Logical Investigations

In the last couple of posts, I have discussed modal logic, and I intend to do so again tonight. I shall also touch on another couple of subjects. The unifying thread of this post is the application of reason to problems, whether those problems be logical or political. The first part of the post is dedicated to modal logic and the second part is focussed on some political issues.

I believe I can sum up the argument I have presented in the last two posts quite succinctly. Modal logic is grounded on perhaps six central claims. These might even be described as axioms. These six are:
1. "It is necessary that p" implies "It is not possible that not-p".
2. "It is not necessary that p" implies "It is possible that not-p".
3. "It is possible that p" implies "It is not necessary that not-p".
4. "It is not possible that p" implies "It is necessary that not-p".
5. "It is possible that p" implies "It is possible that not-p."
6. "It is necessary that p" implies "It is possible that p".

If we accept all six axioms, a paradox appears. Accepting premises 5 and 6 leads to the conclusion that "It is necessary that p" implies "It is possible that not-p", and this contradicts premise 1. I have described this as a paradox but it might better be described as a reductio ad absurdum – one of premises 1, 5 and 6 must be false. The first four premises are generally recognised as foundational axioms within modal logic, so the most obvious candidate for a false premise is premise 6. If we assume it to be false we should then replace it with the following premise, which we shall now assume to be true.
6b. "It is necessary that p" implies "It is not possible that p."

If we now accept the amended list of premises, however, another paradox emerges. Accepting premises 6b and 4 leads to the conclusion that "It is necessary that p" implies "It is necessary that not-p." Although premise 5 says that "It is possible that p" and "It is possible that not-p" can both be true, we cannot accept that the two propositions "It is necessary that p" and "It is necessary that not-p" can both be true. Thus, it seems that whether we accept premise 6 as being true or as being false, if we accept 6 or 6b, either way something like a paradox emerges. The problem can't be with premise 6, and so we are then forced to say that the problem is with premise 5. "It is possible that p" does not imply "It is possible that not-p". But this apparent solution forces us into the awkward position of, effectively, arguing that some or all statements of the form "It is possible that..." are really statements of the form "It is necessary that..." And because the whole point of modal logic is to draw a distinction between necessary and possible sentences, between necessary and contingent facts, the whole enterprise collapses. It collapses because its foundational assumptions are unsound.

It seems to me that there are two potential responses to the problems I have outlined in this and the previous two posts. We can suppose that all facts are necessary or we can suppose that all facts are contingent. I think, at the moment, that all facts in the world are necessary but all the beliefs we form and express about the world are uncertain. There is a gap between the world as it is and our knowledge of the world. This is also the conclusion I defended in the two posts about quantum physics, "Probability and Schrodinger's Cat" and "Probability and Schrodinger's Cat Part 2". The issue is epistemological: can we know anything for sure? What we need to do it seems to me is to abandon the Correspondence Theory of Truth in favour of some better theory of what truth is.

If we accept premise 5 wholeheartedly, the tenet that "It is possible that p" implies "It is possible that not-p" means that any statement of the form "It is possible that..." is empty of semantic content, is, according to a Fregean style analysis, meaningless. So, we can at least conclude that in our discourse about topics, we should try to avoid statements of the form "It is possible that..." and prefer statements of the form "It must be the case that..."

At this point in the post I wish to switch from a discussion of logic to a discussion of politics.

Often in this blog I have illustrated my arguments by telling stories drawn from my own life. I have described my experiences at bFM in the posts "My First Psychotic Episode" and "My First Psychotic Episode and bFM". If the two posts about quantum physics are the most important essays I have written on philosophical issues, these other two posts are the most important I have written about my life and 'illness'. I wish now to describe something that happened at bFM one morning back in 2007, something that I haven't talked about before. I know that this will be an abrupt change in the tone for this post – perhaps because I am going to say a couple of controversial things it is safest to bury my more provocative opinions in the second half of a post that began as something quite dry and abstruse.

I believe I was asked the question on Waitangi Day. Because Waitangi Day is a public holiday, there were only three of us in the station. Mikey Havoc was manning the radio desk; I was writing news stories in a side room; and a young, slightly odd woman who I don''t think I'd met before was reading the news bulletins every half hour. At one point she came out into the side room and asked me, "What's your opinion on abortion?" I couldn't work out clearly why she had asked me this question; it seemed to come out of nowhere. I should have just said that I was pro-choice but instead I equivocated, saying "It depends on your life experiences." Although I wasn't sure why she had asked me this, at some level I kind of knew. They thought I might be a fundamentalist Christian. And for some reason I found it difficult to dissuade her of this idea on the spot, perhaps because it might have seemed to ring false if I had just said that I was pro-choice. I am not one hundred per cent certain why they thought I was a fundamentalist Christian but I can hazard a good guess. A notion that circulates widely among left-leaning atheist heterosexuals almost by osmosis is that gay men who don't come out don't come out because they subscribe to a fundamentalist Christian ideology. I know that many people believe this because I believed the same thing myself. The people at bFM had decided I was one of those. The truth however was that, back then, at the age of twenty-seven, not only was I heterosexual, I was very close to being what is now called New Atheist, was in fact then a fan of Richard Dawkins. Having the people at bFM think I was a fundamentalist Christian was almost as painful to me as having them think I was gay.

