BLOGS

The following Blogs are numbered and dated, the earliest Blog being first.

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BLOG # 1, RE.: INDUCTIVE LOGIC AND THE COVID-19 PANDEMIC

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The definition of “blog” upon which I rely is: “a regular record of your thoughts, opinions, or experiences that you put on the internet for other people to read”, Cambridge English Dictionary. For convenience of future reference I will number my blogs, so this is Blog # 1. None of my blogs should be relied upon as legal advice, because none of them are legal advice. If you want my legal advice, including on issues related to Covid-19, please contact me. For my phone number and e-mail address click here.

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“True ignorance is not the absence of knowledge, but the refusal to acquire it.” Karl Popper (1902-1994), a brilliant philosopher.

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“[T]his civilization has not yet fully recovered from the shock of its birth — the transition from the tribal or "enclosed society," with its submission to magical forces, to the 'open society' which sets free the critical powers of man.” Karl Popper, The Open Society and its Enemies, Vol. 1, at page xvii, Routledge Classics 2003.

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“You can choose whatever name you like for the two types of government. I personally call the type of government which can be removed without violence "democracy", and the other "tyranny".” Karl Popper. As quoted in Freedom: A New Analysis (1954) by Maurice William Cranston, p. 112.

The above three quotes of Karl Popper are relevant to my first blog, which is about inductive logic, and the Covid-19 pandemic.

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Inductive logic is a vital topic for the practice of law, and indeed for survival of the human race, yet this crucial topic is currently overlooked or disregarded by many people in society, resulting in many avoidable deaths from Covid-19.

My sympathies go out to the victims of this terrible pandemic, including society’s heroic health care workers. The victims and health care workers, and society in general, deserve far better from those people who can reduce Covid-caused deaths and harm, yet who do not.

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For those people who can reduce Covid-caused deaths and harm, yet who do not, a poem is apt, The General, by Siegfried Sassoon (1886-1967). He was an English World War I poet, writer, patriot, and soldier decorated for bravery.

The General

“Good-morning, good-morning!” the General said

When we met him last week on our way to the line.

Now the soldiers he smiled at are most of 'em dead,

And we're cursing his staff for incompetent swine.

“He's a cheery old card,” grunted Harry to Jack

As they slogged up to Arras with rifle and pack.

But he did for them both by his plan of attack.

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Philosophers agree, in the modern English-speaking world, on some terminology used for certain concepts in deductive logic. They agree on what they mean by “validity” and “invalidity”, and, on what they mean by a “sound” deductive argument, which means a valid argument with true premisses, thus guaranteeing a certainly true conclusion.

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But alas there is no standard terminology used for certain analogous concepts in inductive logic. This lack of a standard terminology in inductive logic makes describing what inductive logic is, partly an exercise in defining terminology. My definition of an inductive argument is: a claim of cogency between different propositions each asserted to be true to some probability or other.

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In the next blog I will describe the difference between a deductive argument and an inductive argument, which is a very important distinction in logic, and, I will begin to address exactly what makes an inductive argument “cogent” and what makes it “good”. Under my terminology, if an inductive argument does qualify as “good”, its conclusion is probably true.

What has an inductive argument being “good” have to do with the law, and with countering the Covid-19 pandemic ? A great deal, as shown in the next blog, although you presumably know the answers if you already know all of the essential ingredients to form a good inductive argument.

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Various professional soccer leagues around the world finished their seasons during the pandemic. These leagues showed, with comprehensive and frequent Covid-19 testing of all players (and other science-based Covid risk-reducing measures), how people around the world can return to work with very significantly reduced Covid risk. Congratulations to: the German Bundesliga, the English Premier League, the Spanish La Liga, the Italian Serie A, and the United States’ MLS. And congratulations also to these countries' respective 2019-2020 national soccer champions: Bayern Munich, Liverpool, Real Madrid, Juventus, and Portland Timbers.

Hopefully, governments, employers, and employees, will all implement the above tried and tested successful science-based model, using comprehensive and frequent Covid-19 testing (and other science-based risk-reducing measures), because the only realistic alternative is: much avoidable death, harm, bankruptcy, and poverty. And those people who can work from home should work from home, as that also helps to reduce Covid risk. Hopefully, governments, employers, and employees, will respect this fact too, because the only realistic alternative is: much avoidable death, harm, bankruptcy, and poverty. The virus that causes Covid-19 is extremely contagious. In this pandemic, what was initially a viral infection in just one person or in very few people, nine months ago, has now infected over twenty million people around the world, and this despite many efforts to reduce its spread. Even if a vaccine is found, and used widely, this will only help to reduce Covid risk, and so other risk-reducing measures will still be necessary. Ethically and economically our new normal should be based on all that science offers, not on wishful thinking nor the result of callous indifference.

