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I never understood Heraclitus' river analogy. Does it mean that we are constantly changing or changing only by degrees? Why does it say the "same" river if it is in constant flux? It seems like in the fragment "one can never step in the same river twice" that we could interpret the "step" as "never step in the same river" or as "never step into the same waters". Which is correct?

In Plato’s Cratylus, the character Socrates makes thefollowing comment about Heraclitus: “Heraclitus is supposed to say thatall things are in motion and nothing at rest; he compares them to thestream of a river, and says that you cannot go into the same rivertwice" (402a). Ever since Plato, the view that we can’t step twice intothe same river has been attributed to Heraclitus.

However,let’s consider the following two fragments about rivers that manyancient scholars regard as Heraclitus’ own words (in translation):

"On those who enter the same rivers, ever different waters flow– and souls are exhaled from the moist things" [B 12].

"We step and do not step into the same rivers, we are and we are not" [B 49a].

Inthe first fragment, Heraclitus suggests that we do step into the samerivers, even though the water in these rivers changes. The secondfragment raises interpretative problems of its own, but here tooHeraclitus speaks of the same rivers.

So how can we choosebetween the interpretation that Plato seems to give of Heraclitus, thateverything is always changing in every respect (a river is not even ariver from one moment to the next) and a less radical interpretationaccording to which Heraclitus is saying that things are always changingin at least some respect, but, for all that change, may well remainstable in at least some other respect?

Well, first it’s notclear that the position that Plato attributes to Heraclitus is evencoherent. But more importantly, it’s hard to reconcile Plato’sinterpretation with other Heraclitean fragments. Consider, for example:

"Theworld, the same for all, neither any god nor any man made; but it wasalways and is and will be, fire ever-living, kindling in measures andbeing extinguished in measures" [B 30].

Fire isclearly very volatile and is in a constant state of change, butnonetheless Heraclitus is suggesting here, it doesn’t change in respectof being fire. In fact, Heraclitus was reported by Theophrastus assuggesting that the change that an object undergoes in one respect canaccount for its stability in another respect:

"Things which have this movement by nature are preserved and staytogether because of it– if indeed, as Heraclitus says, the barley-drink separates if it is not moving" [B 125] (Theophrastus, On Vertigo 9).

Abarley drink cannot continue to be a barley drink over time, unlessit’s in constant movement. Fire can’t remain fire unless it’s inconstant movement. A river can’t remain a river, unless it’s watercontinues to flow. Or as Heraclitus says:

"Changing, it rests" [B84a].

First of all I want to say I'm sorry for my bad English. For I am Icelandic, I don't get a lot of English classes. ok My friend is always talking about "everything is a goat"; it makes a little sense to me but it is ridiculous. The opposite to everything is nothing. The statement "nothing is a goat" is not right. Isn't there some gap between everything and nothing? Can't we say "something is a goat"? I hope you answer :)

The negation of "Everything is a goat" is not "Nothing is a goat". Asentence and its negation must have opposite truth values; that is, ifone is true, the other is false. A sentence and its negation cannotboth be true and they cannot both be false. But, as I think yourealize, "Everything is a goat" and "Nothing is a goat" canboth be false: if there are some things that aren't goats and somethings that are, then the two claims will be false. So this shows that"Nothing is a goat" is not the negation of "Everything is a goat".Might the negation of "Everything is a goat" be "Something is a goat"?No, for both these claims could be true: imagine that there is at least onegoat and furthermore that everything is a goat.

(All these errors are facilitated by the false assumption that nouns like "nothing" and "everyone" function like "Harry" or "the animal in the shed" do. For more on this error, see Question 49.)

What then isthe negation of "Everything is a goat"? It's "Something is not a goat."If this claim is true then "Everything is a goat" is false. And if it'sfalse — false that there's at least one thing that isn't a goat — thenthat must be because everything is a goat. Finally, what is the negation of"Nothing is a goat"? It's "Something is a goat", for these sentencesalways have different truth values, that is, if one is true the otheris false.

Can 2+2 equal ANY other answer than 4?

It's hard to imagine how I could be convinced to doubt that 2+2 = 4.Whatever argument you gave me, there would surely be some assumption orstep of reasoning in it that was less obvious to me than that 2+2 = 4.Faced with the decision of denying that 2+2 = 4 or of rejecting somestep in your argument, it seems it would always be more rational for meto do the latter.

Do you now want to object: "I'll grant you itwould always be more rational for me to believe that 2+2 = 4 — butstill, couldn't it be false!?"

Isn't everything relative? For example, mathematics was invented by man — did it exist before man invented it?

You would have thought that we would have worked out by now whethermathematics is a human invention or not. We haven't. There is still aheated debate between those who believe that mathematics describes arealm of entities (numbers, sets, functions, etc.) that exist quiteindependently of us and those who believe that the mathematical worldis in some sense constructed as a result of human activity. This is thecontrast between platonism and constructivism that has been touched onelsewhere here.

The fact that we have eyes is proof that a consciousness was present, prior to our creation, which was aware of the existence of light. And while this truth does not confirm the existence of a God, doesn't it verify an intelligence older than our own?

There are many simple creatures that are sensitive to light: Theywill move toward it or away from it. I believe there are some suchcreatures that are single-celled. In any event, such creatures are sosimple that it's hard to think of them as being "conscious" at all, andbiologists can tell a very convincing story of why these creaturesbehave as they do. The explanation rests upon the fact that there somechemicals that react to light: They are "photo-sensitive". There areother, slightly less simple creatures that have very primitive sorts of"eyes" that are simiilarly sensitive to light, but the reaction ofthese creatures to light is more complex, because these creatures haveprimitive nervous systems. And between those creatures and cats, birds,fish, and human beings are all kinds of other creatures with "eyes" ofvarying complexities. It is, perhaps, hard to imagine how exactlyorgans with the complexity of eyes evolved—for one thing, the time scale is immense—but one can see in thedifferences among the species some indication of how it might havehappened.

