This article is republished from The Conversation under a Creative Commons license. Ancient Greek philosophers used paradoxes for all sorts of reasons, from sharpening their dialectical skills and showing philosophical opponents were talking nonsense to serious philosophical inquiry – but also for fun. Some paradoxes were lethal. Philetas of Cos’s epitaph tells us he died tormented by the “liar paradox”. And according to one biographer, Diodorus Cronus killed himself in 284 BC after failing to solve a paradox put to him by fellow philosopher Stilpo of Megara. These stories are fanciful, but they point to something maddeningly true about paradoxes: there cannot be a single, obvious solution. Sometimes there is no good solution. Sometimes there are too many good solutions. Paradoxes point to conceptual glitches or bugs. How to fix these bugs, or whether they can be fixed, is rarely obvious. The three paradoxes that follow are some of the best-known examples from Ancient Greece. 1. The liar paradox “This sentence is false.” Philosophers call that the “liar sentence”. Is it true? If you say “yes, the liar sentence is true”, then things are as it says – yet the liar sentence says it is false. On the other hand, suppose you say “no, the liar sentence is false”. This means things are not as the liar sentence says. But this is exactly what it says, so in this sense the liar sentence is true. In short, there are good reasons to say both that the sentence is true and that it is false. Yet no sentence can be both true and false. This paradox was invented by the philosopher Eubulides of Miletus, who was famous for his paradoxes, in the 4th century BC. His own formulation has been lost, and what I give here is my reconstruction. The liar paradox alienates us from everyday notions like truth, falsehood and self-referential language. But it also calls into question the idea, presupposed by question-and-answer dialectic (dialogue between people holding different points of view about a subject), that every question can be answered “yes” or “no”. It seems there are good reasons to answer both “yes” and “no” to some questions. Some philosophers have concluded this means that both “yes” and “no” are good answers to the question “is the liar sentence true?”. They call this a “glut” of good answers. To apply the liar paradox to your life, when you ask or are asked questions, ask yourself: is there more than one right answer? 2. The horns paradox Have you lost your horns? If you answer “yes”, you must have had horns that you have now lost. If you say “no”, then you have horns that you have not lost. Either way you answer, you suggest you had horns – but that is clearly false. Questions are a key part of philosophy. But they’re also key to how we get information from other people. The liar paradox highlights that some questions have a more than one good answer. The horns paradox highlights another problem – questions have presuppositions. If I ask “have you stopped eating meat?”, then I presuppose you no longer eat meat, but that you used to. These questions look like they should have a “yes” or “no” answer, but in fact there is a gap because we could deny the presupposition. When you ask questions, or are asked questions, first ask yourself: what is being presupposed? 3. The sorites paradox Here are 10,000 grains of sand. Do I have a heap? Yes, of course. I remove a grain, so now I have 9,999 grains. Do I have a heap? Yes. I remove another grain so I have 9,998. Do I have a heap? Yes. Losing a single grain does not affect whether I have a heap. But reiterating this 9,997 more times, I have one grain. That should be a heap, but of course it is not. You could argue both that one grain is a heap, and that it is not. But nothing can be both a heap and not a heap. Another of Eubulides’ greatest hits, the sorites (the “heaper”), uses a heap as an example. But it also heaps question upon question. This paradox challenges us because some concepts have fuzzy edges. When we plug these fuzzy concepts into a question-and-answer dialectic, there are clear yes-or-no answers at the start and end of the sequence. Ten thousand grains is clearly a heap and one grain clearly is not. But there are no clear yes or no answers for some region in the middle. The liar paradox suggests there might be gluts of good answers to yes or no questions; the horns that there might be gaps, where neither “yes” nor “no” is the correct answer. But the sorites shows that there may be gaps that come and go, with fuzzy-edged concepts. But how many of our concepts have fuzzy edges? And do fuzzy concepts track a fuzzy world? Paradoxes highlight glitches in commonplace, everyday activities: asserting truths, asking questions, and describing objects. Thinking carefully about this is fun, certainly. But paradoxes should also make us sensitive to whether every apparently good question has exactly one good answer: some questions have more, some have none. Matthew Duncombe is Associate Professor in Philosophy at the University of Nottingham.