Stay safe.

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Here is a great performance of Beethoven’s Moonlight Sonata, https://www.youtube.com/watch?v=GXjhc8EbY4I, which you may find soothing in these dark days.

Blog posted 8/21/20.

BLOG # 2, RE.: MORE ABOUT INDUCTIVE LOGIC AND THE COVID-19 PANDEMIC

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The definition of “blog” upon which I rely is: “a regular record of your thoughts, opinions, or experiences that you put on the internet for other people to read”, Cambridge English Dictionary. None of my blogs should be relied upon as legal advice or medical advice, because none of them are legal advice or medical advice. If you want my legal advice, including on issues related to Covid-19, please contact me. For my phone number and e-mail address click here.

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“He that judges without informing himself to the utmost that he is capable, cannot acquit himself of judging amiss.” John Locke, An Essay Concerning Human Understanding (c. 1690), Book II, Ch. XXI § 67.

DEDUCTIVE ARGUMENT VS. INDUCTIVE ARGUMENT, AND WHY TRIAL LAWYERS AND HUMANITY IN GENERAL SHOULD UNDERSTAND BOTH

To understand the difference between deductive argument and inductive argument one must know the difference between a “necessary” truth and a “contingent” truth. A necessary truth could not possibly be false in any possible universe, in any circumstances, it can only be true. In contrast, a contingent truth only happens to be true, and, in different circumstances, it could be false. For instance, the German army did not capture Moscow in World War II, but, had there been a mild dry winter in 1941-1942, the German army might have captured Moscow.

In a valid deductive argument if its premisses are true its conclusion is necessarily true. But deduction tells us nothing about contingent truths, nothing about our everyday world, nothing about contingent facts. Nonetheless, deduction is of practical importance, not least because we humans sometimes make invalid deductive arguments, and rely on them, sometimes with destructive - or even fatal - consequences.

I call a well-reasoned inductive argument “cogent”. In a cogent inductive argument if its premisses are true its conclusion is probably true, provided certain other requirements are met. In my next blog I will describe the remaining requirements for an inductive argument to be good. To know what makes an inductive argument good is important for trial lawyers and for humanity in general. If an alleged fact cannot be proved by direct evidence, such as by a witness seeing one man hit another man, the alleged fact can only be proved (if at all) indirectly, that is, in a good inductive argument. Good inductive argument is sometimes crucial in a trial, because there may be no direct evidence of an alleged fact.

INDUCTIVE ARGUMENT AND COUNTERING THE COVID-19 PANDEMIC

Because inductive argument can be informative about contingent truths, and because Covid is killing so many people, all rational humane people who are aware of the pandemic desire a good inductive argument with this conclusion: “therefore, we, the human race, are at minimal risk from Covid”. That desired conclusion is of course contingent, and is not presently supported, given the present level of understanding of the virus and often irresponsible human behavior.

Scientists, by researching for ways to minimize Covid risk, are working to help to reach the desired conclusion in a good inductive argument. But even if they find a safe and very effective vaccine, and a safe and very effective treatment, there will still be some degree of inefficacy, including because many people, including many or all of the young, will not even take the vaccine. Because the virus that causes Covid-19 is very contagious, even with effective vaccines and treatment we will still need mass, frequent, quick, and highly accurate Covid testing (and to isolate those with Covid), in order to attain the desired conclusion in a good inductive argument. No one measure will suffice to eradicate Covid from the world. Multiple and broadly applied layers of different anti-Covid measures are necessary.

MASS COVID TESTING IS A CATEGORICAL MORAL IMPERATIVE AND REQUIRES GOVERNMENTAL ACTION

Each person should be tested for Covid each day and not enter the public if the result is positive. Even with highly accurate testing there will be some false negatives, and so more than mass testing is needed to reach the desired conclusion in a good inductive argument.

The current absence of mass testing is a shocking failure by those people in a position to create mass testing; their failure has resulted in thousands of avoidable deaths.

There are various Covid tests, some based on nasal swabs, some on saliva, some on breath, some on blood, and some using sniffer dogs. Clearly to test everybody every day is a huge logistical undertaking, but there is no rational choice, in order to reach the desired conclusion in a good inductive argument. To achieve such testing requires governmental commitment, to marshal, as quickly and fully as possible, society’s formidable resources to achieve this testing.

On June 20, 2020 Columbia University announced a highly reliable and rapid (approx. 30 minute) saliva-based Covid test. This test can be performed without a laboratory. And, on July 29, 2020, Sorrento Therapeutics Inc. (a publicly traded company) announced it had made a licensing agreement with Columbia for this test. Why has the test not been mass-produced and mass-deployed yet ? I find no evidence on-line that Sorrento has even applied for FDA-approval for this remarkable test. What is going on ?