Ican imaginesomeone's saying that the existence of photo-sensitive chemicals"proves" the existence of a consciousness aware of the existence oflight, but surely there is nothing here that approaches "proof".Rather, someone who makes this kind of remark regards existence ofphoto-sensitive chemicals as a manifestation of God's creative genius,and I would not for a moment question that kind of expression of faith.I deeply respect it and often find myself moved in that direction: Everything is a manifestation of God's creative genius.But this kind of remark has to be understood as an expression of faith. To regard it as anything else is to trivialize it.

Could God have made pi a simpler number?

There are a few distinctions we need to make before we can addressthis question. The work we need to do to make these distinctions is anice example of how philosophy can help us be clearer about whatquestion we're asking.

Ask first: Could π have beena different number? Most philosophers today would answer that it could nothave been, just as Richard Nixon could not have been someone other thanRichard Nixon. The expression "π" is a name of a certain number, andthat number is whatever number it is; itcould not have beena different number. That this is the right thing to say is somethingthat has been widely appreciated only for about the last thirty yearsor so, as a result of groundbreaking work by Saul Kripke.

If that is right, then God could not have madeπ anything other than π, for then π would have been something otherthan π, which it could not have been.

That'sprobably not the intended question, though. Rather, the intendedquestion was probably: Could God have made it the case that the ratioof a circle's circumference to its diameter were something other thanπ, say, 3? Do not say that, in that case, π would have been3. Perhaps we would then have used the expression "π" to refer to 3,but that's different. π is the number that is actually theratio of a circle's circumference to its diameter, and in the imaginedcircumstances the ratio of a circle's circumference to its diamaterwould not have been what it actually is, that is, would not have been πbut would have been some other number, 3. (That's all Kripke, again.)

Ifthat's thequestion, then we need to ask: Could the ratio of a circle'scircumference to its diamater have been other than what it actually is?One other clarification: The ratio of a circle's circumference to itsdiameter will always be π only if we are assuming that the underlyinggeometry is Euclidean. There are plenty of non-Euclidean geometries,and modern physics tells us that the geometry of space is, in fact, notEuclidean. It follows that the ratio of the circumference of an actual circle in actualspace to its diameter is not usually π, though it is usually close,because space is generally quite close to being Euclidean. (What is theratio? It varies: There need be no fixed ratio in non-Euclideangeometries.) So, in a sense, if God created the world, then God didmake a world in which the ratio of a circle'scircumference to its diamater isn't π, and perhaps God could have madea world whose geometry was Euclidean, in which case God could have madea world in which the ratio of a circle's circumference to its diamaterwas always π. But again, I take that not to be the question beingasked, though it's a question worth asking.

The question I take to be at issue is: Could the ratio of a circle'scircumference to its diamater, in a Euclidean space, have been other than what it actually is? Hereagain, most philosophers would answer "no", on the ground thatmathematical facts are necessary, and the fact that the ratio of acircle's circumference to its diamater is π is a mathematical fact ifany is. If so, then God once again could not have made the ratio of acircle's circumference to its diamater, in Euclidean space, something other than π, since it could not have been other than π.

So, with that all said, see question 26,as Jyl suggested, for some discussion of the question how God'somnipotence is supposed to be related to questions of necessity.

When people speak of "morality", why does it always stem from a divine being? Why can't morality stem from reason?

I've often wondered whether anyone actually thinks that God's authority establishes moral principles. Of course, people say so. But when one asks such people why we ought to conform our behavior with the Divine Pronouncements, the answer, if it isn't to concede a moral standard independent of God's will, is usually that, otherwise, one will be cast into darkness with wailing and gnashing of teeth. But if so, then these aren't moral principles at all. They are arbitrary rules enforced through violence and fear.

To say so isn't to say that, for a believer, God need have nothing to do with morality. That God isn't the source of moral principles doesn't imply that God isn't an authority on moral truth in the sense that someone can be an authority on, say, mathematics. (Interesting ambiguity there.) It does imply, however, that if it is wrong to covet one's neighbor's ass, then there has to be a reason other than God's saying so that it's wrong to covet one's neighbor's ass.

Why is stupidity not painful?

Why is stupidity not painful? Huh? It is painful. Every time I do something stupid, I feel the searing pain, I wince like a dog hit by a car. Really. This is supposed to help me not do stupid things, like putting my hand in the flame. Doesn't work much, does it? We continue to do stupid things and feel the pain. So much the worse for both Intelligent Design and Natural Selection.

Is happiness (eudaemonia) possible?

The answer to this question will depend on your conception ofhappiness. Not only do different philosophers differ in their viewabout what constitutes happiness (go here),they also have different views about how much of anything thatcontributes to happiness is required before one counts as happy. Thinkabout it this way. On different philosophical conceptions, differentthings count as good or bad for us. To the extent that we have the goodthings, we are better off. To the extent that we lack the good thingsand possess the bad things, we are less well-off. On a scale from very,very badly off to very, very well-off, there is a point at which onecounts as happy or eudaimon– namely, when one has enough ofwhat is good (and lacks enough of what is bad) to count as living a good life (that is, good foroneself), or as flourishing. Depending on how high on the scale oneplaces happiness and depending on the difficulty of achieving theconstituents of happiness, it will be more or less easy to becomehappy. If one sets the bar extremely high or if the constituents ofhappiness are extremely rare and difficult to attain, then it may wellbe impossible for humans ever to be happy; they can merelyapproach happiness.