So, they say,  autonomy clashes with doing no harm, the latter should prevail, I should lie. Whilst I always take account of relatives’ views, I am not bound by them, and I have never agreed with this view. It usually means it is the relative who cant cope, won’t know what to say if mum starts talking about death. And if we go along with it, the outcome is bad: the patient soon realizes she is dying anyway, but can’t talk about it because her family don’t want to, and so she is alone and isolated just when she most needs family support. So, I explain all this to the relative, and tell the patient the truth.

Two caveats.

First, a patient’s right to the truth doesn’t mean I have a right to ram the truth down her throat, as it were, when she doesn’t want to talk about it. I am guided by the patient’s wishes. So, having examined her and got back test results, I will start in nonspecific terms — there’s a shadow on your x-ray we need to investigate further, say. Then, “Is there anything you want to ask?”, and now we find out how much the patient wants to know, at this stage anyway. Some say no, that’s fine, lets get on with the tests, others ask if it could be cancer. And so it goes as we investigate further. If it turns out to be a fatal condition for which little can be done, I will say so if asked directly, otherwise will talk of treatment which may help for a time. If a patient has, or probably has, a very serious condition, but one which may be curable, and decides to bury her head in the sand, keep clear of doctors and hope for the best, then I will make sure she knows the serious position even though she did not ask me to spell things out.

Second caveat. Docs know only too well that they often get it wrong, so we must always consider very carefully before pronouncing an illness terminal or being too exact or sure about life expectancy. Second opinions may be a good idea.

I hope this is helpful to you.

Seymour asked:

Who, in your opinion, is the most important philosopher of all time?

Answer by Craig Skinner

In my opinion, Aristotle.

To see why, read my article at:

Alex asked:

What is Descartes Methodological Doubt, and why does he insist/want to use it? What is the one “true” idea that is derived from this doubting? What is his proof for God (the trademark version ie the causal argument), and more importantly (ie specifically),what is the problem with it – why does his argument fail – please specify in detail this problem?

Answer by Craig Skinner

Descartes was tired of scholastic philosophy, viewing it as hairsplitting logic, nitpicking metaphysics,  postulated occult powers, preoccupation with theological matters such as transsubstantiation and the holy trinity, and acceptance of Aristotle’s creaky cosmology and physics. On the other hand, he was enthusiastic about the new “mechanical philosophy” (physics), and thought such empirically-based science, coupled with mathematics, might yield more understanding and also control of nature to our benefit.

So he wanted to start from scratch and “build anew from the foundations… to establish… firm and permanent structure in the sciences”.

He says that many of his former beliefs were false or doubtful. So a new foundation had to be a belief that can be relied on as absolutely certain. How to arrive at such a belief? The first Meditation spells this out – his famous method of doubt.

He says he will doubt everything that can conceivably be doubted. This includes all beliefs based on the senses and all beliefs based on reason.

As regards the senses, we can doubt them because

(a) they sometimes deceive us, a commonplace observation.

(b) when I dream I think I am awake and doing things. So, at any time when I think I am awake, I might really be dreaming, and all the assumed external world an illusion.

(c) a malicious demon could put ideas in my mind suggesting an external world when no such thing exists.

As regards reason, he feels that although we think we know, say, 2+3=5 with certainty, again a malicious demon could trick us so that every time we add these numbers we make a mistake, thinking the sum is 5 when it isnt.

He concludes that the heavens, earth, colours, figures, sounds, all external things including his own body may be illusory.

What then is left as his foundational belief, his “one true idea” as you put it?

He tells us this in the second Meditation. He says that if he is doing all this doubting, he must be thinking, and so must exist. “I think therefore I am” (“cogito ergo sum”), as it is famously worded elsewhere in his writings.

Of course by itself this doesnt get him far. The world might consist of just one thinking thing, himself. To guarantee the rest of the world he needs the existence of the guarantor, God, a non-deceiving God at that, to be another certainty. He cant have this of course. First, to say that his clear and distinct idea of God can be relied on because the idea was implanted by God, is to beg the question. Secondly, no proof of God’s existence is sound.

But he has a go. He seems to think that God’s existence is readily evident to any diligent meditator, and that arguments are just heuristic devices to help the slower meditator to the almost self-evident truth that God’s existence is known by clear and distinct perception. So he doesnt set out his arguments formally with premises and conclusion. Also he uses a lot of scholastic terms. We meditators have to work hard to penetrate his arguments.

You ask about the causal argument (Meditation 3)

A fair reconstruction is as follows:

P1. I have the idea of a most perfect (omnipotent, eternal, infinite, benevolent) being (God).

P2. A cause must be at least as great (real) as its effect.

Conclusion: the idea of God cant come from (imperfect) me. Its cause must be God (or, impossibly, greater). God exists.

The argument is valid. To declare it unsound we therefore need to attack the premises. Both are vulnerable to attack.

Objections to P1:

(a) a finite mind cant have an idea of infinity (Gassendi’s view in 5th Objections). Descartes replied that we can. It’s our understanding that’s limited, not the the thing of which we have (limited) understanding. I agree.

(b) the meditator can claim not to have this idea. Descartes assumes we all have the same (God-given) innate ideas. We simply dont need to accept this. I dont.

Objections to P2:

P2 isnt easy to grasp. The discussion is in technical, scholastic terms. Two types of reality (being) are distinguished regarding ideas. The existence of an idea (its formal reality) is distinguished from its content (its objective reality). “Objective” refers to the object contained in the idea, rather like the modern use of “subjective” – it refers to the tree (say) in the mind not the tree in the garden. The notion of degrees of reality is then introduced. Ideas all have the the same degree of formal reality, all being mind states, but they differ in degrees of objective reality – lowest in a mode (modification of a substance eg  colour), intermediate in a finite substance, highest in an infinite substance. P2 therefore expresses the Causal Principle that the degree of formal reality of the cause must be at least as great as the objective reality of the effect, leading to the conclusion that an idea whose content (objective reality) is infinite (such as Descartes’ idea of God) cant have its cause in a finite being (with less than infinite formal reality), such as me, only in God, so that God exists.