The Yale School of Public Health developed a different saliva-based test, and received FDA approval for emergency use, as announced on a Yale website on July 29, 2020. The Yale test requires a laboratory to be performed, unlike the Columbia/Sorrento test, and, is not being commercialized, in contrast to the Columbia/Sorrento test. Does this non-profit decision by Yale (or Abbott’s $5 Covid test) explain why Sorrento has not mass-produced and deployed its test ? Why should Sorrento produce its test if there’s no profit in it ?

Clearly, we need an immense governmental commitment to mass-produce daily Covid tests and to deploy mass daily testing. Thousands of people have avoidably died without this commitment, and thousands more will die if this commitment is not made. While the cost of such testing may be billions, the cost of no such testing is: trillions, thousands of lives avoidably lost, and, perhaps, societal collapse.

OTHER ANTI-COVID MEASURES ARE A CATEGORICAL MORAL IMPERATIVE AND A DUTY OF GOVERNMENT

Why have not all government dogs been trained to detect Covid ? Dogs are used at Dubai airport, Beirut airport, and at Helsinki airport, to detect Covid. Why are there no government-funded kennels, so that private dog-owners can have their dogs trained to detect Covid ?

Why has the government not mass-produced and distributed protective equipment for medical personnel and other workers at high risk of Covid infection ?

Why has the government not mass-produced and distributed masks that simultaneously protect the mouth, nose, and eyes, from Covid ?

Why has the government not mass-produced and distributed Covid antibody tests ?

SOME MATHEMATICS OF MINIMIZING FALSE NEGATIVES IN COVID TESTING

Suppose one uses three different sorts of Covid test, e.g. based on: saliva, breath, and dog-detection, respectively. If each sort of test is 90% accurate, then performing all three tests on a person yields a mere .1 % triple false negative result, assuming the tested person is from a group in which all members of the group have Covid. The probability of a false negative is 10% on each of the three tests, and 10% x 10% x 10% = .1 %. (10% expressed as a probability, where 1 is certain, is .1, and .1 x .1 x .1 = .001 probability, and, x 100 - to convert the probability scale into a percentage - is .1%.)

Of course if all members of the group do not have Covid, then no negative test result is false (from anyone tested in that group), and so the probability of a false negative result is zero. If half the members of the group have Covid and half do not, then the probability of a triple false negative is .05% (again, using the three different tests each of 90% accuracy). Obviously the incidence of Covid in the group affects the percentage of false negatives. There is no opportunity for any error of a false negative among the 50% of group members who do not have Covid, and so they lower the error rate by 50%, making the .1% instead .05%, as .05% is 50% of .1%. Clearly the higher the rate of Covid infection in society, the more significant is the level of accuracy of Covid testing.

In a city of 100,000 people, 10% of whom have Covid, there are 10,000 people with Covid. The probability of any given individual having Covid is 10%. If 100 people from this city enter a building on a day, what is the probability that nobody in the building that day has Covid, if there is no Covid testing measure ? For each given individual, the chance is 90% of not having Covid, but for all 100 people not to have Covid, the probability is tiny, as 90% to the power of 100 = 0.00265%, which is tiny. (By “90% to the power of 100” is meant: 90% multiplied by itself 100 times.) Here is a table that reflects the probability benefit of triple Covid testing, using different sorts of Covid test.

Now suppose that the probability of any given person having Covid is 3%, and a building has 100 people in it.

As one might expect, the higher the rate of Covid infection in society (e.g. 10% vs. 3%), the greater the benefits of using all three Covid tests in trying to prevent those with Covid from entering a building. How many Covid tests do you want the entrants to a building to undergo, for a building you enter: none, one, two, three, or more ?

With just a 10% Covid infection in society, there is an 8.525% benefit to the third test over the second test. As we do not know the Covid infection % in society, and it could exceed 10%, conducting three tests, at least, is prudent, until such time as we do know the Covid infection % in society is 10% or less. If, for instance, the Covid infection % in society is 20%, here’s the table for a building with 100 people in it.

WHAT OUR NEW NORMAL SHOULD BE

People are morally wrong to endanger the lives of others (and their own lives) by Covid-risky behavior. Ethically and economically our new normal should be based on implementing rigorously all that science offers to minimize Covid-risk, not be based on wishful or muddled thinking, nor on false “facts”, nor be the result of callous indifference or complacency.

