We Are Finite. Does This Affect What We Can Know?

§2. What Can We Know?

The theme of this section is that We Are Finite: while our knowledge of the number 3 is intimately associated with experiences of some kind or other of triples of one or another sort, surely nothing like that is the case for our knowledge of the number ω or, for that matter, the number 10101010.

To avoid misunderstanding, let me emphasize that the issue being addressed is not “How can we have knowledge of mathematical objects despite their abstractness?” but rather “How can we have knowledge of infinite mathematical objects despite their huge size and consequent remoteness from experience?” Here is what I mean by remoteness: Not only do we not have experience of infinite mathematical objects, but we do not have any experience of anything suitably like them. The number 2 bears some relation to pairs of objects. The points and lines of Euclidean geometry bear some relation to pencil points and lines. But there does not seem to be anything suitable to play any analogous role for infinite mathematical objects.

Of course infinite mathematical objects are abstract. The issue of remoteness is an addition to that of abstractness. Both are apparent epistemological difficulties caused by the distance of mathematical objects from experience.

But if we divide the problem of the abstract into two parts, the problem of the finite and the problem of the infinite, it becomes clear that the two have quite distinct features.

The problem of the abstract, in Paul Benacerraf’s words, is this [Ben73, p. 409]: “the concept of mathematical truth, as explicated, must fit into an over-all account of knowledge in a way that makes it intelligible how we have the mathematical knowledge that we have. An acceptable semantics for mathematics must fit an acceptable epistemology?” For Benacerraf, an acceptable semantics is a Platonist one, and so his problem is that of the difficulties involved in giving an acceptable account of knowledge of abstract objects. Benacerraf concentrated on a weaker version of the problem: not on accounting for the mathematical knowledge that we have but on accounting for how we can have any mathematical knowledge whatever. “The minimal requirement, then, is that a satisfactory account of mathematical truth must be consistent with the possibility that some such truths be knowable” [Ben73, p. 409]. Philosophers have tended to concentrate on the minimal requirement and to offer up solutions to the problem of the finite to solve it.

Even those skeptical about the existence of any abstract mathematical objects at all want to endorse the truism ‘2 + 2 = 4’ in some way or other that acknowledges that it is better than ‘2 + 2 = 5’ even though they may not grant that it is true. Even without an abstract number 2, one is still faced with explaining the general fact that the members of two nonoverlapping pairs form a quadruple.

Whatever one’s views about mathematical objects, it is necessary to make sense of our counting, computing, and bookkeeping activities. Skepticism about small finite mathematical objects—in particular small natural numbers is just not doubt about the acceptability in some form or other of many of the putative facts about them. Moreover, there are many stories one could tell about a source for genuine knowledge concerning some finite mathematical objects, including, as the most trivial special case, knowledge of their existence. Take, for example, small natural numbers. Various explanations of our knowledge about them might invoke the experience of time, the experience of bunches of physical objects or of patterns exhibited by them, or the sequencing of words in sentences. Other explanations might rely on the exigencies of the construction of theories of the physical world. We are faced with too many ways of accounting for our knowledge of small finite mathematical objects, not too few. For example, Parsons [Par80] showed how to account for such knowledge on the basis of our linguistic capacities, while Maddy [Mad90] showed how to do it on the basis of experiences with medium-sized physical objects.

Benacerraf’s minimal requirement can surely be met with an acceptable solution to the problem of the finite—though I make no claim to know what the actual solution is. That is a question whose answer involves detailed psychological information about how people typically actually acquire knowledge of small finite mathematical objects, and we do not yet have sufficiently detailed information to answer it. Acquisition of the number concept does, however, involve both linguistic components—learning to count aloud—and experience of medium-sized physical objects—counting them using the spoken number sequence. It is therefore likely that the actual solution involves components of both the one proposed by Parsons and the one proposed by Maddy—and probably other components as well.

In sharp contrast to the situation about ‘2 + 2 = 4’, many of those who are skeptical about the existence of infinite combinatorial collections would want to doubt or deny the Axiom of Choice—not only its truth, but its acceptability in any form whatever. General facts about the infinite are not robust in the same way that the facts of counting, computing, and bookkeeping are. Moreover, it is not at all clear what we can fall back on as a source of mathematical knowledge concerning the infinite—what can play the role that bunches and sequences of moments, objects, or words seem so well suited to play for small finite mathematical objects. It is that lack that raises the problem posed by the remoteness of the infinite: it seems that we cannot have grounds to know what we find we actually do know about the infinite.

In Chapter VIII I shall show that as a matter of fact the combinatorial infinite is not remote—it has pretty much the same kinds of ties to experience as do small natural numbers. (That may be a bit misleading see Chapter VIII for a more careful formulation.) That solves the problem of the remoteness of the infinite philosophical problems concerning infinite mathematical objects become just like the familiar ones concerning finite mathematical objects. That is important because the problems concerning finite mathematical objects are not skeptical ones—the genuine doubts about the acceptability of our theory of the infinite are refuted. It also provides the essential missing ingredient for an explanation of the grounds on which mathematicians are entitled to make claims of self-evidence. But before presenting the solution, it is necessary to become clearer on the nature of the problem.

