Therefore, the logical inference is that perpetual economic growth is impossible and that at some point the economy must stop growing. — Peter Gray

It is true that economic growth sticks at some point. It happened with the 1973 oil crisis or the 2008 worldwide mortgage crisis. There has always been (and probably will always be) recession. Some countries experience it more dramatically than others due to countless circumstances and reasons.

However, I do not think that perpetual economic growth is illogical. It isn't, actually. We can see many examples that corroborate this. These examples range from the increase in wages during the mid-19th century to the current era of globalisation. Supposedly, the GDP and other economic factors should grow gradually. Otherwise, the nation would be unhealthy and poor, which would indicate a serious problem rather than simply being illogical.

On the other hand, the fact that an economy could stop growing at some point does not mean that it might not still grow in the near future.

So I was wondering, does philosophy and mathematics have anything to say about the possibility, or otherwise, of perpetual economic growth?" — Peter Gray

Welcome to the forum.

There are a lot of issues associated with economic growth. Many of them have been discussed often here on the forum. The one that strikes me as most significant is demographics. The demographers tell us that, although populations will grow over the next 50 years, after that they’ll start shrinking with a maximum population of about 11 billion and then shrinking to about where we are now.

The US birth rate is right about at the replacement level now, and if it weren’t for immigration, our population would not be increasing. Quite a few other first world nations are seeing population reductions already.

Welcome to the forum!

I’m concerned about the paradox of perpetual economic growth. Boosting economic growth is central to government policy (both this government and the last one) but on the face of it, economic growth at any percentage per year is an exponential function and must eventually result in an infinitely large economy. — Peter Gray

It is only exponential if the rate remains constant, and even then it will never become infinite. Anyway, if your point is that perpetual growth is unsustainable in the long term, Maltus beat you to that insight by 200 years.

I’m not the first person to have noticed this. If you Google for “Is perpetual economic growth possible?” the new AI Overview function says — Peter Gray

That's not a good way to do research.

So I was wondering, does philosophy and mathematics have anything to say about the possibility, or otherwise, of perpetual economic growth?" — Peter Gray

Mathematics has little to do with this - except inasmuch as researchers use mathematics, of course, but that is mostly textbook calculus and statistics. Most of the innovation in this area has been in demographic and economic metrics and modeling, and to a lesser degree in computational methods.

Naturally, a simpleminded mathematical projection pointing to unbounded growth is not going to give you the right answer, just like you cannot predict the height of an adult person by extrapolating their rate of growth at a young age. Even your AI overview is right on this point: it is a complex issue with varied perspectives that has been studied and debated for literally centuries.

In a material sense perpetual economic growth is not possible simply because of the laws of thermodynamics - eventually you reach a state where ethe finite physical inputs of the system are reached.

In an immaterial sense I am not so sure - items such as software and services for example are not constrained by finite physical inputs is exactly the same way.

However, I do not think that perpetual economic growth is illogical. It isn't, actually. We can see many examples that corroborate this. — javi2541997

Surely there can be no example of perpetual economic growth, because by definition, to provide an example of perpetual economic growth, you would need to grow the economy in perpetuity, and then say at the end of perpetuity (whenever that is), "See? I told you so". So the only examples of economic growth which can be provided are for economic growth over a finite and relatively short period.

There are, however, numerous examples of societies which failed to achieve perpetual economic growth. Take, for example, the Roman Empire. It grew from the founding of Rome in 753 BC, reached its peak around 180 AD with the emperor Marcus Aurelius, and declined until the fall of Constantinople in 1453.

However, suppose that instead of starting its decline in 180 AD, the Roman Empire had continued to grow its GDP at around 3% per year (a growth rate which most modern economists would be happy with) until the present day, a period of 1845 years. The total size of the Roman economy would now be 4e+23 times larger than its starting point, or if you want it in more traditional notation, 400000000000000000000000 times larger. So all things considered, it's probably a good thing that the Roman economy began to shrink when it did.

However, suppose that instead of starting its decline in 180 AD, the Roman Empire had continued to grow its GDP at around 3% per year (a growth rate which most modern economists would be happy with) until the present day, a period of 1845 years. The total size of the Roman economy would now be 4e+23 times larger than its starting point, or if you want it in more traditional notation, 400000000000000000000000 times larger. So all things considered, it's probably a good thing that the Roman economy began to shrink when it did. — Peter Gray

Could you please share your thoughts on why you believe economic growth might need to stop at some point? You claim that otherwise, it would not be logical that, if the Roman Empire never ended, its GDP would be around 4e+23 times larger than its starting point. The Roman Empire expanded into a lot of territories, and a large population was involved. Thanks to its power and economic stability, the Roman Empire was the main promoter of civilisation. I can´t see how effective to the Western world was the moment when Roman economy began to shrink. Furthermore, there are some countries whose GDP has grown exactly that percentage since their creation, like the USA or modern Japan.

Maybe we could say gradual economic growth rather than perpetual, because I guess you see it as inconvenient since there is nothing that can last forever.

Well, since the value of money (and thus economies) is inter-subjective and not objective, these values can increase indefinitely, if humans agree to give them those (inflated through our current eyes) values.

Could you please share your thoughts on why you believe economic growth might need to stop at some point? — javi2541997

I don't see it so much as a "belief", more a statement of the obvious. All economies have to be based on something, and in any finite system, that something will eventually run out. The Roman economy was based on territorial expansion, conquest and extracting wealth and slaves from the conquered territories. When they ran out of new places to expand to, or the places they might potentially expand to were so far away that their supply lines were over-stretched, the economy stopped growing. (Invade Scotland, anyone? No, I'll pass on that.). The growth of the Sumerian civilisation was based on increasing the food supply by irrigation. When new sources of water ran out, and crop yields declined because of salination of the soil, their economy stopped growing. The growth of the Easter Island civilisation was based on trees. When they cut down all their trees, their civilisation stopped growing. And so on.

Some people say that because the potential amount of knowledge is infinite, therefore a "knowledge economy" can continue to expand indefinitely, but I'm a little doubtful about that. I get sent lots of knowledge every day in the form of emails. I probably get around 50 of them every day, most of which I don't have time to read. Would my life be improved if I got 500, or 5,000 of them a day? I'm not sure that it would.

Honestly, the decay of some empires is a good example of how you used it. However, I personally think that the economic shrinkage came afterwards, and it wasn't a cause of Roman Empire decay. Furthermore, according to a large number of historians, the decay was produced by many things, but most importantly the division in half of the empire in the early 300s AD.

You claimed that the economy of the Roman Empire stopped growing and then decayed. But this only happened to the Western Roman Empire, while the Byzantine Empire (Eastern Roman Empire) endured until 1453 – the fall of Constantinople to the Ottoman Empire.
So there had been many more causes and reasons for why those empires decayed. Subsequent territories underwent significant and gradual economic growth. Look at Italy or Turkey, for instance.

I have never claimed that economic growth is infinite. I know that it can shrink at some point. But, in general terms, both GDP and GDP per capita gradually grow in most of the modern economies.