SCIENCE IS KING

Reason and evidence are insufficient to convince many people that implementing rigorously all that science offers to minimize Covid-risk, is crucial to minimize that risk. Therefore, other means of mass persuasion are required, so that people do follow science. Besides some new laws, mass messaging is needed. Science must be widely perceived as splendid, which it is. Substitute the word “Science” for the word “Solomon” in George Handel’s coronation anthem, Zadok the Priest, and this yields a broadly appealing sound track for the immense value of science. Here are the words of the anthem:

Zadok the priest

And Nathan the prophet

Anointed Solomon king

And all the people rejoiced, rejoiced, rejoiced

And all the people rejoiced, rejoiced, rejoiced

Rejoiced, rejoiced, rejoiced

And all the people rejoiced, rejoiced,

Rejoiced and said:

God save the king

Long live the king

God save the king

May the king live forever

Amen, amen, alleluia, alleluia, amen, amen

Amen, amen, alleluia, amen

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God save the king

Long live the king

May the king live forever

Amen, amen, alleluia, alleluia, amen

May the king live

May the king live

Forever, forever, forever

Amen, amen, alleluia, alleluia, amen, amen

Alleluia, alleluia, amen, amen, amen

Amen, amen, alleluia, alleluia, alleluia, amen

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God save the king

God save the king

Long live the king

May the king live

May the king live

Forever, forever, forever

Amen, amen, alleluia, alleluia, amen, amen, amen,

Amen, amen, amen, alleluia, amen

Alleluia, alleluia, alleluia,

Amen, alleluia!

Handel wrote Zadok the Priest for the coronation of England’s King George II, in 1727. The purpose of the anthem was one of mass messaging: to promote the English monarchy. The anthem, with its dazzling music, has been played at every English coronation since 1727. And the British monarchy still exists, though many other nations’ monarchies have perished since 1727.

Moreover, since 1992, the music of this anthem has been repurposed for very different mass messaging: to promote the UEFA Champions League. This is the top club soccer competition in Europe. The music of Zadok the Priest, albeit somewhat altered, remains captivating to huge t.v. audiences around the world, who watch this soccer competition.

Ironically, professional soccer is still being played around the world during the pandemic, by adhering to science, including by frequent Covid-testing, as described in my Blog # 1. And various universities in America are operating, by adhering to science, including by frequent Covid-testing. Air travel, domestic and international, to be restored to its pre-Covid level, will also require adhering to science, including by frequent comprehensive Covid-testing. And the same is true throughout the many public contexts of society.

While all non-governmental science-based anti-Covid measures are commendable (unless overpriced), they are woefully insufficient for society as a whole. A massive and relevant governmental science-based response is vital to end Covid. Indeed, a massive fully coordinated international response is vital to end Covid. Gens una sumus. We are one people.

Science is crucial, but cannot alone end Covid. Each of us should obey science.

Stay safe.

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On YouTube there are many fine performances of Zadok the Priest, from around the world. The following performances, from England, Prague, and Korea, may thrill you.

https://www.youtube.com/watch?v=MiXgOQ9_-RI,

https://www.youtube.com/watch?v=C71oMzDKuO4

https://www.youtube.com/watch?v=zWG4k9IMNTg

Blog posted 10/14/20, and modified subsequently.

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BLOG # 3, RE.: MORE ABOUT INDUCTIVE LOGIC AND THE COVID-19 PANDEMIC

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The definition of “blog” upon which I rely is: “a regular record of your thoughts, opinions, or experiences that you put on the internet for other people to read”, Cambridge English Dictionary. None of my blogs should be relied upon as legal advice or medical advice, because none of them are legal advice or medical advice. If you want my legal advice, including on issues related to Covid-19, please contact me. For my phone number and e-mail address click here.

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“Requirement of total evidence: in the application of inductive logic to a given knowledge situation, the total evidence available must be taken as basis for determining the degree of confirmation. …

The theoretical validity of the requirement of total evidence cannot be doubted. If a judge in determining the probability of the defendant’s guilt were to disregard some relevant facts brought to his knowledge; if a businessman tried to estimate the gain to be expected from a certain deal but left out of consideration some risks he knows to be involved; or if a scientist pleading for a certain hypothesis omitted in his publication some experimental results unfavorable to the hypothesis, then everybody would regard such a procedure as wrong.

The requirement has been recognized since the classical period of the theory of probability. Keynes [A Treatise on Probability, (Macmillan 1921)], p.313 refers to ‘Bernoulli’s maxim, that in reckoning a probability, we must take into account all the information which we have.’” Rudolf Carnap (1891-1970), Logical Foundations of Probability, University of Chicago Press, Chicago, 1950, second edition 1962, at pp. 211-212.

THE REQUIREMENTS FOR A GOOD INDUCTIVE ARGUMENT

I call a well-reasoned inductive argument “cogent”. In a cogent inductive argument if its premisses are true then its conclusion is probably also true, provided certain other requirements are met. Such an argument I call “good”, and the only inductive arguments that we are rational to rely upon are good. In my last Blog I indicated I would in my next Blog state the remaining requirements for a good inductive argument. In this Blog I provide a complete statement of the requirements for a good inductive argument.