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To hear older generations tell it, everything was better in the past. Gas cost a few cents a gallon; children respected their elders; toilet paper came with 650 sheets to a roll, and the only thing you had to worry about was the constant existential threat of nuclear apocalypse looming over your head.Now, chances are at least one of those things was news to you, and we’re betting it’s not the gas or the nuclear war. So, to answer your question: yeah, toilet paper used to come in 650-sheet packages. If that’s not hitting you as remarkable, though, here’s the context: today, a regular roll of Charmin sold in the US has just 56 sheets per roll.The incredible disappearing toilet paperThanks to Mark Dent over at The Hustle, we actually have quite a detailed picture of the decades-long toilet paper shrinkflation process. In the 1970s, he writes, “Charmin’s regular roll had 650 sheets of single ply toilet paper […] By 1975, the roll shrunk to 500 and then to 400 in 1979.”But “Charmin was far from done,” he continues. “By 1986, the sheet count had dropped to 380. On eBay, I found nearly identical 1988 Charmin packages – one contained 300 single ply sheets per roll and the other had 280.”Not only are toilet paper manufacturers offering fewer sheets per roll, he points out, but those sheets are also smaller than they used to be. A Charmin regular roll in 1966 used to be made up of square sheets of side length 4.5 inches (11.43 centimeters), he reports – measure one yourself today, and you’ll find it a paltry 3.92-by-4 inch rectangle (9.96 by 10.16 centimeters).Even adjusted for inflation, that results in a price increase of 700 percent per square foot since the 1960s.And, lest you think we’re picking on Charmin in particular, other manufacturers have been just as sneaky. You might think a brand like Scott 1000 would be immune from this kind of shrinkflation – after all, its very name is a promise that each roll comes with that many sheets. And yet long-term analysis by Edgar Dworsky, founder of ConsumerWorld.org, has found that even they have shrunk, with the weight of a standard four-pack going from 32.2 ounces (913 grams) in the past to 23.6 ounces (669 grams) today.Why are toilet paper rolls so much smaller than they used to be?So, what’s behind this egregious shrinkage? In an effort to figure out the root causes, Dent spoke to TTO-BMA, two affiliated companies that track, forecast, and analyze the wood pulp market. As the “single most important ingredient for toilet paper,” Dent explained, there’s no greater driver of the intrinsic cost of a roll than the price of wood pulp.Unfortunately, that price is notoriously volatile, it turns out. That wasn’t always the case – before the 1980s, it was pretty stable – but these days, thanks partly to the emergence of China as a global poopin’ superpower (pooperpower?) and partly to our old friend climate change, the price of toilet paper wood pulp can rocket from just over $600 per metric tonne to more than $900, down to around $750, up to $1,000, and all the way back to $600 again, all in the course of just three years – specifically, 2021-2024, in case you thought those numbers were for illustrative purposes only.For major brands who want consistent quality, there’s no way around this kind of volatility – or at least, that’s what the companies say. Of course, it doesn’t really explain why toilet roll brands in other countries have been less affected by this specific type of shrinkflation: in the UK, for example, the equivalent of Charmin, Cushelle, is still sold with 270 sheets per roll, while other brands boast anywhere from 170 sheets per roll to 380 depending on the brand.The trouble is, US brands are designed to account for a level of snobbery around what Americans use to wipe their poopy holes. The ratios of hard- to soft-wood pulp are slightly different in the US than elsewhere, with around 30 percent comprising the more expensive softwood pulp, TTO-BMA’s D'arcy Schnekenburger told Dent – that’s three times as much as other markets’ standard 10 percent. The reason for that, is to meet a “higher expectation for strength,” he explained – though he adds that “consistency both in their operations and consistency of product are more important than anything else.”