The two Benacerrafian problems—of the finite and the infinite—are both important, and every adequate philosophy of mathematics must be compatible with solutions to them. Nonetheless, the problem of the infinite deserves special emphasis because it is in danger of being lost as the result of the huge amount of attention being devoted to the Benacerrafian problem of the abstract in its simplified guise as the problem of the finite. That loss would be most unfortunate. The problem concerning the infinite was a primary concern of the philosophy of mathematics for many years—as may be seen in the work of Brouwer and that of several philosophers discussed by Benacerraf, such as Hilbert, Gödel, and Quine.

Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994, pgs. 162-165.

You do not doubt that ‘7 – 7 = 0’, but you cannot say ‘∞ – ∞ = 0’. In math lingo, the latter is indeterminate. Does this mean we are incapable of understanding the indeterminate, or is this just the nature of the universe? Consider Eugene Wigner’s lecture, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. He noted, “It is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.”

Still, complete understanding often seems to elude us.

“Fog Everywhere” Continued

[read the previous essay on this topic]

Consider mathematics and the aspect of fog. Nietzsche argued that the world is not knowable to us as a whole. This includes trying to express it with numbers. A recent example is Max Tegmark’s assertion that the universe is not something explained by mathematics; rather, it is itself mathematics. To contrast, Karl Jaspers, summarizing Nietzsche, wrote:

We cannot say what the world as a whole is. It is false to change all processes into a familiar world of our own, and then say: “All is will (everything wills); all is pleasure or pain (everything endures); all is motion (everything flows); all is tone (everything sounds); all is spirit (everything thinks); all is number (everything reckons).” Nietzsche warns us against all notions of the whole: “Let us guard against thinking that the world is a living being…or that the universe is a machine…Let us guard against saying that there are laws of nature…Let us guard against thinking that the world eternally creates novelties.” All these “shadows of God” darken actuality. We are within the world, and the whole of the world is, as a whole, not accessible to us.

Karl Jaspers, Nietzsche: An Introduction to the Understanding of His Philosophical Activity, Henry Regnery Company, 1966, p. 293

Notice in the paragraph quoted above that Nietzsche specifically excludes reducing everything to numbers, in opposition to Tegmark and the simulation hypothesis.

Robert Kanigel describes Srinivasa Ramanujan as “the man who knew infinity” in his biography of the same title, but mathematicians disagree on the ontological status and utility of infinity. The discussion of applying Ramanujan’s sum to arrive at -1/12 is very intricate and complex.

To make things even more puzzling, math students are confronted with the Gaussian integral, with its positive and negative infinities.

You can gain additional insight into infinity with:

Cauchy and Weierstrass had eliminated infinitely small and infinitely great numbers from analysis and replaced them by limits. But the theory of limits that thereby became so central required a clearer theory of the real line, that is to say, a theory of the irrational numbers. And that theory promptly reintroduced the infinite into analysis. The old infinity of infinitesimal and infinite numbers was simply replaced by the new infinity of infinitely large collections.12

In 1831 Carl Friedrich Gauss said [Kli72, p. 994], “I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound.” But only 52 years later, we find this in Cantor’s Grundlagen [Can76, p. 75]: “The idea of considering the infinitely large not only in the form of the unlimitedly increasing magnitude and in the closely related form of convergent infinite series…but to also fix it mathematically by numbers in the definite form of the completed infinite was logically forced upon me, almost against my will since it was contrary to traditions which I had come to cherish in the course of many years of scientific effort and investigations.”

12 See Russell’s Principles of Mathematics [Rus03, p. 304] for a related sentiment.

Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994, pgs. 38-39

In 1961, the great Russian physicist George Gamow’s popular math and physics overview was republished to great acclaim among science and math aficionados. Intriguingly titled One, Two, Three…Infinity, the book gives you a hint that the relationship of numbers and integers to the concept of infinity is still intriguing even after the intricate analyses of Cauchy, Weierstrass et al.

Let us conclude by considering Zeno’s dichotomy paradox of motion, in which “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.” As the goal is divided into halves, one must complete an infinite number of tasks, which Zeno maintains is an impossibility.

[read the previous essay on this topic]

Japan-Watching: Economics in the Age of AI

A Thought Experiment Envisioning A “Fully Automated Society”

from REITI, by IKEUCHI Kenta [池内 健太], Senior Fellow (Policy Economist)

In a world where human labor has become unnecessary because of AI, what should be the focus of the study of economics? In the future, if AI and robots have become capable of producing all goods and services necessary for our society, what kind of economic problems could remain?

Of course, a fully automated society is not predicted for the near future. This article imagines such an extreme type of society as a thought experiment designed to consider economic systems in the age of AI. Here, a fully automated society refers not only to one in which corporate production is automated, but also to one in which the legislative, administrative, and judicial functions of government are substantially supported—and in some cases automated—by AI.

I started thinking about this matter when I heard from a researcher acquaintance that a paper concerning AI’s impact on employment had caused quite a stir on X, and I decided to read it out of curiosity. The paper discussed the possibility that AI-driven job cuts could reduce workers’ incomes, weaken consumer demand, and ultimately backfire on firms themselves (Falk and Tsoukalas 2026). Companies may earn higher profits in the short term by taking advantage of AI to cut back on personnel costs. However, if most companies follow that same approach, overall market demand would weaken because workers are also consumers.

The purpose of this article is not to question the validity of that paper’s argument. Rather, the focus is on what economic problems would remain in a future society if AI not only partially replaces human labor but also produces most goods and services.

