#likelihood — Public Fediverse posts

Icon, Likeness, Likely Story, Likelihood, Probability • 3

Re: Peirce List • Phyllis Chiasson

A more complete excerpt and the translator’s notes are very helpful here.

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

• E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
• The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
• The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

Translator’s Notes

1. If referable to one phenomenon only, a sign has objective necessity ;  if to more than one, its value is a matter of opinion.
2. Strictly an enthymeme.
3. If the signs of an enthymeme in the first figure are true, the conclusion is inevitable.  Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion.  The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
4. i.e. when both premisses are affirmative.
5. Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
6. Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 3

Re: Peirce List • Phyllis Chiasson

A more complete excerpt and the translator’s notes are very helpful here.

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

• E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
• The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
• The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

Translator’s Notes

1. If referable to one phenomenon only, a sign has objective necessity ;  if to more than one, its value is a matter of opinion.
2. Strictly an enthymeme.
3. If the signs of an enthymeme in the first figure are true, the conclusion is inevitable.  Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion.  The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
4. i.e. when both premisses are affirmative.
5. Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
6. Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 3

Re: Peirce List • Phyllis Chiasson

A more complete excerpt and the translator’s notes are very helpful here.

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

• E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
• The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
• The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

Translator’s Notes

1. If referable to one phenomenon only, a sign has objective necessity ;  if to more than one, its value is a matter of opinion.
2. Strictly an enthymeme.
3. If the signs of an enthymeme in the first figure are true, the conclusion is inevitable.  Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion.  The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
4. i.e. when both premisses are affirmative.
5. Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
6. Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 3

Re: Peirce List • Phyllis Chiasson

A more complete excerpt and the translator’s notes are very helpful here.

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

• E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
• The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
• The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

Translator’s Notes

1. If referable to one phenomenon only, a sign has objective necessity ;  if to more than one, its value is a matter of opinion.
2. Strictly an enthymeme.
3. If the signs of an enthymeme in the first figure are true, the conclusion is inevitable.  Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion.  The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
4. i.e. when both premisses are affirmative.
5. Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
6. Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 3

Re: Peirce List • Phyllis Chiasson

A more complete excerpt and the translator’s notes are very helpful here.

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss ;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability :  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.1  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.

An enthymeme is a syllogism from probabilities or signs ;  and a sign can be taken in three ways — in just as many ways as there are of taking the middle term in the several figures :  either as in the first figure or as in the second or as in the third.

• E.g., the proof that a woman is pregnant because she has milk is by the first figure ;  for the middle term is ‘having milk’.  A stands for ‘pregnant’, B for ‘having milk’, and C for ‘woman’.
• The proof that the wise are good because Pittacus was good is by the third figure.  A stands for ‘good’, B for ‘the wise’, and C for Pittacus.  Then it is true to predicate both A and B of C ;  only we do not state the latter, because we know it, whereas we formally assume the former.
• The proof that a woman is pregnant because she is sallow is intended to be by the middle figure ;  for since sallowness is a characteristic of woman in pregnancy, and is associated with this particular woman, they suppose that she is proved to be pregnant.  A stands for ‘sallowness’, B for ‘being pregnant’, C for ‘woman’.

If only one premiss is stated, we get only a sign ;  but if the other premiss is assumed as well, we get a syllogism,2 e.g., that Pittacus is high-minded, because those who love honour are high-minded, and Pittacus loves honour ;  or again that the wise are good, because Pittacus is good and also wise.

In this way syllogisms can be effected ;  but whereas a syllogism in the first figure cannot be refuted if it is true, since it is universal, a syllogism in the last figure can be refuted even if the conclusion is true, because the syllogism is neither universal nor relevant to our purpose.3  For if Pittacus is good, it is not necessary for this reason that all other wise men are good.  A syllogism in the middle figure is always and in every way refutable, since we never get a syllogism with the terms in this relation4 ;  for it does not necessarily follow, if a pregnant woman is sallow, and this woman is sallow, that she is pregnant.  Thus truth can be found in all signs, but they differ in the ways which have been described.

We must either classify signs in this way, and regard their middle term as an index (τεκµηριον)5 (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes6 as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics 2.27, 70a3–70b6).

Translator’s Notes

1. If referable to one phenomenon only, a sign has objective necessity ;  if to more than one, its value is a matter of opinion.
2. Strictly an enthymeme.
3. If the signs of an enthymeme in the first figure are true, the conclusion is inevitable.  Aristotle does not mean that the conclusion is universal, but that the universality of the major premiss implies the validity of the minor and conclusion.  The example (<all> those who have honour, etc.) quoted for the third figure contains no universal premiss or sign, and fails to establish a universal conclusion.
4. i.e. when both premisses are affirmative.
5. Signs may be classified as irrefutable (1st figure) and refutable (2nd and 3rd figures), and the name ‘index’ may be attached to their middle terms, either in all figures or (more probably) only in the first, where the middle is distinctively middle.
6. Alternatively the name ‘sign’ may be restricted to the 2nd and 3rd figures, and may be replaced by ‘index’ in the first.