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However, the statement of the requirements, below, is skeletal, because much can be written on this topic, and in my book, The Solution to an Injustice in Trials (described here), I take many pages to describe the requirements in detail. For instance, the statement of the requirements, below, uses the term “inductive principle” but does not define that term. The book contains both a detailed definition of this term and an approximate definition. In this Blog only the approximate definition is given. An “inductive principle” means, approximately, any assertion that describes any alleged: non-coincidental recurring conditional pattern in contingent reality, be that pattern in nature, e.g. laws of physics, such as the law of gravity, or, be that pattern in Man-made circumstances, e.g. punctuality rates for different airlines. "Contingent reality" is that which actually happens to exist.

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Also, in the statement of the requirements for a good inductive argument, below, I use only one standard, which I call the “Collective Standard" in the book, though the book also provides an "Individual Standard", which is a lower standard for judging if an argument is "good". Quite often a man has available to him only this lower standard for judging an argument, such as where the argument's conclusion falls under an expert topic and he is not an expert in that topic.

The Collective Standard is based on: the collective knowledge of Man relevant to the conclusion of the inductive argument in question. An argument that is good under the Collective Standard may, perhaps, later be refuted, because the collective knowledge of Man relevant to the conclusion may change over time. New evidence may refute an old conclusion.

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The six requirements for a good inductive argument, under the Collective Standard

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Collective Standard Essential 1) Inductive argument. An inductive argument (as an inductive argument is necessary for a good inductive argument; what constitutes an “argument”, and, what constitutes an “inductive argument” are defined in The Solution to an Injustice in Trials, and are outlined respectively under the Author tab, and in Blog # 2 above). And,

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Collective Standard Essential 2) Known probability/ies of proposition/s in premiss/es. The probability/ies of the proposition/s in the premiss or premisses being true is known, to at least some basic approximate degree, under collective human knowledge, as this is a prerequisite to Collective Standard Essential 6. The probability of asserted data (e.g. in premiss/es) being true is unknown, e.g., if: 1) the asserted data only comes from an unreliable source, and, 2) there is no independent and rational way by which to judge the accuracy of the asserted data. And,

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Collective Standard Essential 3) Cogency. The inductive argument is cogent, i.e. well-reasoned, as opposed to merely claiming to be cogent, as a cogent inductive argument is necessary - but not sufficient - for a good inductive argument. By a “cogent” argument is meant any inductive argument in which the premiss/es do support the conclusion, as a matter of reasoning, that is:

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A) the premiss/es of the argument is/are presupposed to be true in any determination of whether or not the argument is cogent, so if a premiss asserts its proposition is 90% probably true, then presupposed, for determining cogency, is that the proposition is 90% probably true, and,

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B) there is some inductive principle or combination of inductive principles, that is both:

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1) relevant to the premiss/es to support the conclusion, and,

2) sufficiently probably true to support the conclusion.

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The inductive principle, or combination of principles, to be used in judging if any inductive argument is cogent – the applicable principle/s, is/are always, among all of the inductive principles known to Man to be relevant to the premiss/es to support the conclusion, that principle, or combination of principles, which is known to Man to have the highest probability of being true.

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An argument can be cogent despite having a false premiss known to be false. This possibility of cogency (despite a known false premiss) exists because whether an argument is cogent is determined on the presupposition the premisses are true.

And, under collective human knowledge, the probability of applicable inductive principle/s being true is known to at least some basic approximate degree, as otherwise cogency is not satisfied.

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The probability of an inductive principle being true is unknown, e.g., if: 1) data that ostensibly supports the principle as being probably true only comes from an unreliable source, and, 2) there is no independent and rational way by which to judge the probability of the principle being true. And,

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Collective Standard Essential 4) No omniscient conclusion. The argument’s conclusion does not assert or imply that the proposition in the conclusion is absolutely certainly true or is absolutely certainly false, but rather asserts or implies any other probability (than 100% or 0%) that said proposition is true or is false. A conclusion of an inductive argument consists of two parts: 1) a stated proposition, and, 2) a probability asserted for that proposition being true. This yields various possibilities, including the following possibilities.

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Possibility 1: a specified probability number. The probability that a conclusion asserts for its proposition being true may be any number from 0% to 100%, but 0% or 100% do not satisfy Collective Standard Essential 4, making any such argument bad for that reason.

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Possibility 2: a specified probability number preceded by “at least”. Another possibility in a conclusion is an assertion of “at least”, with a probability % specified for the proposition in the conclusion being true, e.g. “at least 90% proposition X is true”.