“They won’t even change the supplier of their softwood if they can help it,” he said.A Tissue IssueAnd, you might think, so what? So toilet paper is getting smaller and more expensive; that’s the price of a comfy butthole baby! But all this devotion to “consistency” has a much more troubling consequence: it’s destroying some of the most ecologically important areas in not just North America, but the entire world. “Now, more than ever, it is clear that the impacts of manufacturing single-use tissue products from forest fiber are not only severe but also avoidable,” argues the Natural Resources Defense Council’s 2023 Issue With Tissue Fifth Edition report. “Companies know that there are more responsible ways to create tissue products than using forest fiber – namely, using recycled materials and responsibly sourced alternative fibers – and many have already embraced these solutions in their product lines,” it says. “Yet the largest, most powerful tissue companies have failed to adopt these more sustainable sourcing practices. Instead they remain entrenched in a destructive ‘tree-to-toilet pipeline’ model that continues to come at an extreme cost to Indigenous communities, the climate, threatened species, and forests like the boreal in Canada.”Luckily, this latest in the series of reports has found that consumer behavior is shifting, with more people prioritizing sustainability in their buying habits – and, in turn, more brands offering sustainable toilet tissue products. But if you’re hoping to match brand loyalty with environmental mindfulness, you may be out of luck: “Of the toilet paper brands surveyed in the tissue scorecard’s fifth edition, half of the brands that received A and B grades were launched within only the past five years,” the report notes – while “the ‘Big Three’ U.S. tissue producers – Procter & Gamble, Kimberly-Clark, and Georgia-Pacific – make their flagship household tissue brands almost exclusively from forest fiber, consistently earning them failing scores.”What can we do about it?While the report has much to say about what policymakers and corporations should be doing to mitigate the damage, it can often be hard to see what difference we can make as individuals. But in fact, the authors write, “consumers have enormous power in helping steer the market toward greater sustainability.” So, you could, as 500,000 people recently did to Proctor & Gamble (the company behind brands such as Charmin, Bounty, and Puffs), petition corporations to add sustainable options to their lineups, the report suggests – or, failing that, ask local store managers to stock more of those options. There are also more everyday changes you could make: actually buying more sustainable options, including tissue made with recycled content, and simply using less where you can.The best part: not only will it help the environment, but it will also save you money. After all, with the way this shrinkflation is going, if we don’t start changing our tissue habits, then we’re literally just throwing money down the toilet.

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The Department of Homeland Security's record of obstructing its Office of Inspector General could hamper the OIG's investigations of the July 13 attempted assassination of former President Donald J. Trump, two lawmakers warned Aug. 20. In a letter to DHS Secretary Alejandro Mayorkas, U.S. Sen. Chuck Grassley (R-Iowa) and U.S. Rep. Barry Loudermilk (R-Ga.) rapped DHS for not cooperating with the Office of Inspector General and for insisting on heavy redactions to reports issued by DHS Inspector General Joseph V. Cuffari. The most recent example, they said, was the OIG report on the mistakes made by the U.S. Secret Service at and near the U.S. Capitol on Jan. 6, 2021 — especially its response to the pipe bomb found outside the Democratic National Committee office while Vice President-elect Kamala Harris was in the building. The Secret Service is part of DHS. 'DHS’ rampant lack of transparency is a disservice to the American taxpayer.' “The Biden-Harris DHS is keeping its watchdog on a tight leash by imposing unlawful access restrictions and delaying information sharing, which has interfered with DHS OIG’s ability to disclose its full findings to Congress and the American people in a timely manner,” Grassley said in a statement. “DHS’ rampant lack of transparency is a disservice to the American taxpayer and highly concerning in light of recent Secret Service-related communication failures,” he said. In an Aug. 2 letter to Grassley, Cuffari said his office has been handicapped for years by the DHS’ lack of cooperation. “Since 2021, my office has consistently reported DHS’s delays and denials to our requests for information which we need to do our jobs and to which we are entitled, consistent