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 2
• https://inquiryintoinquiry.com/2026/05/19/icon-likeness-likely-story-likelihood-probability-2-a/

Re: Peirce List • Phyllis Chiasson
• https://web.archive.org/web/20131211153209/http://comments.gmane.org/gmane.science.philosophy.peirce/11234
• https://web.archive.org/web/20131211034001/http://permalink.gmane.org/gmane.science.philosophy.peirce/11235

I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 2
• https://inquiryintoinquiry.com/2026/05/19/icon-likeness-likely-story-likelihood-probability-2-a/

Re: Peirce List • Phyllis Chiasson
• https://web.archive.org/web/20131211153209/http://comments.gmane.org/gmane.science.philosophy.peirce/11234
• https://web.archive.org/web/20131211034001/http://permalink.gmane.org/gmane.science.philosophy.peirce/11235

I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 2
• https://inquiryintoinquiry.com/2026/05/19/icon-likeness-likely-story-likelihood-probability-2-a/

Re: Peirce List • Phyllis Chiasson
• https://web.archive.org/web/20131211153209/http://comments.gmane.org/gmane.science.philosophy.peirce/11234
• https://web.archive.org/web/20131211034001/http://permalink.gmane.org/gmane.science.philosophy.peirce/11235

I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 2
• https://inquiryintoinquiry.com/2026/05/19/icon-likeness-likely-story-likelihood-probability-2-a/

Re: Peirce List • Phyllis Chiasson
• https://web.archive.org/web/20131211153209/http://comments.gmane.org/gmane.science.philosophy.peirce/11234
• https://web.archive.org/web/20131211034001/http://permalink.gmane.org/gmane.science.philosophy.peirce/11235

I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 2
• https://inquiryintoinquiry.com/2026/05/19/icon-likeness-likely-story-likelihood-probability-2-a/

Re: Peirce List • Phyllis Chiasson
• https://web.archive.org/web/20131211153209/http://comments.gmane.org/gmane.science.philosophy.peirce/11234
• https://web.archive.org/web/20131211034001/http://permalink.gmane.org/gmane.science.philosophy.peirce/11235

I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 2

Re: Peirce List • Phyllis Chiasson

I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 2

Re: Peirce List • Phyllis Chiasson

I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 2

Re: Peirce List • Phyllis Chiasson

I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 2

Re: Peirce List • Phyllis Chiasson

I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 2

Re: Peirce List • Phyllis Chiasson

I’m still a bit fuzzy on how Aristotle’s account relates to Peirce’s usage, though I’m pretty sure Peirce must have taken Aristotle’s usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’.  For the conclusion which is reached through the first figure is most generally accepted and most true.  (Aristotle, Prior Analytics, 2.27.70b1–6).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Icon, Likeness, Likely Story, Likelihood, Probability • 1
• https://inquiryintoinquiry.com/2026/05/17/icon-likeness-likely-story-likelihood-probability-1-a/

Here's a likely locus classicus for “icon” in its logical sense —

❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

❝For example, that the envious are malevolent or that those who are loved are affectionate.

❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 1
• https://inquiryintoinquiry.com/2026/05/17/icon-likeness-likely-story-likelihood-probability-1-a/

Here's a likely locus classicus for “icon” in its logical sense —

❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

❝For example, that the envious are malevolent or that those who are loved are affectionate.

❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 1
• https://inquiryintoinquiry.com/2026/05/17/icon-likeness-likely-story-likelihood-probability-1-a/

Here's a likely locus classicus for “icon” in its logical sense —

❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

❝For example, that the envious are malevolent or that those who are loved are affectionate.

❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 1
• https://inquiryintoinquiry.com/2026/05/17/icon-likeness-likely-story-likelihood-probability-1-a/

Here's a likely locus classicus for “icon” in its logical sense —

❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

❝For example, that the envious are malevolent or that those who are loved are affectionate.

❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 1
• https://inquiryintoinquiry.com/2026/05/17/icon-likeness-likely-story-likelihood-probability-1-a/

Here's a likely locus classicus for “icon” in its logical sense —

❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

❝For example, that the envious are malevolent or that those who are loved are affectionate.

❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference —

Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource —

Theme One Program • User Guide • Appendix A
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide

#Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
#Logic #Mathematics #Probability #ProbableReasoning #Induction
#Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

Icon, Likeness, Likely Story, Likelihood, Probability • 1

Here’s a likely locus classicus for “icon” in its logical sense —

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.  (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

Related Discussion

• Peirce List • Benjamin Udell • Michael Shapiro

Icon, Likeness, Likely Story, Likelihood, Probability • 1

Here’s a likely locus classicus for “icon” in its logical sense —

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.  (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

Related Discussion

• Peirce List • Benjamin Udell • Michael Shapiro

Icon, Likeness, Likely Story, Likelihood, Probability • 1

Here’s a likely locus classicus for “icon” in its logical sense —

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.  (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

Related Discussion

• Peirce List • Benjamin Udell • Michael Shapiro

Icon, Likeness, Likely Story, Likelihood, Probability • 1

Here’s a likely locus classicus for “icon” in its logical sense —

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.  (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

Related Discussion

• Peirce List • Benjamin Udell • Michael Shapiro

Icon, Likeness, Likely Story, Likelihood, Probability • 1

Here’s a likely locus classicus for “icon” in its logical sense —

A probability (εικος) is not the same as a sign (σηµειον).  The former is a generally accepted premiss;  for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:  e.g., that the envious are malevolent or that those who are loved are affectionate.  A sign, however, means a demonstrative premiss which is necessary or generally accepted.  That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.  (Aristotle, Prior Analytics, 2.27.70a3–10).

Reference

• Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

Resource

• Theme One Program • User Guide • Appendix A

Related Discussion

• Peirce List • Benjamin Udell • Michael Shapiro

Here's a new paper summarizing methods for evaluating whether the absence of a statistically significant difference (from a NHST) is actually no difference--test of equivalence, confidence interval bounds, likelihood ratios, Bayes factors, and Bayesian estimation. There's nothing new here, but it's a nice readable overview that might be worth citing for some audiences.

https://royalsocietypublishing.org/doi/full/10.1098/rsbl.2025.0506?af=R

#Science #Statistics #Likelihood #BayesFactors

Ah yes, the groundbreaking 2018 #tutorial on "likelihood," where the real mystery is not statistical analysis, but navigating the dark arts of enabling #JavaScript and #cookies. 🍪🔍 Because who needs math when you can unravel the secrets of #browser #settings instead? 🙄
https://journals.sagepub.com/doi/10.1177/2515245917744314 #likelihood #tech #humor #HackerNews #ngated

Introduction to the concept of likelihood and its applications (2018)

https://journals.sagepub.com/doi/10.1177/2515245917744314

#HackerNews #Introduction #likelihood #applications #statistics #research #2018

After doing very sophisticated* web searching, it seems that it is not uncommon typo, and I could not find a definition.

So, there seems to be an opening for introducing a new term. Maybe outside #Statistics, shall we talk about a #Likeligood Function in #WelfareEconomics?
Or does it describe a new equilibrium in #GameTheory, the one that is likely good?

#Likelihood

* 😂 😂 😅

I thought it was an innocent, unassuming typo.

But now I see a need to figure out whether "Likeligood estimation" is actually a thing...

#Statistics #RabbitHole #Likelihood

'Determine the Number of States in Hidden Markov Models via Marginal Likelihood', by Yang Chen, Cheng-Der Fuh, Chu-Lan Michael Kao.

http://jmlr.org/papers/v26/23-0343.html

#markov #bayesian #likelihood

'Approximate Information Tests on Statistical Submanifolds', by Michael W. Trosset, Carey E. Priebe.

http://jmlr.org/papers/v25/19-272.html

#likelihood #submodel #statistical

Reduced #Likelihood of #Hospitalization with #JN1 or #HV1 #SARS-CoV-2 #Variants Compared to #EG5 Variant, J Infect Dis.: https://academic.oup.com/jid/advance-article/doi/10.1093/infdis/jiae364/7717186?utm_source=advanceaccess&utm_campaign=jid&utm_medium=email&nbd=25018031857&nbd_source=campaigner

JN.1 and HV.1 variants may be associated with a lower #risk of severe illness. The severity of #COVID19 may have attenuated as predominant circulating SARS-CoV-2 lineages shifted from EG.5 to HV.1 to JN.1.