In the years since, sometimes this question has come back to haunt me. I felt that I needed to give it a definitive answer, and I've never been able to. Logically, the issue is simple. We can take it as axiomatic that it is ethically wrong to take human life, and so the question becomes 'At what point during gestation does a foetus become human?' It seems obvious that a zygote or blastocyst isn't human but it also seems obvious that after say eight months a foetus is quite close to becoming a baby. Sometime during pregnancy an embryo becomes a foetus, and then a little later the foetus becomes a person. This is simple logic but expressing it can elicit hostile, distraught and emotional reactions both from people who are pro-choice and people who are pro-life. Somehow this topic came up in a conversation I had recently with my brother and he angrily stated that women have the right to do whatever they want with their bodies. I tried, in what I felt was a sober and dispassionate way, to express the problem, saying, "It's a philosophical issue. At what point are we dealing with two individuals rather than one?" But there is no arguing with some people. Someone other who weighed in on this issue was David Foster Wallace. In an essay about language and lexicography entitled "Authority and American Usage" Wallace digressed to express his views on abortion. His argument was more complicated and sophisticated than mine (it is a long time ago that I read it and so can't paraphrase it) but, like me, he ended up going right down the middle, noting in a joking way that the position he was taking would invite disapproval, condemnation, personal attacks, from people on both sides of the political spectrum.

The problem is that we lack a clear enough definition of 'human' that would enable us to adjudicate the rights and wrongs of this issue. When in doubt however, one should go with the opinions of those one trusts and likes, with one's political tribe. So I guess I should say that I'm pro-choice. If I could go back in time, though, and could change the answer I gave to the girl at bFM, I would say, instead, "It's none of my business."

Several months ago, I wrote a post in which I talked about Israel. I didn't express myself as well as I could have in that post and suffered the additional horror that I published the post the same day as the Christchurch Mosque attack (after it happened but before I had heard about it). I wish now to discuss Israel again, in a different way. I want to apply logic to this ethical minefield.

What is a nation-state? Rather than give a full definition, I simply want to say that today most Western countries are multicultural and multi-ethnic. Consider my country, New Zealand. The indigenous people here are the Maori. In 1840, a large number of Maori chiefs and representatives of the British Crown signed an enormously important document, the Treaty of Waitangi,  in which Maori were given the rights of British citizens, were guaranteed ownership of their lands, and ceded sovereignty to the Crown. Unfortunately the Maori translation of the Treaty was somewhat different than the English original, leading to disagreements about land and sovereignty culminating in all out war between the English and many Maori tribes a few years later. The treaty then languished for well over a century until, starting in 1974 and 1975, steps were taken to redress historical injustices. The Waitangi Tribunal was established to award monetary compensation to iwi who had been illegally dispossessed of their lands and rights ('iwi' being the Maori word for tribe). The word 'reparations' in not appropriate in the New Zealand context but I would like to throw it in here because New Zealand history may provide a useful analogy to an issue very much in the air in American politics.

Maori still face discrimination and systemic bias today, as Lizzie Marvelly pointed out in an opinion piece in Saturday's Herald. But it seems to me that New Zealand is perhaps the most successful post-colonial country in the world, the country that has done and is doing the most in terms of addressing the historical crimes of colonisation. A problem we face though is that New Zealand is officially bi-cultural and factually, today, multi-cultural. We receive and welcome immigrants from all over Europe, from India, from the Middle East, and from East Asia, and this complicates the picture. To be absolutely clear, I have no problem with this. It's not a good thing or a bad thing, it's just a thing. It means that I have a wonderful array of different types of restaurant I can go to when I want to eat out. In New Zealand, as in most other developed countries, a person becomes a member of a country by moving here with her family, by applying for and being granted New Zealand citizenship, by staking her future on a life here in this country. This seems normal in the world today. Like New Zealand, the modern UK is multi-cultural and multi-ethnic, having accepted large numbers of immigrants from the West Indies, from Pakistan, and more recently Poland among other places. And of course the United States is a nation of immigrants. Multi-culturalism is far more the rule than the exception.