First objection: the idea of God can come from me – having some degree of perfection, I can posit higher and higher degrees indefinitely (Mersenne’s view in 2nd Objections). I agree.

Second objection: animals and plants (greater) derive from inanimate causes (lesser), Mersenne’s view in 2nd Objections. I agree.

Third objection: P2 is just an assertion. No evidence is given for it. I  would generalize Mersenne’s objection to say that simple things plus simple rules can lead to complex things eg laws of nature plus simple initial conditions in our universe has yielded, atoms, compounds, galaxies, life and minds, so that the Causal Principle is false. To assume that a finite mind needs an infinite mind to cause it begs the question as to God’s existence.

In short, the first premise can simply be denied, the second premise is false and question begging.

In the end, Descartes doesnt get further than the cogito, so that, far from establishing a new foundation, his philosophical legacies are the idea of scepticism, and, arising from his idea that I am essentially a thinking thing, the notion of mind -body dualism. Scepticism is a commonplace now in philosophy, science and everyday thinking – we all accept that certainty is only to be found in logic and mathematics. Dualism displaced Aristotle’s substance/form view, but has proved sterile, and the superiority of Aristotle’s view is increasingly recognized.


Frem asks:

What do you call ‘mental sanity’? Would anyone dare to answer?

Answer by Craig Skinner

Here’s an answer, although I dont feel daring.

“Sanity” means “health” (Latin sanus=healthy) so that “mental sanity” means “mental health”. However,the term is rarely used when speaking of physical health, so that “sanity”/”insanity” refer to mental health/disease (and some physical diseases eg syphilis, can also produce mental disease).

The notion of “insanity” is narrower than “mentally ill” Most mentally ill people are not insane. “Insanity” implies that the disease is bad enough to cause loss of reason, inability to tell right from wrong, and is a term used by lawyers rather than doctors these days, as “not guilty by reason of insanity” is a common defence to a murder charge. Among doctors and nurses, the terms “delirium” and “psychosis” are respectively used for fleeting and persistent loss of reason. Delirium can be due to feverish illness, drugs or alcohol, and psychosis is usually due to schizophrenia or severe bipolar disorder.

In short, sanity implies mental health, or mental illness insufficient to cause loss of reason. The term is often used loosely to express praise in other contexts (eg sane policies).

There is a tendency for lawyers to extend the insanity defence beyond the conditions I have mentioned, to include, for example, genetic variants known to be associated with aggression, or people with damage to the amygdala causing lack of emotional response to another’s suffering, the “my brain made me do it” defence. One difficulty for the defendant here is that if the defence be accepted, and nothing can be done to change the brain, he is liable to be locked up for at least as long as if he plead guilty.

I wonder if your mention of anyone “daring” to answer, reflects the view that there is no real sanity/insanity distinction, just labelling by the regime in power of their views and those expressed by opponents. It is true that some regimes have labelled troublesome “dissidents” insane and locked them up, and this still goes on. But this is abuse of psychiatry, and shameful activity by doctors involved. It doesnt mean that mental illness is an arbitrary social construct. Tell that to my sister with schizophrenia or my cousin with bipolar disorder whose lives were ruined by their illness, although greatly helped by medication and ECT.


Kenneth asked:

Does there exist a philosophical term for a general “Hate/ disgust for the contemporary society/ modern world”.  I think it’s becoming quite widespread. I would myself like to suggest: Pan-misanthropy.

Answer by Craig Skinner

You clearly dont have in mind, say,  the desperation of ordinary people in contemporary Syria, or those starving to death in poor countries.  Rather, an attitude of people in stable societies who can count on a roof over their heads, clean water  and enough to eat.

I dont think a negative view specifically of the modern world is specially common in philosophers.

Of course, since time immemorial, the older generation has thought the world is going to the dogs, morals are getting lax, respect for elders has gone, violence is on the rise, community spirit is gone etc. This is usually coupled with a rosy view of their young day when we all helped each other and had no need to lock our doors. The word that springs to mind here is “nostalgia”. The facts are against these oldies. All research shows the world to be a safer, more healthy place now than it ever was. If the level of violence, robbery and murder in Oxford was what it was in medieval times or in a typical stone-age society, I’d be frightened to go there for a pub lunch. Never mind disease, early death, oppression and lack of civil liberty in the good old days.

Among philosophers, despair is sometimes expressed, not about the modern world, but about the perennial human condition. Bertrand Russell, reflecting on the vast, empty, purposeless universe and future extinction of the solar system revealed by science, famously said in 1903:

“Only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built.” (‘A Free Man’s Worship’)

Despite this he went on to live a very long enjoyable, productive and interesting life.

Another famously pessimistic philosopher who enjoyed a long and comfortable life was Schopenhauer.

And then we have the existentialists expressing “angst” and “ennui” about the human condition, usually while drinking coffee in upmarket cafes or debating in nicely-furnished drawing rooms.

Existentialist joke:

Scene: family car en route to holiday destination.

Small boy: Dad, Dad! I feel ennui.

Father: Well, I’m not stopping. You should have reconciled yourself to the absurdity of life before we got into the car.

Dont trust philosophers bearing despair. Dont join the panmisanthropists, as you term them. If you feel it coming on, think again. You can make a difference.



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