Gottfried Leibniz held that no two distinct objects can have exactly the same properties.

But, Max Black asked, “Isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron, had a diameter of one mile, that they had the same temperature, colour, and so on, and that nothing else existed. Then every quality and relational characteristic of the one would also be a property of the other.”

(We might object that the two spheres are discernible because they occupy different positions in space, but this is true only if we have a third object to use as a reference point in establishing the “objective” location of each sphere. If the only things in the universe are the two spheres, then their positions can be established only in relation to each other, and these would always be identical — for example, each sphere is five miles from another sphere.)

“Now if what I am describing is logically possible,” wrote Black, “it is not impossible for two things to have all their properties in common.”

Sort of vaguely related:

On a visit to Princeton, E.H. Moore began a lecture by saying, “Let a be a point and let b be a point.”

Solomon Lefschetz asked, “But why don’t you just say, ‘Let a and b be points’?”

Moore said, “Because a may equal b.”

In Indiscrete Thoughts, Gian-Carlo Rota writes, “Lefschetz got up and left the lecture room.” Rota calls this “an example of mathematical pedantry.”

(Max Black, “The Identity of Indiscernibles,” Mind 61:242 [April 1952], 153-164.)

CUNY philosopher Noël Carroll notes, “It is a remarkable fact about the creatures of horror that very often they do not seem to be of sufficient strength to make a grown man cower. A tottering zombie or a severed hand would appear incapable of mustering enough force to overpower a co-ordinated six-year-old. Nevertheless, they are presented as unstoppable, and this seems psychologically acceptable to audiences.” Why is this?

(From his Philosophy of Horror, 1990.)

Shozo Hayama spent 50 years collecting jinmenseki, rocks that resemble human faces, before founding the Chinsekikan (“hall of curious rocks”) in Chichibu, Japan, two hours northwest of Tokyo.

Inside are 900 such rocks, from Elvis and Jesus to E.T. and Nemo from Finding Nemo. The only requirement is that the effects occur naturally, without human artifice.

Hayama passed away in 2010, but his daughter keeps the museum running today.

(Thanks, Randy.)

In 1967, a foot powder was elected mayor of a town in Ecuador.

During municipal elections in Picoazá, an urban parish of 4,000 people on the Pacific coast, a foot deodorant company called Pulvapies offered the advertising slogan “Vote for any candidate, but if you want well-being and hygiene, vote for Pulvapies.”

That’s innocent enough. But “on the eve of the election, the company distributed a leaflet the same size and color as the official voting papers, saying: ‘For Mayor: Honorable Pulvapies,'” reported the New York Times.

The result was that, when the votes were counted, the foot powder had been elected by a clear majority. Dozens of defeated candidates threatened to sue the pharmaceutical company that ran the ads, leaving the national election tribunal to sort out the mess. I haven’t been able to learn the outcome. It’s a shame — that’s one candidate that would have served both left and right.

(Thanks, Ethan.)

In the Pisco Valley on Peru’s Nazca Plateau is a band of 5,000 to 6,000 holes, each about 1 meter in diameter and 100 centimeters deep. The band, which averages about 20 meters in width, starts at the edge of a valley and extends about 1.5 kilometers up a hill understandably known as Cerro Viruela, or Smallpox Hill. (You can see its extent in Google Earth.)

No one knows who dug the holes or why. They’re circular and lined with stone, resembling pits found elsewhere that serve as resting places for mummies. But these are empty. Possibly they were designed for storage by users of the Inca road system, or possibly they were used to measure quantities of produce owed as tribute to the Inca state. Archaeologists are still investigating.

In Plymouth, Tobago, lies a tomb with an enigmatic inscription:

Within these walls are deposited the bodies of Mrs. Betty Stiven and her child. She was the beloved wife of Alex B Stiven to the end of his days will deplore her death which happened upon the 25th day of Nov. 1783 in the 23rd year of her age. What was remarkable of her, she was a mother without knowing it, and a wife without letting her husband know it except by her kind indulgences to him.

Theories abound, but there’s no consensus as to its meaning.

What is sound? We’re told that it’s a wave traveling through a medium, but we don’t hear sounds as existing in the air; we hear them as located at the place where they’re generated. Is sound a quality of an object or of the surrounding medium?

“Listening to the birds outside your window, the students outside your door, the cars going down your street, in the vast majority of cases you will perceive those sounds as being located at the place where they originate,” writes St. Joseph’s University philosopher Robert Pasnau. “But if sounds are in the air, as the standard view holds, then the cries of birds and of students are all around you. This is not how it seems.”

Properly speaking, then, where should we say a sound is located? At its point of origin, or filling the air?

(Robert Pasnau, “What Is Sound?” Philosophical Quarterly 49:196 [July 1999], 309-324.)

There’s something beautifully useless about this: The gardens at Rousham House, in Oxfordshire, occupy only 25 acres, so landscape architect William Kent added a sham ruin on the brow of a distant hill to give the impression that the house’s landscape extended far beyond its boundaries.

Horace Walpole wrote that Kent “felt the delicious contrast of hill and valley changing imperceptibly into each other, tasted the beauty of the gentle swell, or concave scoop, and remarked how loose groves crowned an easy eminence with happy ornament, and while they called in the distant view between their graceful stems, removed and extended the perspective by delusive comparison.”

A golfer takes a swing at a golf ball. Fortunately it’s a good shot, and the ball heads for the cup. Unfortunately, a squirrel, rather dangerously positioned near the cup, kicks the ball away, thus decreasing the ball’s chance of landing in the cup. Fortunately, the ball then hits the branch of a nearby tree and is deflected into the cup.

“Question: was the squirrel’s kick a cause of the hole-in-one?” asks Australian National University philosopher Helen Beebee. “According to some philosophers’ intuitions, the answer is yes. According to others, the answer is no: the ball went in despite the kick. According to a third view, the kick was a cause of the hole-in-one and the hole-in-one occurred despite the kick.” Who’s right?

(Helen Beebee, “Do Causes Raise the Chances of Effects?”, Analysis 58:3 [July 1998], 182-190. The original example is due to Deborah A. Rosen.)