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Possibility 3: a specified probability number preceded by “greater than or equal to”. Another possibility in a conclusion is an assertion of “greater than or equal to”, with a probability % specified for the proposition in the conclusion being true, e.g. “greater than or equal to 90% proposition X is true”.

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Possibility 4: probability just in words. Just words, not numbers, can be used in a conclusion to assert a probability of its proposition being true, e.g. where “probably” means greater than 50% and less than 100%. (If “probably” in any given conclusion does include 100% this violates Collective Standard Essential 4.) E.g. “probably proposition X is true”, which means “over 50%” but not 100% proposition X is true”.

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Possibility 5: a probability range expressed with numbers. A conclusion can state the probability of its proposition being true in a probability range, with numbers, e.g. proposition X is 70%-80% probably true.

Possibility 6: a default implied assertion of 100% probability. If no probability number and no probability in words are expressed in the conclusion for the proposition in the conclusion being true, then, by default, the conclusion implicitly asserts a 100% probability for the truth of its claimed proposition, and so fails to satisfy Collective Standard Essential 4.

So there are different sorts of possibilities for the probability claimed in the conclusion, for its proposition being true. The above list of such possibilities is not exhaustive.

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Collective Standard Essential 4 is required for “good” inductive argument because inductive argument is, inherently, less than absolute in what it can prove. Yet, many inductive arguments in life fail to meet this Essential of good inductive argument. Such is human dogmatism. Some words of Oliver Cromwell (1599-1658) serve to underscore this Essential of good inductive argument: “I beseech you, in the bowels of Christ, think it possible you may be mistaken.” Cromwell wrote this to the Scots after the execution of King Charles I, because the Scots recognized Charles’ eldest surviving son as the rightful King. And,

Collective Standard Essential 5) Total evidence. The argument includes in its premiss/es all collective human knowledge that is relevant to the conclusion (whatever probability the conclusion asserts for its proposition being true), with two exceptions: 1) any such knowledge that is not “conclusion-altering” need not be included in the premiss/es in order for the inductive argument to be good (the precise meaning of “conclusion-altering” is stated in The Solution to an Injustice in Trials), and, 2) knowledge of any inductive principle that is relevant to the conclusion is not required in the premiss/es in order for an inductive argument to be good. (Essential 5 satisfies a requirement for good inductive argument that logicians call "total evidence". This is shown in The Solution to an Injustice in Trials, quoting the logician Rudolph Carnap). And,

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Collective Standard Essential 6) Justified premiss/es, but with one harmless exception, and, sufficiency for the conclusion. For a premiss of an inductive argument to have any probative power the premiss must be justified, that is, the premiss must: 1) assert correctly the probability of its indicated proposition being true (i.e. that asserted probability is supported by evidence), and, 2) that probability must be greater than 0%. A proposition of 0% probability of being true, in a premiss, has no probative value and so cannot factually support (or refute) the conclusion of any inductive argument. If an argument is cogent then every premiss that is required for the argument to be cogent must be humanly known to be justified (as defined above), in order to satisfy Collective Standard Essential 6 of good inductive argument. And if an argument is not cogent, any and every unjustified premiss in it violates Collective Standard Essential 6. Such an argument is defective both as a matter of logic (it is spurious), and as a matter of fact (due to its unjustified premiss/es), and so is not good / is bad.

However, a cogent argument may have a premiss that is not required for cogency: a premiss irrelevant to the conclusion. An irrelevant premiss in a cogent argument can be unjustified without violating Collective Standard Essential 6. Only an irrelevant unjustified premiss is harmless, and is the only exception to the rule that for every inductive argument all of its premisses must be justified (as defined above) for the argument to satisfy Collective Standard Essential 6.

The premiss/es and applicable inductive principle/s (if any) must achieve sufficient proof to satisfy the conclusion of an inductive argument, in order for the argument to be good. Whether the premiss/es and applicable inductive principle/s (if any) do provide sufficient proof to satisfy the conclusion of an inductive argument depends on what/how much the premiss/es and applicable inductive principle/s (if any) do prove (if anything), and, on whether what they prove (if anything) satisfies exactly what the conclusion asserts, not less than the conclusion asserts, nor more than the conclusion asserts. For the premiss/es and applicable inductive principle/s to prove the conclusion, the premiss/es and applicable inductive principle/s must, together, be sufficiently probably true to prove the conclusion. This is illustrated further below. To determine what the premiss/es and applicable inductive principle/s do prove (if anything), requires having basic approximate probability numbers for the propositions in the premiss/es being true, and for the applicable inductive principle/s being true. Without such knowledge, regarding a given argument, Collective Standard Essential 6 cannot be met, and so the argument in question is not good / is bad. This is the fate of many inductive arguments in life. With such knowledge, there are some rules of probability for using this knowledge, to determine if Collective Standard Essential 6 is met. These rules of probability concern in which sorts of circumstances probabilities should be multiplied, to yield an overall probability, and, in which other sorts of circumstances probabilities should be added, to yield an overall probability.