Scarcity Will Continue to Be a Problem

There has already been extensive research regarding the impact of AI on employment. For example, Acemoğlu and Restrepo (2019) argued that while automation may replace existing human jobs, it may also create new ones. Moreover, the possibility that technological advances could free humans from labor and greatly alleviate economic problems was discussed long ago by Keynes (1930).

If AI and robots become capable of producing goods and services on a sufficiently large scale, would economic problems disappear? That would not necessarily be the case. Even in a fully automated society, scarce resources such as land, location, natural environments, energy, and rare metals will remain limited. Moreover, social status, influence, and political decision-making power are deeply connected to human intentions and perception, and cannot simply be delegated to AI. More land will not become available simply because more people wish to live in convenient urban locations. Quiet natural environments, advanced healthcare resources, social attention, and political influence also cannot be maximized for everyone at the same time.

Therefore, even in a fully automated society, some economic problems will remain. However, the main focus will shift from the “problem of insufficient ordinary commodities” to “how to allocate fundamentally scarce resources.” As production capacity increases, the value of true scarcity only becomes clearer.

In that case, the roles of markets and prices will still exist. Prices are not merely figures that allow for corporate earnings; they convey information about which resources are scarce and to what extent, how much demand there is for those resources, and what supply constraints there are. That perspective connects to a classic argument made by Hayek (1945), who argued that prices function as a mechanism through which dispersed information can be aggregated.

However, if AI becomes deeply integrated into the market, the concept of price itself may change. At present, prices serve as one-dimensional signals representing the levels of various factors, such as scarcity, quality, demand, supply, environmental impact, and future risks, expressed in terms of a single metric, that is, monetary value. If AI agents become capable of processing large volumes of information on behalf of consumers and companies, it is possible that multi-dimensional market signals that convey information concerning all those various factors, including quality, environmental impact, congestion, delivery time, reliability and social impact may come into use. Narita (2025) also discussed the possibility that the roles of money and prices may change, with more diverse evaluation standards becoming involved in economic coordination.

For People to Enjoy Affluence

In a fully automated society, how people participate in the market and society will become more important than ever. If the premise that people earn income through labor becomes obsolete, it will be necessary to develop a mechanism whereby purchasing power is distributed to everyone. In this context, universal basic income (UBI) may be reframed not only as relief for the unemployed, but as a form of fundamental purchasing power used by people to express their preferences. Managi [馬奈木 俊介] (2025) also pointed out that governance over the equitable distribution of the benefits of AI is essential.

Moreover, UBI may not be limited to simple monetary payments. In the future, UBI may take the form of a system combining other benefits as well, including energy use quotas, rights of access to basic healthcare services and education, and rights to refuse or control the use of personal data. In a fully automated society, UBI would therefore be a matter not only of how much to provide, but also of what kinds of access to guarantee and over what time horizon.

Another important issue is whether it is appropriate to treat people merely as consumers. In a fully automated society, the need for people to work for a living may diminish. However, even without such a necessity, humans will likely still possess the desire to create or to be creative. It is human nature to try new things and to try to surprise or impress other people. The spirit of fun and curiosity, a desire for self-expression, an inquisitive mind, and an appetite for challenges are deeply and fundamentally connected to human nature. Therefore, when designing a future UBI system, it will be important to treat people not merely as consumers but as agents who can participate in creation and exploration.

Additionally, the question of who owns and controls AI systems, robots, foundation models, and computing infrastructure is also a major issue. Even if a certain level of income is distributed to everyone, there may remain a power gap between those who control AI systems and robots and those who merely have access to them, in place of the income gap that currently exists in society.

All of the above-mentioned points for debate are relevant to the study of economics. How scarce resources should be allocated, how to guarantee people’s range of choices, and how to design ownership and controlling rights are problems central to economics. A fully automated society is not a near-future prediction. However, this extreme thought experiment serves as a useful guide for considering economic systems in the age of AI. Economics in the age of AI is not about discarding the intellectual legacy of economics, but about inheriting it and extending it toward a new society.

References

June 12, 2026

“Fog everywhere” and Other Confusions

Charles Dickens gives us wonderful sociopolitical insight in his serial Bleak House, with his imagery of impenetrable fog in the second paragraph of chapter 1:

Fog everywhere. Fog up the river, where it flows among green aits and meadows; fog down the river, where it rolls deified among the tiers of shipping and the waterside pollutions of a great (and dirty) city. Fog on the Essex marshes, fog on the Kentish heights. Fog creeping into the cabooses of collier–brigs; fog lying out on the yards and hovering in the rigging of great ships; fog drooping on the gunwales of barges and small boats. Fog in the eyes and throats of ancient Greenwich pensioners, wheezing by the firesides of their wards; fog in the stem and bowl of the afternoon pipe of the wrathful skipper, down in his close cabin; fog cruelly pinching the toes and fingers of his shivering little ’prentice boy on deck. Chance people on the bridges peeping over the parapets into a nether sky of fog, with fog all round them, as if they were up in a balloon and hanging in the misty clouds.

Charles Dickens, Bleak House. Bradbury & Evans, 1852-1853.

Think of the Trump–Epstein cover-up and the machinations of the U.S. government to attempt to conceal everything in a similar fog. We discussed another dimension of our ignorance with Friedrich Nietzsche’s assertion that we “are unknown to ourselves”.