with the law,” Cuffari wrote. This has included “delays in fulfilling and outright denials of OIG’s requests for records and information.” Blaze News reached out to the DHS for a response to the Grassley-Loudermilk letter. Congressional investigators in July called out parallels between Secret Service failures during the Jan. 6 pipe-bomb incident and the July 13 shooting of Trump in Butler Township, Pa. Grassley and Loudermilk said the Aug. 2 release of a heavily redacted version of the OIG’s report on Jan. 6 is the latest example of the DHS' record of obstruction. The letter to Mayorkas cited four major examples where the DHS delayed or restricted OIG access to materials needed to complete an investigation or audit. 'The department’s continued actions don’t lend much credibility and may cause unnecessary harm.' “I am very concerned that the department would interfere at all regarding what information DHS OIG provides to Congress or what information the DHS OIG can obtain during their investigations,” Loudermilk said in a statement. “The OIG has an independent reporting relationship to Congress. Under no circumstances should the secretary interfere in the Inspector General’s work.” Cuffari’s Jan. 6 investigation began in February 2021, but the final report was not submitted to the Secret Service director for comments until April 2024. Sources told Blaze News that the DHS originally wanted to redact the entire report. That notion created a fury on Capitol Hill. A bomb-sniffing dog searches a vehicle at the garage entrance of the Democratic National Committee headquarters in Washington, D.C., on Jan. 6, 2021.U.S. Capitol Police CCTV The OIG report faulted the Secret Service for not conducting a proper sweep outside the DNC building with bomb-sniffing dogs and for failing to have an explosives disposal team on site during the sweep, among other missteps. “The Secret Service’s inability to spot the pipe bomb on January 6 is part of the same pattern of incompetence that nearly led to the assassination of President Trump,” said U.S. Rep. Thomas Massie (R-Ky.). “The agency needs serious reform before another one of its protectees pays the ultimate price for its ongoing negligence.” Cuffari was not able to analyze Secret Service communications from Jan. 6 because its agents’ phones were wiped of all data as part of a phone system migration. Thousands of destroyed text messages could have answered key questions about Secret Service decisions and movements on Jan. 6. The OIG report said the deletions happened despite warnings from Cuffari and four congressional committees that the Secret Service should preserve its documents and electronic communications from Jan. 6. Grassley and Loudermilk expressed concerns that the DHS behavior could hamper Cuffari’s investigations into the attempted assassination of former President Trump. “It is clear that some of the access issues outlined by the DHS OIG show signs of much-needed improvements in cooperation and communication from the department, which is unfortunately a common trend in the department’s actions,” they wrote to Mayorkas. “We have seen the seriousness of the consequences, such as the actions that transpired on July 13, 2024, when former President Trump was nearly assassinated, one innocent man was killed, and two others seriously injured. Yet, the department’s continued actions don’t lend much credibility and may cause unnecessary harm,” Grassley and Loudermilk wrote. The lawmakers gave Mayorkas until end of business on Aug. 27 to provide a justification for every redaction of the Jan. 6 report, confirm in writing steps being taken to ensure that the OIG has the access necessary for the Trump shooting investigations, and pledge in writing that the DHS will not tell the OIG not to disclose information on Secret Service law enforcement functions during the probes of the July 13 attack. Legislation passed in 1978 created Offices of Inspectors General at various federal agencies to deter fraud, promote efficiency, and provide timely information to Congress on government operations. In July, Grassley introduced a bipartisan bill to protect Offices of Inspectors General from partisan influence and promote their role as independent watchdogs. Grassley is the ranking member on the Senate Budget Committee. Loudermilk is chairman of the House Administration Subcommittee on Oversight. Like Blaze News? Bypass the censors, sign up for our newsletters, and get stories like this direct to your inbox. Sign up here!

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