Probabilities that can both happen in combination (but not necessarily simultaneously) should be multiplied. E.g. if a coin is tossed twice the overall probability that the coin lands heads twice (heads and heads) is: 1/2 x 1/2 = 1/4. In some cases in which probabilities can both happen in sequence, the former probability affects the latter probability. E.g. with 13 spades in a deck of 52 cards, the overall probability of the first two cards drawn from the deck being spades is 13/52 (for the first card being a spade) x 12/51 (for the second card being a spade given the first card was a spade) = .058.

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Probabilities that are mutually exclusive possibilities should be added. E.g. the overall probability of rolling a "1" or a "2" with a single roll of a six-sided die is: 1/6 + 1/6 = 2/6. E.g. the overall probability of getting at least one heads in two tosses of a coin is: ¼ + ¼ + ¼ = ¾. Each of these ¼ probabilities contains at least one heads and each is a mutually exclusive possibility, respectively: heads heads, heads tails, and tails heads. Only the tails tails possibility (also a ¼ probability) fails to include a single heads.

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If a premiss does not explicitly assert a probability for its indicated proposition being true, then, by default, the premiss implicitly asserts a 100% probability for its indicated proposition being true.

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Next are an inductive argument, some probability data, and analysis, to illustrate how to determine if an inductive argument satisfies Collective Standard Essentials 3 and 6, and is good.

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Premiss: The ship Mary was made in John’s shipyard.

Conclusion: So, the ship Mary was probably painted black and white.

90% probably true applicable inductive principle: all ships made in John’s shipyard are painted black and white.

Is the argument cogent, as required by Collective Standard Essential 3 ? To determine cogency, the premiss is presupposed to be true. The above premiss is silent as to the probability it asserts for its proposition, and so by default the premiss means: to a 100% probability the ship Mary was made in John’s shipyard. If the premiss is true this means that its asserted 100% probability for its proposition is correct/actual/justified, i.e. if the premiss is true then 100% the ship Mary was made in John’s shipyard.

The above 90% probably true principle links to the 100% premiss (assumed to be true), and together they yield a 90% probability that the Mary was painted black and white, because 100% (for the assumed premiss) x 90% (for the applicable inductive principle) = 90% that the ship Mary was painted black and white. And that 90% probability satisfies the conclusion, which merely asserts that “the ship Mary was probably painted black and white”. So, the above argument is cogent. But does the above argument satisfy Collective Standard Essential 6 ? No, unless we know that the above premiss is justified.

Now suppose we learn, related to the premiss, that to a 60% probability the ship Mary was made in John’s shipyard. With this new knowledge the above argument remains bad, as it definitely has an unjustified relevant premiss: an assertion of a 100% probability that the ship Mary was made in John’s shipyard. But notably, from the above data, the premiss of the bad argument can be altered, to make a good argument with the same conclusion as the above bad argument. The premiss of the altered argument is: to a 60% probability the ship Mary was made in John’s shipyard. This premiss is justified (by asserting the justified 60% probability, not unjustifiably asserting 100%), and so the altered/justified premiss does not render the altered argument bad, unlike the unjustified premiss which rendered the unaltered argument bad. And this altered argument, with its new and justified premiss, is cogent, as shown next.

There is an applicable inductive principle that links the justified premiss to the conclusion, that the ship Mary was probably painted black and white. The above 90% probably true principle links to the justified premiss’s assertion of 60%, and together they yield an at least 54% probability that the Mary was painted black and white, as 60 % (for the probability asserted in the premiss) x 90% (for the applicable inductive principle) = at least 54 % that the ship Mary was painted black and white. And that at least 54% probability satisfies the conclusion, which merely asserts that “the ship Mary was probably painted black and white”.

Explanation for multiplying probabilities, and for “at least”. The above 54% comes from 60% x 90% = 54%. The 60% and 90% concern two conjoined possibilities that can both happen, and so they are appropriately multiplied together (= 54%), per probability’s multiplication rule. The “at least” in “at least 54%” is because of the possibility that if Mary was made not in John’s shipyard, Mary nonetheless was painted black and white.

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N.B. that any proposition of 0% probability of being true, i.e. a certainly false proposition, has no probative power. Thus to use a probability of 0% for a premiss, in calculating the probability of the proposition in the conclusion, is a basic mistake. A false premiss is unusable for judging a conclusion. Otherwise, every conclusion could be refuted by including it in an argument with a false premiss, as 0% (for the false premiss) x any % (for the applicable principle/s) = 0% for the proposition in the conclusion.