Let’s consider a third level of our confusion and how we attempt to extricate ourselves by expressing the world around us through mathematics. For example, the square root of -1 is i. ii is approximately 0.208. To a student encountering this concept for the first time, it can be inscrutable that an imaginary number to the power of itself results in a real number. To quote Wikipedia:

In electrical engineering, signal processing, and similar fields, signals that vary periodically over time are often described as a combination of sinusoidal functions (see Fourier analysis), and these are more conveniently expressed as the sum of exponential functions with imaginary exponents, using Euler’s formula.

Wikipedia, Euler’s formula [with added links]

The esteemed physicist Roger Penrose has said on multiple occasions that he believes the realm of imaginary numbers or complex analysis will be more informative in physics than real numbers. (See his classic book, The Road to Reality: A Complete Guide to the Laws of the Universe.)

Let’s conclude with our inevitable mortality as living beings as another source of perplexity and confusion. As we grow older, half of our mind is fixated on the enjoyment we get from life, while the other half is focused on the anxiety that it is not forever. We attempt to sidestep this anxiety by clinging to the escapist thought that “Besides, it’s always the others who die.”

Economics-Watching: Bank of Japan Updates (June 25th)

[from the Bank of Japan (日本銀行), June 25, 2026]

Economic Activity, Prices, and Monetary Policy in Japan

Speech at a Meeting with Local Leaders in Hyogo

TAMURA Naoki [田村 直樹], Member of the Policy Board, June 25, 2026

Read the full translated speech [Archived PDF]

Flow of Funds Accounts (Retroactive Revision and 1st Quarter 2026, Preliminary Figures)

The Bank released the following data today.

The Overview of Japan, US, and the Euro area is renewed once a year after the Flow of Funds Accounts is released in June.

The Bank of Japan retroactively revises data for the Flow of Funds Accounts (FFA), in principle once a year, to reflect information updates, such as newly obtained source data and institutional changes, and to incorporate revised estimation methods. The retroactive revision of 2026 was implemented on June 25 and data from the first quarter of 2005 onward has been updated accordingly. The majority of the revision contents are unchanged from the Planned Retroactive Revision to the Flow of Funds Accounts [Archived PDF] released on May 25, 2026.

To download the retroactively revised data, please use the BOJ Time-Series Data Search.

Monthly Report on the Services Producer Price Index

Read the full May report [Archived PDF]

Updates to the Bank of Japan’s statistical data are available at BOJ Time-Series Data Search.

Is Reality Fundamentally Analyzable or Opaque?

Imagine your childhood. You’re looking out a window in the early afternoon. You see the clouds in the sky, the passers-by and traffic down the street. You have no trouble differentiating a police car from an ambulance. A summary of this can be expressed in the philosophical quote, “your version of the world shows up for you, like a friend at the bus stop.”

All of this suffers from an invasion from two sides: clarity and opacity. Consider the last sentence of the preface from Frederich Nietzsche’s On the Genealogy of Morality (below):

Preface

I

We are unknown to ourselves, we knowers, we ourselves, to ourselves, and there is a good reason for this. We have never looked for ourselves, — so how are we ever supposed to find ourselves? How right is the saying: ‘Where your treasure is, there will your heart be also’;1 our treasure is where the hives of our knowledge are. As born winged-insects and intellectual honey-gatherers we are constantly making for them, concerned at heart with only one thing — to ‘bring something home’. As far as the rest of life is concerned, the so-called ‘experiences’, — who of us ever has enough seriousness for them? or enough time? I fear we have never really been ‘with it’ in such matters: our heart is simply not in it — and not even our ear! On the contrary, like somebody divinely absent-minded and sunk in his own thoughts who, the twelve strokes of midday having just boomed into his ears, wakes with a start and wonders ‘What hour struck?’, sometimes we, too, afterwards rub our ears and ask, astonished, taken aback, ‘What did we actually experience then?’ or even, ‘Who are we, in fact?’ and afterwards, as I said, we count all twelve reverberating strokes of our experience, of our life, of our being — oh! and lose count … We remain strange to ourselves out of necessity, we do not understand ourselves, we must confusedly mistake who we are, the motto2 ‘everyone is furthest from himself’ applies to us for ever, — we are not ‘knowers’ when it comes to ourselves…

  1. Gospel according to Matthew 6.21.
  2. ‘Jeder ist sich selbst der Fernste’ is a reversal of the common German saying, ‘Jeder ist sich selbst der Nächste’ ‘Everyone is closest to himself’ i.e. ‘Charity begins at home’, cf. also Terence, Andria IV. 1.12.
Nietzsche, Frederich, On the Genealogy of Morality, Translated by Carol Diethe, Cambridge University Press, 1994, pp. 3-4.

Go back to our initial example of the childhood window. On one hand, our version of the world shows up for us. On the other, since “we are not ‘knowers’ when it comes to ourselves”, we show up as an opaque version of ourselves. As he states at the beginning of the preface, we are unknown to ourselves. If asked, you would most likely not remember the point at which you could differentiate the police car from an ambulance. Imagine meeting a friend during that same period, and instead of thinking of the enjoyable conversation you will have, but the concern that all of these things are impermanent.

The Danish thinker Søren Kierkegaard teaches us that the reason we are opaque to ourselves is that the self is a synthesis waiting to be made. This synthesis would connect the momentary pleasures of time with friends and the impermanence of these things.

