"This matters because it has the added implication that poverty rates have been misestimated due to misreporting in surveys, and that misestimation has contributed to the appearance of poverty among Blacks and Hispanics relative to Asians and Whites." Important correction.
"measurement error is greater for Blacks and Hispanics than for Asians and Whites."
In absolute terms, sure, but in relative terms we have 43.8%, 39.3%, 46.5%, and 41.8% under-estimates respectively in Study 2. So, if anything, it seems more accurate to say that measurement error in Study 2 is greater for Asians and Blacks than for Hispanics and Whites. It seems like the groups under-report at more similar rates, and the disparities in absolute errors mostly reflects large differences in receipt rate.
"Whites averaged a reported receipt of $3,324 ($3,409) versus a true average of $3,660 ($3,607). For Blacks, these figures were $3,648 ($3,825) and $4,080 ($4,172); for Hispanics, they were $3,576 ($3,528) and $4,092 ($3,638); and for Asians, they were $3,708 ($2,803) and $3,912 ($3,286)."
Is this average out of everyone in each racial group, or only out of everyone in each racial group who receives SNAP benefits? And is this the same for TANF and UI?
The challenges to understanding truth in postmodern contexts do raise important questions about the nature of truth, but their applicability to logic and probability is more limited. Here's an analysis of how these concepts intersect:
## Logic and Truth
Logic, as a formal system of reasoning, is generally considered to be objective and universal, largely immune to postmodern skepticism:
- **Formal Logic**: The rules of formal logic, such as modus ponens or the law of non-contradiction, are based on abstract reasoning rather than empirical observation. These logical principles are considered true regardless of cultural context or individual perspective.
- **Mathematical Logic**: Similarly, mathematical logic operates on axioms and proofs that are not subject to cultural relativism. The truth of a mathematical statement, once proven, is considered absolute within its axiomatic system.
## Probability and Truth
Probability theory, while rooted in mathematics, does intersect with some of the challenges posed by postmodern skepticism:
- **Objective vs. Subjective Probability**: There's a distinction between objective probability (based on frequencies of events) and subjective probability (based on degrees of belief). Subjective probability can be influenced by cultural factors and individual perspectives, aligning more closely with postmodern critiques.
- **Interpretation of Probability**: The philosophical interpretation of what probability means (e.g., frequentist vs. Bayesian approaches) can be subject to debate and cultural influences.
## Chance, Randomness, and Truth
The existence of chance and randomness does affect our understanding of truth, particularly in scientific contexts:
- **Probabilistic Truth**: In quantum mechanics, for instance, the truth of certain statements is inherently probabilistic. This challenges classical notions of deterministic truth.
- **Statistical Truth**: In fields like epidemiology or social sciences, truths are often expressed in statistical terms, acknowledging inherent uncertainty.
- **Chaos Theory**: The existence of chaotic systems in nature demonstrates that even in deterministic systems, long-term prediction (and thus, certain kinds of truth claims) can be impossible due to sensitivity to initial conditions.
## Reconciling Postmodern Skepticism with Logic and Probability
While postmodern skepticism raises valid points about the cultural construction of knowledge, it's important to note:
1. **Pragmatic Utility**: Even if absolute truth is elusive, logical and probabilistic reasoning have demonstrated immense practical value in advancing human knowledge and technology.
2. **Intersubjective Agreement**: In scientific and mathematical communities, there's often a high degree of consensus on logical and probabilistic truths, suggesting a level of objectivity that transcends individual or cultural biases.
3. **Meta-Logical Stability**: The tools we use to question the nature of truth (including postmodern critiques) often rely on logical principles, suggesting a foundational role for logic in human reasoning.
In conclusion, while postmodern skepticism offers valuable insights into the cultural and subjective aspects of truth, the domains of logic and probability maintain a high degree of objectivity and universal applicability. The existence of chance and randomness adds complexity to our understanding of truth, particularly in scientific contexts, but does not fundamentally undermine the validity of logical and probabilistic reasoning.
"Another that I find interesting is that more extreme response styles are related to lower intelligence ...." That is my rule-of-thumb impression on X
"This matters because it has the added implication that poverty rates have been misestimated due to misreporting in surveys, and that misestimation has contributed to the appearance of poverty among Blacks and Hispanics relative to Asians and Whites." Important correction.
"measurement error is greater for Blacks and Hispanics than for Asians and Whites."