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Cogent and good. The “at least 54%” satisfies the probability asserted in the conclusion for Mary being painted black and white, i.e. the probability asserted by “probably” in the conclusion, which “probably” is met by “at least 54%”. So the altered argument is cogent, thus satisfying Collective Standard Essential 3.

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The altered argument, with its altered and justified premiss, also satisfies Collective Standard Essential 6. And, the altered argument also satisfies Collective Standard Essentials 1, 2, and 4, as the reader can judge. As for satisfying Collective Standard Essential 5, the “total evidence” requirement, the argument is assumed to satisfy that, which is a fair assumption to make in this purely explanatory context of illustrating good inductive argument. Thus, because the argument satisfies all six Collective Standard Essentials, the argument is a good inductive argument, under that standard.

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More data. Now suppose there is some more probability data, for another applicable inductive principle regarding the above argument: an 80% probably true applicable inductive principle: all ships not made in John’s shipyard are painted black and white. The probability analysis for that argument now is: (60% x 90%) + (40% x 80%) = the probability Mary was painted black and white. Thus 54% + 32% = 86% probability Mary was painted black and white. The “86%” satisfies the probability asserted in the conclusion for Mary being painted black and white, i.e. the probability asserted by “probably” in the conclusion.

Explanation for adding probabilities. The above 60% and 40% cover two mutually exclusive events (as to where Mary was made), and so their respective associated probabilities (obtained by multiplication, 54% and 32% respectively) are appropriately added together (= 86%), per probability’s addition rule.

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Whenever the probability of the proposition asserted in the conclusion can be calculated, one always multiplies the probability/ies in the premiss/es by the probability/ies of the applicable inductive principle/s, and, if mutually exclusive possibilities are also involved, one also adds their probabilities (respectively obtained by multiplication), as shown above.

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DEVELOPMENTS IN THE COVID PANDEMIC SINCE MY LAST BLOG, OF 10/14/20

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Since my last Blog hundreds of thousands of more people have died from Covid-19, but, several effective Covid-19 vaccines have been approved. The discovery of these effective vaccines is a triumph of science.

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But if we, the human race, are not vaccinated in far greater numbers than at present, Covid may easily continue to spread. The more the virus replicates, the more chance it will mutate, and, the higher the risk it will mutate into a “Doomsday” virus. By a “Doomsday” virus I mean a virus that is absolutely lethal, massively contagious, and, takes weeks to manifest itself noticeably after a person catches it. Such a virus is possible, and could destroy the entire human race.

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Clearly the human race must plan to be ready for the mutations. Hopefully a Doomsday virus is both very unlikely and will never happen. But hope is not a strategy. If a Doomsday virus does arrive, the human race may have little time to counter it, which makes preparation key.

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In 2020 Joe Biden ran for election as U.S. President on a platform of science, and won, obtaining 81,283,098 votes. His opponent, who did not run on a platform of science, obtained 74,222,958 votes. There is much messaging to do, to convert many people in America and around the world, to embrace science. Those opposed to Covid vaccination and to mask-wearing endanger humanity.

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What all rational humane people who are aware of the pandemic desire is a good inductive argument with this conclusion: “therefore, we, the human race, are at minimal risk from Covid”. There is far to go before that conclusion can be reached in a good inductive argument.

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Globally maximizing: scientific research into Covid, Covid vaccinations (including booster shots if need be), Covid-testing, tracing, and quarantining, Covid antibody-testing, widespread use of Covid-sniffing dogs, travel bans and travel pre-conditions, lockdowns, mask-wearing, social-distancing, hand-sanitizing, and widespread use of any and all other effective anti-Covid measures, is how to minimize the Covid risk and to maximize the probability of eradicating the virus from the world.

## We must deploy science to the fullest and fastest possible extent, in order to reach, as quickly as possible, in a good inductive argument, the desired conclusion.

## There are logistical limits to what humanity can do to counter Covid, but there is no limit to what Covid can do to humanity. The longer we take to eradicate the virus, the higher the probability it will eradicate us. “Gentlemen, it is the microbes who will have the last word.” Louis Pasteur (1822-1895), a brilliant scientist. His chilling thought has not caused humanity to co-operate globally to kill the virus, but global co-operation is surely vital for that victory.

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## An enormous amount of intelligent action is required to defeat Covid, and this requires much human energy. Yet the pandemic saps the energy of many people. You may find suitably energizing the following two superb performances of Bach's Third Brandenburg Concerto.

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## Stay safe.

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https://www.youtube.com/watch?v=mB1M2HaEbI4

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https://www.youtube.com/watch?v=HmW92wOdRdI