Consider the opacity built into science. Science claims that ultimately, there is a logical, mathematical way of understanding what you see while looking out the window. Contrast this with the Dutch historian Pieter Geyl’s assertion that history is an “argument without end.” It could be that scientific inquiry is also a quest without end.

What is the great takeaway from all of this? On Kierkegaard’s side, we face the opacity wall and on the materialist side, we still have the opacity of what we have yet to understand. With each discovery, we continue to see more that we do not yet understand.

Japan-Watching: Ministry of Finance, Japan

Preliminary determination of Anti-Dumping Duty Investigation of Nickel-added cold-rolled stainless steel coil, sheet, and strip originating in the People’s Republic of China and the Separate Customs Territory of Taiwan, Penghu, Kinmen, and Matsu

  1. Upon receipt of an application from NIPPON STEEL CORPORATION [日本製鉄株式会社], Nippon Yakin Kogyo Co., Ltd. [日本冶金工業株式会社], NAS Stainless Steel Strip MFG. Co., Ltd. [ナス鋼帯株式会社の画像] and NIPPON KINZOKU CO., LTD. [日本金属株式会社] on May 12, 2025, the Ministry of Finance (MOF) [財務省] and the Ministry of Economy, Trade and Industry (METI) [経済産業省] began conducting an investigation since July 22, 2025, to determine whether or not to impose an anti-dumping duty on Nickel-added cold-rolled stainless-steel coil, sheet, and stripa originating in the People’s Republic of Chinab and the Separate Customs Territory of Taiwan, Penghu, Kinmen, and Matsu.
    1. Note: An alloy steel containing 10.5% or more of chromium and containing by weight more than 0.6% nickel. The characteristics of this product are that it combines corrosion resistance, the functionality of steel, and a beautiful and clean design by manufacturing methods. Also, it is used in various fields of demand.
    2. Note: Excluding the regions of Hong Kong and Macau.
  2. MOF and METI have explored objective evidence collected from interested parties, including suppliers in the People’s Republic of China and the Separate Customs Territory of Taiwan, Penghu, Kinmen, and Matsu, providing opportunities for them to present evidence and to express their views. As a result, MOF and METI today made a preliminary determination in the anti-dumping investigation of the product, presuming the fact of the importation of the dumped product and the fact of the material injury to the domestic industry caused by such importation. (Public Notice on June 19, 2026)

    MOF and METI will continue the investigation in accordance with the provisions of the international rules under the WTO Agreements and related domestic laws and regulations, providing the interested parties with an appropriate opportunity to present evidence and express their views relating to the preliminary determination.

    Following the further investigation, the Government of Japan will determine whether or not the product has been imported into Japan at dumped prices and if such dumped imports have caused material injury to the domestic industry, and make a decision whether or not to impose a definitive anti-dumping duty on the product.

    The interim report on preliminary determination offers details of the investigation.
Reference

Public Notice on June 19, 2026 [Archived PDF]

Interim report on preliminary determination [Archived PDF]

[Provisional Translation, June 19, 2026, Ministry of Finance, Ministry of Economy, Trade and Industry]

Extension of the Period of Investigation of Nickel-added cold-rolled stainless steel coil, sheet and strip originating in the People’s Republic of China and the Separate Customs Territory of Taiwan, Penghu, Kinmen, and Matsu

  1. With regard to the Anti-Dumping Duty Investigation on Nickel-added cold-rolled stainless-steel coil, sheet, and stripa originating in the People’s Republic of Chinab and the Separate Customs Territory of Taiwan, Penghu, Kinmen, and Matsu, the Ministry of Finance (MOF) [財務省] and the Ministry of Economy, Trade and Industry (METI) [経済産業省] have decided to extend the period of investigation by three months until September 21, 2026. The purpose of this extension is to carefully review the evidence and relevant documents submitted by interested parties, while ensuring full transparency and fairness throughout the investigation process.
    1. Note: An alloy steel containing 10.5% or more of chromium and containing by weight more than 0.6% nickel. The characteristics of this product are that it combines corrosion resistance, the functionality of steel, and a beautiful and clean design by manufacturing methods. Also, it is used in various fields of demand.
    2. Note: Excluding the regions of Hong Kong, China, and Macau, China.
  2. MOF and METI have been conducting the investigation since July 22, 2025. The investigation was to be concluded within one year, but the period can be extended by six months at most if it is found necessary for special reasons.
Reference

Notice of the Ministry of Finance Relating to the Extension of the Period of Investigation (No. 178, June 19, 2026) [Archived PDF]

[Provisional Translation, June 19, 2026, Ministry of Finance, Ministry of Economy, Trade and Industry]

Issues Re-opened through Liquidity Enhancement Auction on June 19, 2026

SecuritiesIssue NumbersRe-opened Amounts (billion yen face value)
10-Year363133.7
10-Year3648.4
10-Year36534.8
10-Year36927.7
10-Year37048.9
20-Year12875.1
20-Year129110.6
20-Year1329.0
20-Year1332.5
20-Year1364.9
20-Year14216.0
20-Year1436.8
20-Year1532.0
20-Year1549.9
20-Year1590.7
30-Year65.0
30-Year70.1
30-Year135.0
30-Year140.1
30-Year1514.1
30-Year160.2
30-Year1725.6
30-Year194.9
30-Year2053.0
30-Year238.6
30-Year2432.4
30-Year268.9

Result of Liquidity Enhancement Auction on June 19, 2026 (For JGB Market Special Participants)

Auction DateIssue DateAmounts of Competitive Bids (billion yen)Amounts of Bids Accepted (billion yen)Highest Accepted Spread*Allotment for Bids at the Highest Accepted SpreadAverage Accepted Spread*
6/196/221,897.8648.9+0.020%98.6666%+0.016%
Note

These columns indicate the spreads from the reference rate.