In absolute terms, sure, but in relative terms we have 43.8%, 39.3%, 46.5%, and 41.8% under-estimates respectively in Study 2. So, if anything, it seems more accurate to say that measurement error in Study 2 is greater for Asians and Blacks than for Hispanics and Whites. It seems like the groups under-report at more similar rates, and the disparities in absolute errors mostly reflects large differences in receipt rate.
Anyone have a copy of the Dutton and Kierkegaard article?
"Whites averaged a reported receipt of $3,324 ($3,409) versus a true average of $3,660 ($3,607). For Blacks, these figures were $3,648 ($3,825) and $4,080 ($4,172); for Hispanics, they were $3,576 ($3,528) and $4,092 ($3,638); and for Asians, they were $3,708 ($2,803) and $3,912 ($3,286)."
Is this average out of everyone in each racial group, or only out of everyone in each racial group who receives SNAP benefits? And is this the same for TANF and UI?
Average among recipients.
The challenges to understanding truth in postmodern contexts do raise important questions about the nature of truth, but their applicability to logic and probability is more limited. Here's an analysis of how these concepts intersect:
## Logic and Truth
Logic, as a formal system of reasoning, is generally considered to be objective and universal, largely immune to postmodern skepticism:
- **Formal Logic**: The rules of formal logic, such as modus ponens or the law of non-contradiction, are based on abstract reasoning rather than empirical observation. These logical principles are considered true regardless of cultural context or individual perspective.
- **Mathematical Logic**: Similarly, mathematical logic operates on axioms and proofs that are not subject to cultural relativism. The truth of a mathematical statement, once proven, is considered absolute within its axiomatic system.
## Probability and Truth
Probability theory, while rooted in mathematics, does intersect with some of the challenges posed by postmodern skepticism:
- **Objective vs. Subjective Probability**: There's a distinction between objective probability (based on frequencies of events) and subjective probability (based on degrees of belief). Subjective probability can be influenced by cultural factors and individual perspectives, aligning more closely with postmodern critiques.
- **Interpretation of Probability**: The philosophical interpretation of what probability means (e.g., frequentist vs. Bayesian approaches) can be subject to debate and cultural influences.
## Chance, Randomness, and Truth
The existence of chance and randomness does affect our understanding of truth, particularly in scientific contexts:
- **Probabilistic Truth**: In quantum mechanics, for instance, the truth of certain statements is inherently probabilistic. This challenges classical notions of deterministic truth.
- **Statistical Truth**: In fields like epidemiology or social sciences, truths are often expressed in statistical terms, acknowledging inherent uncertainty.
- **Chaos Theory**: The existence of chaotic systems in nature demonstrates that even in deterministic systems, long-term prediction (and thus, certain kinds of truth claims) can be impossible due to sensitivity to initial conditions.
## Reconciling Postmodern Skepticism with Logic and Probability
While postmodern skepticism raises valid points about the cultural construction of knowledge, it's important to note:
1. **Pragmatic Utility**: Even if absolute truth is elusive, logical and probabilistic reasoning have demonstrated immense practical value in advancing human knowledge and technology.
2. **Intersubjective Agreement**: In scientific and mathematical communities, there's often a high degree of consensus on logical and probabilistic truths, suggesting a level of objectivity that transcends individual or cultural biases.
3. **Meta-Logical Stability**: The tools we use to question the nature of truth (including postmodern critiques) often rely on logical principles, suggesting a foundational role for logic in human reasoning.
In conclusion, while postmodern skepticism offers valuable insights into the cultural and subjective aspects of truth, the domains of logic and probability maintain a high degree of objectivity and universal applicability. The existence of chance and randomness adds complexity to our understanding of truth, particularly in scientific contexts, but does not fundamentally undermine the validity of logical and probabilistic reasoning.
Citations:
[1] https://iep.utm.edu/truth/
[2] https://philarchive.org/archive/ROSTTA-16
[3] https://plato.stanford.edu/entries/truth/
[4] https://philosophynow.org/issues/86/What_Is_Truth
[5] https://onlinelibrary.wiley.com/doi/abs/10.1111/papq.12298
[6] https://www.gotquestions.org/what-is-truth.html
[7] https://en.wikipedia.org/wiki/Theories_of_truth
[8] https://www.britannica.com/topic/truth-philosophy-and-logic