The significant anomaly to this general consensus of what a modern liberal democracy is, is Israel. When it seemed Benjamin Netanyahu had won re-election just last week, in his victory speech he repeatedly referred to Israel as a "Jewish state" and came back again and again to the word 'zionism' in his oration. In 2018 the Knesset passed a law known as the "nation state law" and for an excellent piece of reportage about this law I recommend an article on the Internet which presents my case in many ways better than I could myself (https://www.vox.com/world/2018/7/31/17623978/israel-jewish-nation-state-law-bill-explained-apartheid-netanyahu-democracy). The situation in Israel/Palestine is analogous to the situation in apartheid era South Africa. You might want to say to me, "As a Gentile New Zealander, you have no right to have an opinion on this issue." But New Zealanders have a way of becoming concerned about what happens in other countries. Some of my older New Zealand readers may remember the Springbok Tour protests in 1981, a milestone event in New Zealand's history that provided the backdrop to a story I published in this blog, "The Good Ol' Days."

Logically, it seems to me, a country that privileges one ethnicity and one religion over all others is racist. Israel, in its conception, is racist. Of course, Israel is not alone in privileging one group over others – Saudi Arabia and Iran, for example, are both officially Islamic states. But, unlike Saudi Arabia and Iran, Israel pretends to be a liberal Western democracy and pushes back against those who accuse it of illiberality by accusing them of racism.

The conversation about this issue on the Left is clouded, distorted, by knee-jerk emotion; often any opposition to the Israeli Right is conflated with anti-semitism. The mistake I made in the previous post about Israel was that, for whatever reason, perhaps because the collective unconscious had been stirred by events I wasn't consciously aware of, I didn't do a good enough job distinguishing between principled opposition to Netanyahu and anti-semitism. But they are two totally different things. In fact, a deeply disturbing truth is that there are white supremacists in the United States who approve of Israel and hold it up as a kind of role model, who think America should become a whites-only country in the same way that Israel is a Jews-only country. A kind of zionist anti-semitism exist. I know this claim about some white supremacists is shocking but, although I can't direct the reader to any relevant site to prove it, I have seen a white supremacist on the Internet who made this argument, and it is a rational position for some white-supremacists to take.

On his show a couple of weeks ago, Bill Maher said that people who support Palestinian self-determination are ignorant of history. In writing this post I have done a little research into the history of Israel and the Palestinian Territories, and this research has not dissuaded me of my opinion that the currently prevailing situation is morally untenable. Rather than rehash the whole history of the region, I direct the reader to the articles on wikipedia about the birth of Israel and the string of Arab-Israeli wars that have occurred since 1947. I hope that these essays are more or less correct. Something important I learned from them is that there has never been a Palestinian state. Prior to World War 1, the area then known as Palestine was a province of the Ottoman Empire; during WW1 it was taken over by the British. Between 1947 and the Six-Day War in 1967, the West Bank was ruled by Jordan, and the Gaza Strip by Egypt. The idea of a possible independent Palestinian state wasn't floated formally until the Palestinian Declaration of Independence in 1988.

Defenders of Israel's actions, ranging from officials in the Israeli administration to supposedly objective bystanders like Bill Maher and Sam Harris, argue that Israel is fighting for its very right to exist, that the Arab populations living around and within Israel's borders wish to wipe Israel off the map. Such opinions, I understand, are bolstered by literal readings of statements such as the founding constitution of Hamas. However, we need a better answer to this problem than the stupid idea that either Israel or the Palestinians should just disappear. The UN answer has been for a long time the two-state solution. What I wish to suggest, tentatively, is that the whole area, Israel and the Palestinian Territories together, should become a single country, a modern liberal state that is multicultural and accepts that it is made up of many ethnic groups. I believe that this is Noam Chomsky's preferred answer to this almost irresolvable problem.

My views on Israel are shaped by my experience of living as a Pakeha New Zealander in a multicultural county that has for a long time been seeking to atone for the evils of colonialism. We can't undo colonialism, in the same way that liberal Americans can't undo slavery – all we can do is apologise, make restitution and ensure that Maori today are treated at least as fairly as Pakeha. Maori themselves know that we can't return to pre-1840 New Zealand; there may be some Maori who wish to rise up in revolt and restore Maori sovereignty over our islands, but, if so, I've never heard of one or met one. We all, Maori and Pakeha alike, have to live with our colonial history. In the previous post about Israel, I said, "Whether the establishment of the state of Israel was a good thing or a bad thing is irrelevant. Israel has been around for over seventy years and isn't going anywhere." The best answer, in a utopian world, would be for Israel and Palestine to amalgamate, and for Jewish and Arab citizens alike to be granted equal citizenship under the law. Of course, this raises the question – what should we call this country? Israel or Palestine? In New Zealand, we use the English name for the country, New Zealand, and the Maori name, Aotearoa, almost interchangeably and often use both. For a number of years now, before sporting fixtures, it has been customary to sing both the Maori and English versions of the national anthem. In the same way, the nation known as Israel and the Palestinian Territories should belong to both groups, to the indigenous inhabitants as much as to the settlers.

I hope this post makes sense. I have found it extraordinarily difficult to write, and I hope I have expressed myself clearly. I hope that nothing horrible happens in the world tomorrow. I am going away to Whanganui for a week tomorrow and, when I get back, my next post is probably going to be about philosophy again. I'll work out then what to write about.