Auction Result of Treasury Discount Bills on June 19, 2026

Issue NumberAuction DateIssue DateMaturity DateAmounts of Compet. Bids (billion yen)Amounts of Bids Accepted (billion yen)Lowest Accepted Price (per 100 yen)Yield at the Lowest Accepted PriceAllotment for Bids at the Lowest Accepted PriceWeighted Average Price (per 100 yen)Yield at the Average PriceAmounts of Non-price compet. Auction Ⅰ* (billion yen)
13896/196/229/249,637.503,150.3899.76300.9224%79.2411%99.76600.9107%949.60
Note

For JGB Market Special Participants.

Interest Rate (June 2026)

Date1Y2Y3Y4Y5Y6Y7Y8Y9Y10Y15Y20Y25Y30Y40Y
6/11.123%1.4%1.558%1.775%1.948%2.094%2.243%2.397%2.538%2.682%3.225%3.567%3.871%3.863%3.8%
6/21.114%1.38%1.522%1.722%1.889%2.019%2.157%2.31%2.447%2.577%3.141%3.493%3.801%3.81%3.742%
6/31.126%1.401%1.56%1.767%1.943%2.077%2.219%2.373%2.508%2.645%3.183%3.521%3.817%3.817%3.748%
6/41.148%1.417%1.579%1.787%1.966%2.105%2.242%2.395%2.535%2.671%3.225%3.554%3.835%3.833%3.749%
6/51.14%1.412%1.574%1.778%1.955%2.096%2.233%2.391%2.532%2.669%3.222%3.551%3.838%3.841%3.753%
6/81.144%1.42%1.588%1.793%1.978%2.128%2.274%2.432%2.575%2.715%3.269%3.604%3.878%3.876%3.789%
6/91.146%1.42%1.582%1.784%1.962%2.101%2.242%2.398%2.537%2.669%3.217%3.543%3.824%3.823%3.759%
6/10%1.147%1.426%1.594%1.796%1.971%2.112%2.257%2.412%2.549%2.681%3.218%3.538%3.806%3.811%3.739%
6/111.149%1.427%1.592%1.792%1.963%2.108%2.258%2.411%2.551%2.682%3.23%3.554%3.821%3.823%3.774%
6/121.15%1.417%1.579%1.772%1.938%2.077%2.218%2.373%2.511%2.643%3.189%3.508%3.77%3.767%3.713%
6/151.141%1.409%1.556%1.743%1.901%2.039%2.175%2.322%2.46%2.589%3.143%3.461%3.73%3.725%3.674%
6/161.147%1.414%1.585%1.783%1.945%2.084%2.227%2.382%2.522%2.655%3.206%3.52%3.763%3.747%3.692%
6/171.139%1.398%1.552%1.745%1.897%2.034%2.182%2.335%2.479%2.613%3.17%3.49%3.741%3.709%3.654%
6/181.146%1.4%1.553%1.746%1.898%2.045%2.193%2.353%2.497%2.628%3.19%3.512%3.765%3.737%3.68%

Treasury Discount Bills to Be Auctioned on June 26, 2026

1. Auction Date:June 26, 2026
2. Issue Date:June 29, 2026
3. Maturity Date:September 28, 2026
4. Offering Amount:About 4,100 billion yen
5. Others:The above offering amount may be changed. In such a case, the revised amount will be announced on the day before the auction date.

[Provisional Translation, June 19, 2026, Ministry of Finance]

Japan-Watching: Ministry of Foreign Affairs of Japan

First Meeting of the Study Group on Strengthening Japan-Africa Economic Partnership

At TICAD 9 held last August, Mr. ISHIBA Shigeru (石破 茂), then Prime Minister of Japan, announced the establishment of the “Study Group on Strengthening Japan–Africa Economic Partnership” as one of the concrete initiatives of the Japanese Government’s policy on Africa. The first meeting of this study group is scheduled for June 18 in a hybrid format.

Under the framework of a “Free and Open Indo-Pacific (FOIP)”, this study group will address African economic integration, a top priority for the African Union (AU). Through strengthening economic cooperation between Japan and Africa, the study group aims to support business expansion of Japanese companies in the African market. To this end, the study group will discuss various topics including measures to promote regional economic integration in Africa, review of trade and investment between Japan and Africa, and the strengthening of economic relations between Japan and Africa. The study group will prepare a report by the end of the fiscal year 2027, which will be submitted to the Minister for Foreign Affairs.

(Reference 1) Japanese Members

Prof. WATANABE Yorizumi (渡邊 頼純), Professor Emeritus, Keio University; Dr. KIMURA Fukunari (木村 福成), President, JETRO Asian Economic Research Institute; Mr. FUJITA Ryoji (藤田 亮二), Executive Officer, Toyota Tsusho Corporation (Representative from Keidanren); WATANABE Tatsuro (渡邉 達郎), Managing Executive Officer, Mitsui O.S.K. Lines (Representative from Keizai Doyukai); IGARASHI Katsuya (五十嵐 克也), Director and Head of International Department, the Japan Chamber of Commerce and Industry; and representatives from the Ministry of Foreign Affairs, Ministry of Finance, Ministry of Agriculture, Forestry and Fisheries, and Ministry of Economy, Trade and Industry.