'MAP- and MLE-Based Teaching', by Hans Ulrich Simon, Jan Arne Telle.

http://jmlr.org/papers/v25/23-1086.html

#likelihoods #priors #likelihood

'On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture Models', by Yangjing Zhang, Ying Cui, Bodhisattva Sen, Kim-Chuan Toh.

http://jmlr.org/papers/v25/22-1120.html

#hessian #denoising #likelihood

`Intuitively, if the restricted #estimator is near the maximum of the #likelihood function, the score should not differ from zero by more than sampling error. While the finite sample #distributions of score tests are generally unknown, they have an #asymptotic χ2-distribution under the null #hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical #significance.`

https://en.wikipedia.org/wiki/Score_test

#statistics #stats #significanceTest #significanceTesting

`Intuitively, if the restricted #estimator is near the maximum of the #likelihood function, the score should not differ from zero by more than sampling error. While the finite sample #distributions of score tests are generally unknown, they have an #asymptotic χ2-distribution under the null #hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical #significance.`

https://en.wikipedia.org/wiki/Score_test

#statistics #stats #significanceTest #significanceTesting

`Intuitively, if the restricted #estimator is near the maximum of the #likelihood function, the score should not differ from zero by more than sampling error. While the finite sample #distributions of score tests are generally unknown, they have an #asymptotic χ2-distribution under the null #hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical #significance.`

https://en.wikipedia.org/wiki/Score_test

#statistics #stats #significanceTest #significanceTesting

`Intuitively, if the restricted #estimator is near the maximum of the #likelihood function, the score should not differ from zero by more than sampling error. While the finite sample #distributions of score tests are generally unknown, they have an #asymptotic χ2-distribution under the null #hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical #significance.`

https://en.wikipedia.org/wiki/Score_test

#statistics #stats #significanceTest #significanceTesting

Variational Elliptical Processes

Maria Margareta Bånkestad, Jens Sjölund, Jalil Taghia, Thomas B. Schön

Action editor: Sinead Williamson.

https://openreview.net/forum?id=djN3TaqbdA

#gaussian #variational #likelihood

@lulu_powerful so, now you'll have to define #likelihood for us, please?

#probability #math #ScienceComm

Feynman on Scientific Method

https://youtu.be/EYPapE-3FRw
>Physicist Richard Feynman explains the scientific and unscientific methods of understanding nature.
#science #guesswork #likelihood

@ZfdG

Even though this post is in German, the research article "Classification of Tragedies and Comedies in Calderón de la Barca’s Comedias Nuevas" has been published in English at https://zfdg.de/2022_012

We analyze 112 comedies of the Spanish Golden Age dramatist, explore 4 methods to classify them using #word #embeddings, compute #log #likelihood #probability, use #skipgram & #fasttext to characterize the corpus, and contrastive vocabulary analysis to characterize both genres

The research article "#Classification of Tragedies and Comedies in Calderón de la Barca’s Comedias Nuevas", written by @sebastianpado and me, has just been published:
https://revistas.uned.es/index.php/RHD/article/view/34588/
We analyze 112 comedies of the Spanish Golden Age dramatist and explore 4 methods to classify them into tragedies and comedies using #word #embeddings. We also employ the calculation of #log #likelihood #probability, #skipgram and #fasttext to characterize the corpus as well as ...

'Maximum likelihood estimation in Gaussian process regression is ill-posed', by Toni Karvonen, Chris J. Oates.

http://jmlr.org/papers/v24/22-1153.html

#gaussian #posedness #likelihood

'A Likelihood Approach to Nonparametric Estimation of a Singular Distribution Using Deep Generative Models', by Minwoo Chae, Dongha Kim, Yongdai Kim, Lizhen Lin.

http://jmlr.org/papers/v24/21-1099.html

#generative #distributions #likelihood

@vortex_egg

Yes, we need to become comfortable with uncertainty in our increasingly complex environment — in fact that should already have be the case, especially for issues that are complex enough to be 'interesting.'

And even more than being comfortable with uncertainty, we need to get much better at thinking of things in terms of likelihood and probability — even getting clear on the difference between these two terms.

So becoming comfortable with Bayesian thinking will equip us to more effectively deal with both uncertainty, and reasoning, as we try to make sense of the flood of social media, consumer-marketing, politics, and multiple flavors of bullshit.

And by the way, it also helps with the simpler, more straightforward stuff like new science, technology, and data…

#uncertainty #probability #likelihood # Bayesian #reason #reasoning #ToolsForThinking #complexity #sensemaking

Various features of #parasites and #hosts may influence the #likelihood of #evolutionary transitions of parasites between #freshwater and #marine environments and vice versa. These include: parasite location (endoparasitism > ectoparasitism); #life cycle #complexity (simple > complex); host #specificity (#generalist > #specialist); transmission mode (#trophic > #environmental) https://doi.org/10.1093/icb/icac050 #EvolutionaryBiology #Paleobiology #Paleontology

Feynman on Scientific Method

https://youtu.be/EYPapE-3FRw
>Physicist Richard Feynman explains the scientific and unscientific methods of understanding nature.
#science #guesswork #likelihood