(Reference 2) African Members

Mr. Lacina Koné, Director General and CEO, Smart Africa Alliance; Mr. Kulekani Mathe, CEO, Business Unity South Africa (BUSA); Dr. E. Olawale Ogunkola, Professor of Economics, University of Ibadan, Nigeria; and representatives from the United Nations Economic Commission for Africa (UNECA), the African Continental Free Trade Area (AfCFTA) Secretariat, and the African Union Commission (AUC).

(Note) In addition, relevant Ministries, agencies, and individuals with expertise are expected to attend depending on the agenda.

(Reference 3) Attachment

Establishment of the Study Group on Strengthening Japan-Africa Economic Partnership [Archived PDF]

G7 Evian Summit

Working Session on “Reviving a Balanced, Shared and Sustainable Economic Growth”

On June 17, commencing at 10:30 a.m. (local time. 5:30 p.m. on June 17, Japan time.) for approximately 120 minutes, Ms. TAKAICHI Sanae (高市 早苗), Prime Minister of Japan, attended the G7 Evian Summit Working Session on “Reviving balanced, inclusive, and sustainable economic growth for the benefit of all”. The overview of the session is as follows.

  1. Prime Minister TAKAICHI stated that the G7 and like-minded countries should maintain close communication to reduce uncertainty in the global economy.
    Prime Minister TAKAICHI also stated that it is a common challenge for many countries to promote self-sustaining growth, by addressing non-market policies and practices (NMPPs) and the resulting excess capacity which are drivers of widening global imbalances.
  2. Furthermore, Prime Minister TAKAICHI stated that G7 members and the countries participating in this session should also demonstrate their contribution to reducing imbalances for their own balanced growth as well as for the stability of the global economy and financial markets. Prime Minister TAKAICHI added that making use of data-driven, objective analyses and policy advice by the IMF and the OECD is extremely beneficial in advancing these efforts.
  3. Prime Minister TAKAICHI expressed her hope that the G7 and like-minded countries would lead the global economy through frank discussions. She also stated that she looked forward to discussions at the G20, chaired by President Donald Trump of the United States, on reducing uncertainty in the global economy and becoming stronger and more prosperous together.

Situation in Iran (Signing of a Memorandum of Understanding between the United States and Iran)

(Message from Foreign Minister MOTEGI Toshimitsu [茂木 敏充])

On June 18 (Japan Standard Time), the United States and Iran signed a Memorandum of Understanding and the cessation of hostilities was declared. Japan once again welcomes the fruition of the diplomatic efforts made by the parties as well as the countries that played a role in mediation.

Hereafter, it is important that free and safe navigation through the Strait of Hormuz is swiftly reestablished through the steady implementation of this MoU by all parties. Japan also considers it of critical importance that vessels be able to transit the Strait of Hormuz without being subject to additional costs, as has been the case thus far.

Japan strongly hopes that a final agreement on matters such as Iran’s nuclear issue will be achieved as soon as possible through further negotiations between the United States and Iran. Japan will also support the peaceful resolution of the Iranian nuclear issue including through coordination with the International Atomic Energy Agency (IAEA).

After the conclusion of a final agreement, Japan intends to play an active role in the reconstruction and recovery of the region. Japan will also continue to make every diplomatic effort, in close coordination with the international community, toward the realization of peace and stability throughout the Middle East region.

Parliamentary Vice-Minister for Foreign Affairs ERI’s Visit to the United States

From June 21 to June 24, Ms. ERI Arfiya (英利 アルフィヤ), Parliamentary Vice-Minister for Foreign Affairs of Japan, will visit New York, United States.

During her visit, Parliamentary Vice-Minister ERI will attend the United Nations General Assembly High-Level Meeting on HIV/AIDS and deliver a statement in the meeting. She will also hold meetings with representatives of international organizations.

(Reference) Schedule
June 21Departure from Tokyo
 Arrival at New York
June 22Participation in the United Nations General Assembly High-Level Meeting on HIV/AIDS, etc.
June 23Meetings with representatives of international organizations, etc.
 Departure from New York
June 24Arrival at Tokyo

The 7th Japan-Australia Cyber Policy Dialogue

On June 18, the 7th Japan–Australia Cyber Policy Dialogue was held in Tokyo, Japan.

  1. This whole-of-government meeting was co-chaired by Mr. MIYAKE Fumito (三宅 史人), Ambassador in charge of Cyber Policy and Deputy Director-General of the Foreign Policy Bureau, Ministry of Foreign Affairs (MOFA) of Japan, and Ms. Jessica Hunter, Ambassador for Cyber Affairs and Critical Technology, Department of Foreign Affairs and Trade (DFAT), Australia, with the participation of officials from, on the Japanese side, MOFA, National Cybersecurity Office (NCO), National Police Agency (NPA), Ministry of Defense (MOD), Ministry of Internal Affairs and Communications (MIC) and Ministry of Economy, Trade and Industry (METI), and on the Australian side, DFAT, Department of Industry and Australian Signals Directorate (ASD)’s Australian Cyber Security Centre (ACSC) and Department of Home Affairs (DHA).
  2. At this dialogue, following the enactment of Japan’s Cyber Response Capability Strengthening Act and Necessary Arrangement of Relevant Acts last year, as well as the adoption of its new Cybersecurity Strategy, the two sides exchanged views on broad range of topics, such as each country’s respective cybersecurity strategy and policy, and cooperation at both the bilateral and multilateral levels.
  3. Furthermore, building on the “Japan–Australia Strategic Cyber Partnership” which Ms. TAKAICHI Sanae (高市 早苗), Prime Minister of Japan and the Hon. Anthony Albanese, Prime Minister of Australia concurred on launching at the Japan–Australia Summit Meeting in May of this year, the two sides exchanged views on efforts and cooperation in a wide range of areas including the defense and deterrence of cyber threats, capacity-building, public-private partnerships, and artificial intelligence (AI) and cybersecurity.
  4. Both sides confirmed that they will continue to work closely together in the field of cyber, including through the Japan–Australia Cyber Policy Dialogue.

[from the Ministry of Foreign Affairs of Japan, 18-19 June, 2026]

Songs and Tweaking Our Understanding, Part 2

Let’s look at three songs: “Cabaret” (from the musical of the same title), “Is That All There Is?” and “More Than a Woman” by the Bee Gees.

In “Cabaret” the character Sally Bowles sings, “Start by admitting from cradle to tomb / It isn’t that long a stay / Life is a cabaret, old chum…” She asserts that life is so short that one shouldn’t take it seriously and should be treated as boisterous fun.

Earlier, she sang:

I used to have this girlfriend known as Elsie
With whom I shared four sordid rooms in Chelsea
She wasn’t what you’d call a blushing flower
As a matter of fact, she rented by the hour

The day she died the neighbors came to snicker:
“Well, that’s what comes from too much pills and liquor”
But when I saw her laid out like a queen
She was the happiest corpse I’d ever seen

Does the idea of a happy corpse ring true? As a corollary of this, is it plausible that a smile survives hours after death?

While “Cabaret” compares life to the titular cabaret, there are many other songs with simplified comparisons of life, none of which cover the full breadth of human experience. The French philosopher Maurice Merleau-Ponty wrote that the world is inexhaustible, and to extend this, so too is life.

In “Is That All There Is?” each question has several levels. When confronted with the fire that claims her childhood home, the disappointment of the circus and finally the loss of her love, the song echoes “Cabaret” with the chorus:

Is that all there is?
If that’s all there is my friends, then let’s keep dancing
Let’s break out the booze and have a ball

Much like the way “Cabaret” repeats “Life is a cabaret, old chum / Come to the cabaret”.

In “More Than a Woman” by the Bee Gees, they sing, “We can take forever, just a minute at a time”. Can we visualize this in the concrete terms of the song? In Western tradition, we often associate the search for forever with young love. What does it mean to fuse the momentary and the forever?

The Bee Gees song gives us an entry to the changing sense of time experienced by a living person, as contrasted to the objective time of a fossil carbon-dated by a paleontologist.

Songs and Tweaking Our Understanding

In any public place, you’re likely to be surrounded by faces reflecting an unshakeable puzzlement of people who have sleepwalked through life. Songs capture this perplexity. Take “Hier encore” by Charles Aznavour, which has subsequently been translated into a myriad of languages and covered by many artists.

Yesterday, when I was young
The taste of life was sweet as rain upon my tongue
I teased at life as if it were a foolish game
The way the evening breeze may tease a candle flame
The thousand dreams I dreamed, the splendid things I planned
I always built, alas, on weak and shifting sand
I lived by night and shunned the naked light of day
And only now I see how the years ran away

Yesterday, when I was young
So many drinking songs were waiting to be sung
So many wayward pleasures lay in store for me
And so much pain my dazzled eyes refused to see
I ran so fast that time and youth at last ran out
I never stopped to think what life was all about
And every conversation I can now recall
Concerned itself with me, me and nothing else at all

Yesterday, the moon was blue
And every crazy day brought something new to do
I used my magic age as if it were a wand
And never saw the waste and emptiness beyond
The game of love I played with arrogance and pride
And every flame I lit too quickly, quickly died
The friends I made all seemed somehow to drift away
And only I am left on stage to end the play

There are so many songs in me that won’t be sung
I feel the bitter taste of tears upon my tongue
The time has come for me to pay for yesterday
When I was young
Young, young…

Notice that “Yesterday, when I was young” is a poetic conceit discussing his youth. Orbiting this thought is a song by Crosby, Stills & Nash, the first of which is “Wasted on the Way”, regretting the singers’ wasted lives. Another is “We May Never Pass This Way (Again)” by Seals & Crofts. These songs tweak our understanding by reminding us in a painful, yet melodious way, that we are all swept along by life’s pressures and events.

Imagine that one is aware of this trend early enough to avoid it and attempts to sidestep this fate. However, there’s a danger on the other side of mindless snarling rebellion, in the vein of Billy Idol’s “Rebel Yell”.

Finally, there are musical styles such as Portuguese fado, characterized by mournful tunes and lyrics that straddle the loss of one’s true love and the loss of Portuguese influence in the world, such as Latin America supplanting Portugal as the center of Portuguese culture. In all of these, the “once upon a time” is at the level of youth, one’s romance and eventually life, which “never comes again”.

Perhaps the most sobering line in popular music is “all we are is dust in the wind” (from “Dust in the Wind” by Kansas). One might benefit from a moment of quiet reflection on this lyric.